db_produce_summaries.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Intro]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Importation de modules\n",
    "import requests\n",
    "import psycopg2\n",
    "import lxml.html\n",
    "from lxml import etree\n",
    "from importlib import reload\n",
    "import sqlite3 as sql\n",
    "\n",
    "import pandas as pd\n",
    "from importlib import reload\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from itables import init_notebook_mode, show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import urllib3\n",
    "### Avoid disturbing messages while scraping\n",
    "urllib3.disable_warnings(urllib3.exceptions.InsecureRequestWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import settings as st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### POur ne pas demander le password — ou variable d'environnement améliorer\n",
    "# https://www.delftstack.com/howto/python/import-python-file-from-path/#import-a-module-with-a-full-file-path-in-python-35from importlib.machinery import SourceFileLoader\n",
    "\n",
    "MODULE_PATH = \"c:\\\\Users\\\\Rexjohn\\\\Folder-1\\\\addmodule.py\"\n",
    "MODULE_NAME = \"addmodule\"\n",
    "\n",
    "modulevar = SourceFileLoader(MODULE_NAME, MODULE_PATH).load_module()\n",
    "\n",
    "modulevar.printingstatement()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PostgreSQL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Documentation\n",
    "\n",
    "* https://www.psycopg.org/docs/usage.html\n",
    "* https://towardsdatascience.com/python-and-postgresql-how-to-access-a-postgresql-database-like-a-data-scientist-b5a9c5a0ea43\n",
    "  * noter toutefois que la connection directe avec psychopg2 et pandas ne marche plus\n",
    "  \n",
    "__NB__ \n",
    "* soit on passe par du SQL pur, et alors on peut utiliser _psycopg2_ comme on utilise sqlite3\n",
    "* soit on utilise Pandas, mais là il faut un objet SQLAlchemy pour accéder à la base de données  \n",
    "  \n",
    "  \n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "conn = psycopg2.connect(host=\"localhost\", port = 5432, database=\"espace_intellectuel\", \n",
    "                        user=\"postgres\", password=st.dbw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<connection object at 0x7f101c47ca40; dsn: 'user=postgres password=xxx dbname=espace_intellectuel host=localhost port=5432', closed: 0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def sql_explore(q):\n",
    "    errors_list = []\n",
    "    elem = []\n",
    "    with conn.cursor() as curs:\n",
    "        try:   \n",
    "            ### Décommenter pour nouvelle exécution\n",
    "            curs.execute(q)\n",
    "            elem = curs.fetchall()\n",
    "            conn.commit()\n",
    "        except Exception as e:\n",
    "            errors_list.append([i[2], e])\n",
    "            print(e)\n",
    "    return [elem, errors_list]        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1 = \"\"\"\n",
    "SELECT COUNT(*), min(ts_creation), max(ts_creation)\n",
    "FROM astronomers.mathshistory;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lines count: 1, errors count: 0, \n",
      "First lines: [(3010, datetime.datetime(2023, 4, 10, 8, 12, 17, 768436), datetime.datetime(2023, 4, 10, 8, 21, 16, 982924))]\n"
     ]
    }
   ],
   "source": [
    "result = sql_explore(q1)\n",
    "print(f'Lines count: {len(result[0])}, errors count: {len(result[1])}, \\nFirst lines: {result[0][:5]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "q2 = \"\"\"\n",
    "SELECT pk_mathshistory, \"name\", dates, url FROM astronomers.mathshistory WHERE xml_is_well_formed(page_html_txt) IS FALSE ;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Muliple cards per URL ?\n",
    "# No one, empty set\n",
    "q = \"\"\"\n",
    "select pk_mathshistory, dates, \"name\", url , page_html\n",
    "from astronomers.mathshistory m \n",
    "where biography  like '%Summary%'\n",
    "order by length(biography)\n",
    "limit 100;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lines count: 23, errors count: 0, \n",
      "First lines: [(36, '1256-1321', 'Ibn al-Banna', 'https://mathshistory.st-andrews.ac.uk/Biographies/Al-Banna/', '<root><div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h1>al-Marrakushi ibn Al-Banna</h1>\\n  </div>\\n</div>\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-8\">\\n    <h3>Quick Info</h3>\\n\\n    \\n    <dt>Born</dt>\\n    <dd>\\n      29 December 1256 <br/>  <a href=\"../../Map/#Marrakesh\" target=\"_blank\"> Marrakesh, Morocco </a> \\n    </dd>\\n     \\n    <dt>Died</dt>\\n    <dd>\\n      13 July 1321 <br/> Marrakesh, Morocco\\n    </dd>\\n     \\n    <hr/>\\n    <dt>Summary</dt>\\n    <dd><span class=\"markup\"><strong>Ibn al-Banna</strong> was an Islamic mathematician who wrote a large number of works including an introduction to Euclid\\'s <em>Elements</em>, an algebra text and various works on astronomy.</span></dd>\\n    \\n  </div>\\n\\n   \\n  <div class=\"col-md-4 biography-thumbnail-container\">\\n    \\n    <a href=\"pictdisplay/\" target=\"_blank\">\\n      \\n      <img class=\"biography-thumbnail\" src=\"al-banna.jpg\" alt=\"Thumbnail of Ibn al-Banna\"/>\\n      \\n      <br/>\\n      View one larger picture</a>\\n    \\n  </div>\\n  \\n</div>\\n\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Biography</h3>\\n    <span class=\"markup\"><strong>Ibn al-Banna</strong> is also known as Abu\\'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi. It is a little unclear whether al-Banna was born in the city of Marrakesh or whether it was the region of Marrakesh which was named Morocco by Europeans. There is a claim that al-Banna was born in Granada in Spain and moved to North Africa for his education. What is certain is that he spent most of his life in Morocco.\\n<br/>\\n\\n<br/>\\nThe Marinids tribe were allies of the Umayyad caliphs of Córdoba. The tribe lived in eastern Morocco then, under their ruler Abu Yahya, they began to conquer the region. The Marinids captured Fez in <span class=\"non-italic\">1248</span> and made it their capital. They captured Marrakesh from the ruling Almohads tribe in <span class=\"non-italic\">1269</span>, thus taking control of the whole of Morocco. Having conquered Morocco, the Marinids tried to help Granada to prevent the Christian advance through their country. The strong link between Granada and Morocco may account for the confusion as to which country al-Banna was a native.\\n<br/>\\n\\n<br/>\\nMorocco was certainly the country that al-Banna was educated in, learning the leading mathematical skills of the period. He studied geometry in general, and <a class=\"mlink\" data-popup=\"../Euclid/popup/\" href=\"../Euclid/\">Euclid</a>\\'s <em>Elements</em> in particular. He also studied fractional numbers and learnt much of the impressive contributions that the Arabs had made to mathematics over the preceding <span class=\"non-italic\">400</span> years. The Marinids had a strong culture for learning and Fez became their centre of learning. At the university in Fez Al-Banna taught all branches of mathematics, which at this time included arithmetic, algebra, geometry and astronomy. Fez was a thriving city with a new quarter being built housing the Royal Palace and the adjoining Great Mosque. Many students studied under al-Banna in this thriving academic community.\\n<br/>\\n\\n<br/>\\nIt is clear that al-Banna wrote a large number of works, in fact <span class=\"non-italic\">82</span> are listed by Renaud <span class=\"non-italic\">(</span>see for example <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;H P J Renaud, Ibn al-Banna de Marrakech, sufi et mathématicien, &lt;em&gt;Hesperis&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;25&lt;/span&gt;&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(1938)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;13&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;42&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-9\"><span class=\"non-italic\">9</span></a><span class=\"non-italic\">]</span></span><span class=\"non-italic\">)</span>. Not all are on mathematics, but the mathematical texts included an introduction to <a class=\"mlink\" data-popup=\"../Euclid/popup/\" href=\"../Euclid/\">Euclid</a>\\'s <em>Elements</em>, an algebra text and various works on astronomy. One difficulty with the works on mathematics is knowing how much of the material which al-Banna presents is original and how much is simply his version of work by earlier Arab mathematicians which has been lost. We should certainly say that al-Banna does not claim any originality and, indeed, the style of his writing would suggest that he is collecting together ideas that he has learnt from other mathematicians.\\n<br/>\\n\\n<br/>\\nTwo \"firsts\" for al-Banna are that he seems to have been the first to consider a fraction as a ratio between two numbers <span class=\"non-italic\">(</span>see <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;M Zarruqi, Fractions in the Morroccan mathematical tradition between the &lt;span class=&quot;non-italic&quot;&gt;12&lt;/span&gt;th and &lt;span class=&quot;non-italic&quot;&gt;15&lt;/span&gt;th centuries A.D. as found in anonymous manuscripts &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Arabic&lt;span class=&quot;non-italic&quot;&gt;)&lt;/span&gt;, in &lt;em&gt;Deuxième Colloque Maghrebin sur l\\'Histoire des Mathématiques Arabes&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Tunis, &lt;span class=&quot;non-italic&quot;&gt;1990)&lt;/span&gt;, A&lt;span class=&quot;non-italic&quot;&gt;97&lt;/span&gt;-A&lt;span class=&quot;non-italic&quot;&gt;109&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-12\"><span class=\"non-italic\">12</span></a><span class=\"non-italic\">]</span></span> for more details<span class=\"non-italic\">)</span> and he is the first to use the expression almanakc <span class=\"non-italic\">(</span>in Arabic al-manakh meaning weather<span class=\"non-italic\">)</span> in a work containing astronomical and meteorological data.\\n<br/>\\n\\n<br/>\\nPerhaps al-Banna\\'s most famous work is <em>Talkhis amal al-hisab</em> <span class=\"non-italic\">(</span>Summary of arithmetical operations<span class=\"non-italic\">)</span> and the <em>Raf al-Hijab</em> which is al-Banna\\'s own commentary on the <em>Talkhis amal al-hisab</em>. It is in this work that al-Banna introduces some mathematical notation which has led certain authors to believe that algebraic symbolism was first developed in Islam by ibn al-Banna and <a class=\"mlink\" data-popup=\"../Al-Qalasadi/popup/\" href=\"../Al-Qalasadi/\">al-Qalasadi</a> <span class=\"non-italic\">(</span>see for example <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;G Arrighi, Review of some mathematical symbols &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Italian&lt;span class=&quot;non-italic&quot;&gt;)&lt;/span&gt;, &lt;em&gt;Physis - Riv. Internaz. Storia Sci.&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;27&lt;/span&gt;&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(1&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;2)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(1985)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;163&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;179&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-6\"><span class=\"non-italic\">6</span></a><span class=\"non-italic\">]</span></span><span class=\"non-italic\">)</span>. We refer the reader to the biography of <a class=\"mlink\" data-popup=\"../Al-Qalasadi/popup/\" href=\"../Al-Qalasadi/\">al-Qalasadi</a> where we present arguments to show that neither al-Banna nor <a class=\"mlink\" data-popup=\"../Al-Qalasadi/popup/\" href=\"../Al-Qalasadi/\">al-Qalasadi</a> were the inventors of mathematical notation.\\n<br/>\\n\\n<br/>\\nThere are, however, many interesting mathematical ideas and results which appear in the <em>Raf al-Hijab</em>. For example it contains <a class=\"gllink\" data-popup=\"../../Glossary/continued_fraction/\" href=\"../../Glossary/#continued_fraction\">continued fractions</a> and they are used to compute approximate square roots. Other interesting results on summing series are the results\\n<div class=\"indent-paragraph\"><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup><mn>1</mn><mn>3</mn></msup><mo>+</mo><msup><mn>3</mn><mn>3</mn></msup><mo>+</mo><msup><mn>5</mn><mn>3</mn></msup><mo>+</mo><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mo>+</mo><mo stretchy=\"false\">(</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn><msup><mo stretchy=\"false\">)</mo><mn>3</mn></msup><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy=\"false\">(</mo><mn>2</mn><msup><mi>n</mi><mn>2</mn></msup><mo>−</mo><mn>1</mn><mo stretchy=\"false\">)</mo></mrow><annotation encoding=\"application/x-tex\">1^{3} + 3^{3} + 5^{3} + ... + (2n-1)^{3} = n^{2}(2n^{2} - 1)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">1</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">3</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">5</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.66666em;vertical-align:-0.08333em;\"/><span class=\"mord\">.</span><span class=\"mord\">.</span><span class=\"mord\">.</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mopen\">(</span><span class=\"mord\">2</span><span class=\"mord mathdefault\">n</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.064108em;vertical-align:-0.25em;\"/><span class=\"mord\">1</span><span class=\"mclose\"><span class=\"mclose\">)</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.064108em;vertical-align:-0.25em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mopen\">(</span><span class=\"mord\">2</span><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord\">1</span><span class=\"mclose\">)</span></span></span></span></span> and\\n<br/>\\n\\n<br/>\\n<span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup><mn>1</mn><mn>2</mn></msup><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mo>+</mo><mo stretchy=\"false\">(</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn><msup><mo stretchy=\"false\">)</mo><mn>2</mn></msup><mo>=</mo><mstyle mathsize=\"1.2em\"><mfrac><mn>1</mn><mn>6</mn></mfrac><mstyle mathsize=\"1em\"><mo stretchy=\"false\">(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy=\"false\">)</mo><mn>2</mn><mi>n</mi><mo stretchy=\"false\">(</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy=\"false\">)</mo></mstyle></mstyle></mrow><annotation encoding=\"application/x-tex\">1^{2} + 3^{2} + 5^{2} + ... + (2n-1)^{2} = \\\\large\\\\frac{1}{6}\\\\normalsize (2n + 1)2n(2n - 1)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">1</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">3</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.897438em;vertical-align:-0.08333em;\"/><span class=\"mord\"><span class=\"mord\">5</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.66666em;vertical-align:-0.08333em;\"/><span class=\"mord\">.</span><span class=\"mord\">.</span><span class=\"mord\">.</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mopen\">(</span><span class=\"mord\">2</span><span class=\"mord mathdefault\">n</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.064108em;vertical-align:-0.25em;\"/><span class=\"mord\">1</span><span class=\"mclose\"><span class=\"mclose\">)</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.402352em;vertical-align:-0.414em;\"/><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"/><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8236266666666667em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"/></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span/></span></span></span></span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"/></span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord sizing reset-size6 size6\">2</span><span class=\"mord mathdefault sizing reset-size6 size6\">n</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span><span class=\"mord sizing reset-size6 size6\">2</span><span class=\"mord mathdefault sizing reset-size6 size6\">n</span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord sizing reset-size6 size6\">2</span><span class=\"mord mathdefault sizing reset-size6 size6\">n</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span></span></span></span></span>.</div>\\nPerhaps the most interesting of all is the work on <a class=\"gllink\" data-popup=\"../../Glossary/binomial_coefficient/\" href=\"../../Glossary/#binomial_coefficient\">binomial coefficients</a> which is described in detail in <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;R Rashed, &lt;em&gt;The development of Arabic mathematics : between arithmetic and algebra&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;London, &lt;span class=&quot;non-italic&quot;&gt;1994)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span> and <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;R Rashed, &lt;em&gt;Entre arithmétique et algèbre: Recherches sur l\\'histoire des mathématiques arabes&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Paris, &lt;span class=&quot;non-italic&quot;&gt;1984)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-3\"><span class=\"non-italic\">3</span></a><span class=\"non-italic\">]</span></span>. If we denote the binomial coefficient <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>p</mi></mrow><annotation encoding=\"application/x-tex\">p</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"/><span class=\"mord mathdefault\">p</span></span></span></span></span> choose <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>k</mi></mrow><annotation encoding=\"application/x-tex\">k</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.69444em;vertical-align:0em;\"/><span class=\"mord mathdefault\" style=\"margin-right:0.03148em;\">k</span></span></span></span></span> by <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mi>k</mi></msub></mrow><annotation encoding=\"application/x-tex\">_{p}C_{k}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.969438em;vertical-align:-0.286108em;\"/><span class=\"mord\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span></span></span></span></span> then al-Banna shows that \\n<div class=\"indent-paragraph\"><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mn>2</mn></msub><mo>=</mo><mstyle mathsize=\"1.2em\"><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle mathsize=\"1em\"><mi>p</mi><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo stretchy=\"false\">)</mo></mstyle></mstyle></mrow><annotation encoding=\"application/x-tex\">_{p}C_{2} =  \\\\large\\\\frac{1}{2}\\\\normalsize p(p-1)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.969438em;vertical-align:-0.286108em;\"/><span class=\"mord\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.402352em;vertical-align:-0.414em;\"/><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"/><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8236266666666667em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"/></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span/></span></span></span></span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"/></span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span></span></span></span></span></div>\\nand then that \\n<div class=\"indent-paragraph\"><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mn>3</mn></msub><mo>=</mo><mstyle mathsize=\"1.2em\"><mfrac><mn>1</mn><mn>3</mn></mfrac><mstyle mathsize=\"1em\"><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mn>2</mn></msub><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mn>2</mn><mo stretchy=\"false\">)</mo></mstyle></mstyle></mrow><annotation encoding=\"application/x-tex\">_{p}C_{3} =  \\\\large\\\\frac{1}{3}\\\\normalsize _{p}C_{2}(p-2)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.969438em;vertical-align:-0.286108em;\"/><span class=\"mord\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.402352em;vertical-align:-0.414em;\"/><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"/><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8236266666666667em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"/></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span/></span></span></span></span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"/></span><span class=\"mord sizing reset-size6 size6\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord sizing reset-size6 size6\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">2</span><span class=\"mclose sizing reset-size6 size6\">)</span></span></span></span></span>.</div>\\nHe writes <span class=\"non-italic\">(</span>see for example <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;R Rashed, &lt;em&gt;The development of Arabic mathematics : between arithmetic and algebra&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;London, &lt;span class=&quot;non-italic&quot;&gt;1994)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span> or <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;R Rashed, &lt;em&gt;Entre arithmétique et algèbre: Recherches sur l\\'histoire des mathématiques arabes&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Paris, &lt;span class=&quot;non-italic&quot;&gt;1984)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-3\"><span class=\"non-italic\">3</span></a><span class=\"non-italic\">]</span></span><span class=\"non-italic\">)</span>:-\\n<blockquote>... the ternary combination is thus obtained by multiplying the third of the third term preceding the given number; and so we always multiply the combination that precedes the combination sought by the number that precedes the given number, and whose distance to it is equal to the number of combinations sought. From the product, we take the part that names the number of combinations.</blockquote>\\nAlthough this is a little difficult to interpret, what al-Banna is stating here is that \\n<div class=\"indent-paragraph\"><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mi>k</mi></msub><msub><mo>=</mo><mi>p</mi></msub><msub><mi>C</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mstyle mathsize=\"1.2em\"><mfrac><mn>1</mn><mi>k</mi></mfrac><mstyle mathsize=\"1em\"><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mo stretchy=\"false\">(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo></mstyle></mstyle></mrow><annotation encoding=\"application/x-tex\">_{p}C_{k} =  _{p}C_{k-1}\\\\large\\\\frac{1}{k}\\\\normalsize (p - (k - 1) )</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.969438em;vertical-align:-0.286108em;\"/><span class=\"mord\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\"><span class=\"mrel\">=</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.402352em;vertical-align:-0.414em;\"/><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361079999999999em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span><span class=\"mbin mtight\">−</span><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.208331em;\"><span/></span></span></span></span></span><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"/><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8236266666666667em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"/></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span/></span></span></span></span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"/></span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\" style=\"margin-right:0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span><span class=\"mclose sizing reset-size6 size6\">)</span></span></span></span></span>.</div>\\nHe then goes on to give the familiar <span class=\"non-italic\">(</span>to us<span class=\"non-italic\">)</span> result\\n<div class=\"indent-paragraph\"><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mrow/><mi>p</mi></msub><msub><mi>C</mi><mi>k</mi></msub><mo>=</mo><mstyle mathsize=\"1.2em\"><mfrac><mn>1</mn><mrow><mi>k</mi><mo stretchy=\"false\">!</mo></mrow></mfrac><mstyle mathsize=\"1em\"><mi>p</mi><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mn>2</mn><mo stretchy=\"false\">)</mo><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mi mathvariant=\"normal\">.</mi><mo stretchy=\"false\">(</mo><mi>p</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo stretchy=\"false\">)</mo></mstyle></mstyle></mrow><annotation encoding=\"application/x-tex\">_{p}C_{k} = \\\\large\\\\frac{1}{k!}\\\\normalsize  p(p - 1)(p - 2)...(p - k + 1)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.969438em;vertical-align:-0.286108em;\"/><span class=\"mord\"><span/><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15139200000000003em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">p</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span/></span></span></span></span></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">C</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span/></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1.402352em;vertical-align:-0.414em;\"/><span class=\"mord sizing reset-size6 size7\"><span class=\"mopen nulldelimiter sizing reset-size7 size6\"/><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8236266666666667em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right:0.03148em;\">k</span><span class=\"mclose mtight\">!</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"/></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"/><span class=\"sizing reset-size7 size4 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">\\u200b</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span/></span></span></span></span><span class=\"mclose nulldelimiter sizing reset-size7 size6\"/></span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">2</span><span class=\"mclose sizing reset-size6 size6\">)</span><span class=\"mord sizing reset-size6 size6\">.</span><span class=\"mord sizing reset-size6 size6\">.</span><span class=\"mord sizing reset-size6 size6\">.</span><span class=\"mopen sizing reset-size6 size6\">(</span><span class=\"mord mathdefault sizing reset-size6 size6\">p</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">−</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:0.77777em;vertical-align:-0.08333em;\"/><span class=\"mord mathdefault sizing reset-size6 size6\" style=\"margin-right:0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/><span class=\"mbin sizing reset-size6 size6\">+</span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"/></span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"/><span class=\"mord sizing reset-size6 size6\">1</span><span class=\"mclose sizing reset-size6 size6\">)</span></span></span></span></span></div>\\nAs Rashed points out in <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;R Rashed, &lt;em&gt;The development of Arabic mathematics : between arithmetic and algebra&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;London, &lt;span class=&quot;non-italic&quot;&gt;1994)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span>, this is only a small step from the <a class=\"gllink\" data-popup=\"../../Glossary/pascal_triangle/\" href=\"../../Glossary/#pascal_triangle\">Pascal triangle</a> results given three hundred years earlier by <a class=\"mlink\" data-popup=\"../Al-Karaji/popup/\" href=\"../Al-Karaji/\">al-Karaji</a>, then still one hundred years before al-Banna by <a class=\"mlink\" data-popup=\"../Al-Samawal/popup/\" href=\"../Al-Samawal/\">al-Samawal</a>. However Rashed writes:-\\n<blockquote>... in our opinion, there is something more fundamental than <span class=\"non-italic\">[</span>the Pascal triangle<span class=\"non-italic\">]</span> results; it is precisely the combinatorial appearance of ibn al-Banna\\'s exposition, together with the relation he partially establishes between <a class=\"gllink\" data-popup=\"../../Glossary/polygonal_number/\" href=\"../../Glossary/#polygonal_number\">polygonal numbers</a> and <a class=\"gllink\" data-popup=\"../../Glossary/combination/\" href=\"../../Glossary/#combination\">combinations</a>. It concern, in the first place, <a class=\"gllink\" data-popup=\"../../Glossary/triangular_number/\" href=\"../../Glossary/#triangular_number\">triangular numbers</a> and combinations of <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>p</mi></mrow><annotation encoding=\"application/x-tex\">p</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"/><span class=\"mord mathdefault\">p</span></span></span></span></span> objects in twos, and then polygonal numbers of order <span class=\"non-italic\">4</span> and combinations of <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>p</mi></mrow><annotation encoding=\"application/x-tex\">p</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"/><span class=\"mord mathdefault\">p</span></span></span></span></span> objects in threes.</blockquote>\\n</span>\\n  </div>\\n</div>\\n\\n\\n  \\n\\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>References <span class=\"nonoscript\">(<a href=\"#\" id=\"references-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n  \\n<div class=\"row\" id=\"references-list\">\\n    <div class=\"col-md-12\">\\n      <ol name=\"references\">\\n        \\n        <li id=\"reference-1\"><span class=\"markup\">J Vernet, Biography in <em>Dictionary of Scientific Biography</em> <span class=\"non-italic\">(</span>New York <span class=\"non-italic\">1970</span>-<span class=\"non-italic\">1990)</span>.\\n<br/>\\nSee <a href=\"http://www.encyclopedia.com/doc/1G2-2830900255.html\">THIS LINK</a>.</span></li>\\n        \\n        <li id=\"reference-2\"><span class=\"markup\">R Rashed, <em>The development of Arabic mathematics : between arithmetic and algebra</em> <span class=\"non-italic\">(</span>London, <span class=\"non-italic\">1994)</span>.</span></li>\\n        \\n        <li id=\"reference-3\"><span class=\"markup\">R Rashed, <em>Entre arithmétique et algèbre: Recherches sur l\\'histoire des mathématiques arabes</em> <span class=\"non-italic\">(</span>Paris, <span class=\"non-italic\">1984)</span>.</span></li>\\n        \\n        <li id=\"reference-4\"><span class=\"markup\">M Aballagh, Les fondements des mathématiques à travers le \\'Raf al-Hijab\\' d\\'Ibn al-Banna <span class=\"non-italic\">(1256</span>-<span class=\"non-italic\">1321)</span>, in <em>Histoire des mathématiques arabes, Algiers, <span class=\"non-italic\">1986</span></em> <span class=\"non-italic\">(</span>Algiers, <span class=\"non-italic\">1988)</span>, <span class=\"non-italic\">133</span>-<span class=\"non-italic\">156</span>.</span></li>\\n        \\n        <li id=\"reference-5\"><span class=\"markup\">M Aballagh, Les fractions entre la théorie et la pratique chez Ibn al-Banna al-Murrakusi <span class=\"non-italic\">(1256</span>-<span class=\"non-italic\">1321)</span>, in <em>Histoire de fractions, fractions d\\'histoire</em> <span class=\"non-italic\">(</span>Basel, <span class=\"non-italic\">1992)</span>, <span class=\"non-italic\">247</span>-<span class=\"non-italic\">258</span>; <span class=\"non-italic\">405</span>-<span class=\"non-italic\">406</span>; <span class=\"non-italic\">411</span>.</span></li>\\n        \\n        <li id=\"reference-6\"><span class=\"markup\">G Arrighi, Review of some mathematical symbols <span class=\"non-italic\">(</span>Italian<span class=\"non-italic\">)</span>, <em>Physis - Riv. Internaz. Storia Sci.</em> <strong><span class=\"non-italic\">27</span></strong> <span class=\"non-italic\">(1</span>-<span class=\"non-italic\">2)</span> <span class=\"non-italic\">(1985)</span>, <span class=\"non-italic\">163</span>-<span class=\"non-italic\">179</span>.</span></li>\\n        \\n        <li id=\"reference-7\"><span class=\"markup\">A Djebbar, <em>Enseignement et recherche mathématiques dans le Maghreb des XIIIe-XIVe siècles : étude partielle</em> <span class=\"non-italic\">(</span>Orsay, <span class=\"non-italic\">1981)</span>.</span></li>\\n        \\n        <li id=\"reference-8\"><span class=\"markup\">R Rashed, Materials for the study of the history of amicable numbers and combinatorial analysis <span class=\"non-italic\">(</span>Arabic<span class=\"non-italic\">)</span>, <em>J. Hist. Arabic Sci.</em> <strong><span class=\"non-italic\">6</span></strong> <span class=\"non-italic\">(1</span>-<span class=\"non-italic\">2)</span> <span class=\"non-italic\">(1982)</span>, <span class=\"non-italic\">278</span>-<span class=\"non-italic\">209</span>.</span></li>\\n        \\n        <li id=\"reference-9\"><span class=\"markup\">H P J Renaud, Ibn al-Banna de Marrakech, sufi et mathématicien, <em>Hesperis</em> <strong><span class=\"non-italic\">25</span></strong> <span class=\"non-italic\">(1938)</span>, <span class=\"non-italic\">13</span>-<span class=\"non-italic\">42</span>.</span></li>\\n        \\n        <li id=\"reference-10\"><span class=\"markup\">H P J Renaud, Sur les dates de la vie du mathématicien arabe marocain Ibn al-Banna, <em>Isis</em> <strong><span class=\"non-italic\">27</span></strong> <span class=\"non-italic\">(1937)</span>, <span class=\"non-italic\">216</span>-<span class=\"non-italic\">218</span>.</span></li>\\n        \\n        <li id=\"reference-11\"><span class=\"markup\">J Samsó and E Millás, The computation of planetary longitudes in the zij of Ibn al-Banna, <em>Arabic Sci. Philos.</em> <strong><span class=\"non-italic\">8</span></strong> <span class=\"non-italic\">(2)</span> <span class=\"non-italic\">(1998)</span>, <span class=\"non-italic\">165</span>; <span class=\"non-italic\">167</span>; <span class=\"non-italic\">259</span>-<span class=\"non-italic\">286</span>.</span></li>\\n        \\n        <li id=\"reference-12\"><span class=\"markup\">M Zarruqi, Fractions in the Morroccan mathematical tradition between the <span class=\"non-italic\">12</span>th and <span class=\"non-italic\">15</span>th centuries A.D. as found in anonymous manuscripts <span class=\"non-italic\">(</span>Arabic<span class=\"non-italic\">)</span>, in <em>Deuxième Colloque Maghrebin sur l\\'Histoire des Mathématiques Arabes</em> <span class=\"non-italic\">(</span>Tunis, <span class=\"non-italic\">1990)</span>, A<span class=\"non-italic\">97</span>-A<span class=\"non-italic\">109</span>.</span></li>\\n        \\n      </ol>\\n    </div>\\n  </div>\\n    \\n  \\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>Additional Resources <span class=\"nonoscript\">(<a href=\"#\" id=\"additional-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n\\n  \\n<div class=\"row\" id=\"additional-list\">\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other pages about Ibn al-Banna:</p>\\n      <ol name=\"additional\">\\n        \\n        <li><a href=\"../../Timelines/timelineb.html\"><span class=\"markup\">See Ibn al-Banna on a timeline</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other websites about Ibn al-Banna:</p>\\n      <ol name=\"otherweb\">\\n        \\n        \\n        <li><a href=\"http://www.filaha.org/author_ibn_al_banna.html\" target=\"_blank\"><span class=\"markup\">Filaha texts</span></a></li>\\n        \\n        \\n        <li><a href=\"http://www.encyclopedia.com/doc/1G2-2830900255.html\" target=\"_blank\"><span class=\"markup\">Dictionary of Scientific Biography</span></a></li>\\n        \\n        \\n        <li><a href=\"http://www.ams.org/mathscinet/MRAuthorID/639236\" target=\"_blank\"><span class=\"markup\">MathSciNet Author profile</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n  </div>\\n    \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Cross-references\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"xrefs-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"xrefs-list\">\\n  <div class=\"col-md-12\">\\n    <ol name=\"xrefs\">\\n      \\n      <li><a href=\"../../HistTopics/Arabic_mathematics/\">History Topics: <span class=\"markup\">Arabic mathematics : forgotten brilliance?</span></a></li>\\n      \\n      <li><a href=\"../../HistTopics/Arabic_numerals/\">History Topics: <span class=\"markup\">The Arabic numeral system</span></a></li>\\n      \\n    </ol>\\n  </div>\\n</div>\\n \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    Written by <span class=\"markup\">J J O\\'Connor and E F Robertson</span>  \\n    <br/>\\n    Last Update November 1999\\n  </div>\\n</div>\\n\\n\\n\\n<div class=\"row\">\\n          <div class=\"cr-footer col-md-4\">\\n            DJF/JOC/EFR<br/>\\n            <a href=\"../../Miscellaneous/copyright/\">Copyright information</a><br/>\\n            <a href=\"../../Miscellaneous/accessibility/\">Accessibility statement</a>\\n          </div>\\n          <div class=\"links-footer col-md-6\">\\n            <a href=\"https://www.st-andrews.ac.uk/mathematics-statistics/\" target=\"_blank\">School of Mathematics and Statistics</a>\\n            <br/>\\n            <a href=\"http://www.st-andrews.ac.uk/\" target=\"_blank\">University of St Andrews, Scotland</a>\\n          </div>\\n          <div class=\"col-md-2\">\\n            <img src=\"../../static/img/st-andrews-logo.png?h=e46f195e\" alt=\"University of St. Andrews logo\"/>\\n          </div>\\n        </div>\\n        \\n<div class=\"row\">\\n          <div class=\"col-md-12\">\\n            If you have comments, or spot errors, we are always pleased to\\n            <a href=\"../../Miscellaneous/contact_us/\">hear from you</a>.\\n          </div>\\n        </div>\\n      </root>'), (2939, '1950-', 'Gamal Ismail', 'https://mathshistory.st-andrews.ac.uk/Biographies/Ismail/', '<root><div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h1>Gamal Ali Fouad Ismail</h1>\\n  </div>\\n</div>\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Quick Info</h3>\\n\\n    \\n    <dt>Born</dt>\\n    <dd>\\n      29 October 1950 <br/>  <a href=\"../../Map/#Zagazig\" target=\"_blank\"> Zagazig, El Sharkia, Egypt </a> \\n    </dd>\\n      \\n    <hr/>\\n    <dt>Summary</dt>\\n    <dd><span class=\"markup\"><strong>Gamal Ismail</strong> is an Egyptian mathematician who became Professor of Pure Mathematics at the University College of Women for Art, Science and Education at Ain Shams University in Cairo in <span class=\"non-italic\">1995</span>.</span></dd>\\n    \\n  </div>\\n\\n  \\n</div>\\n\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Biography</h3>\\n    <span class=\"markup\"><strong>Gamal Ismail</strong> was the daughter of Ali Fouad Ismail Sabry and Souad Ahmed Mahmoud. She studied at Ain Shams University, Cairo, Egypt, where she was awarded the degree of Bachelor of Science in <span class=\"non-italic\">1972</span>. She was then employed as a demonstrator at the Women\\'s College in Cairo.\\n<br/>\\n\\n<br/>\\nOn <span class=\"non-italic\">21</span> February <span class=\"non-italic\">1974</span> she married Hussein Abdel Wahab Abdel Gawad. They had three children, Assmaa Ismail, Ayman Ismail and Ihab Ismail. She continued to study for a Master of Science Degree and for this degree she wrote the thesis <em>Numerical treatment of systems of linear equations</em> which she submitted to Ain Shams University in February <span class=\"non-italic\">1976</span> as partial fulfilment of the requirements for the degree. She gives the following Acknowledgements for the help she received:-\\n<blockquote>The author is greatly indebted to Professor Dr Abbas I Abdel Karim, Professor of Mathematics and Head of Department, University College of Women, Ain Shams University for suggesting the topic of this thesis, for his helpful guidance and kind advice throughout the supervision of this research work. Sincere thanks are expressed to Prof Dr M S El Mohandis, Professor of Mathematics, University College of Women, for his kind help and encouragement.</blockquote>\\nLet us quote the beginning of the Summary of the thesis:-\\n<blockquote>This thesis contains five main chapters. The first chapter is considered as fundamental for solving sets of linear simultaneous equations. The most important problem of numerical algebra is the development of algorithms for the solution. Essentially there are two reasons why this is such a basic problem. First of all, today nearly every linear problem in applied mathematics - as a boundary value problem for a linear ordinary or partial differential equation is reduced by appropriate techniques to a system of linear equations, especially when electronic computers are to be employed for its solution. Secondly, nonlinear problems can in most cases be solved by approximating them by linear problems. There are several different methods for the solution of sets of equations, the method used depending on the calculating aids available, the type of equations to be solved and the accuracy required in the solution. In general, there are two type of numerical techniques for solving simultaneous linear equations: direct methods, which are finite, and indirect methods which are infinite. The two methods are useful, both have advantages and limitations.</blockquote>\\nAfter being awarded a Master of Science Degree, Ismail was appointed as an assistant lecturer in mathematics at Ain Shams University in <span class=\"non-italic\">1976</span>. She continued to undertake research for a doctorate advised by Abbas I A Karim and in <span class=\"non-italic\">1983</span> they published the joint paper <em>The stability of multistep formulae for solving differential equations</em>. The authors give the following Abstract <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;A I A Karim and G A Ismail, The stability of multistep formulae for solving differential equations, &lt;em&gt;Internat. J. Comput. Math. &lt;/em&gt;&lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;13&lt;/span&gt;&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(1)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(1983)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;53&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;67&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-3\"><span class=\"non-italic\">3</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>By the numerical treatment of differential equations, the question of stability is still important. It is advantageous to state alternative methods for investigating the stability of multi-step formulae. Among these methods are: determination of the characteristic roots, graphical method, Hermitian form obtained from the characteristic equation or from the multi-step formula, application of Newton\\'s theorem and using Sturm\\'s theorem. The stability of an illustrative formula is discussed by using each of these methods.</blockquote>\\nIsmail was awarded a Ph.D. in <span class=\"non-italic\">1985</span> for her thesis <em>Accuracy of the multi-step methods for solving differential equations</em>. This work was not published. She was promoted from assistant lecturer to lecturer in mathematics. No papers by Ismail appear to have been published for ten years after the award of her thesis, but in <span class=\"non-italic\">1995</span> she was promoted to associate professor and appointed as manager of the Computer Unit at the Women\\'s College of Ain Shams University. Her next publication, a joint paper with Iman H Ibrahim, was <em>Variable step stiffly stable methods </em>which appeared in <span class=\"non-italic\">1996</span>. A paper with the same authors and title was published two years later in which the Introduction begins as follows <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;G A F Ismail and I H Ibrahim, Variable step stiffly stable methods, &lt;em&gt;Int. J. Comput. Math.&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;66&lt;/span&gt; &lt;/strong&gt;&lt;span class=&quot;non-italic&quot;&gt;(3&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;4)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(1998)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;227&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;240&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-1\"><span class=\"non-italic\">1</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>There is much current interest in the problem of devising numerical methods of stiff ODEs.  Stiffly stable variable step methods of order <span class=\"non-italic\">3</span> and <span class=\"non-italic\">4</span> are established. Some stability  properties of multistep formulas will be discussed, some theorems and lemmas are proved ...</blockquote>\\nFurther papers by Ismail followed: <em>A new higher order effective P-C methods for stiff systems</em> <span class=\"non-italic\">(1998)</span>; <em>Stability of nonequidistant variable order multistep methods for stiff systems</em> <span class=\"non-italic\">(2000)</span>; <em>A numerical technique for the <span class=\"non-italic\">3</span>-D Poisson equation</em> <span class=\"non-italic\">(2003)</span>, <em>Efficient numerical solution of <span class=\"non-italic\">3</span>D incompressible viscous Navier-Stokes equations</em> <span class=\"non-italic\">(2004)</span> and <em>A new approach to construct linear multistep formulae for solving stiff ODEs </em><span class=\"non-italic\">(2005)</span>.\\n<br/>\\n\\n<br/>\\nAlso in <span class=\"non-italic\">2005</span> Ismail published <em>Modified technique for solving advance-delay differential systems</em> in the journal <em>Mathematical and computer modelling</em>. This was unfortunate for, in the following year, the Editor-in-Chief of <em>Mathematical and computer modelling</em> requested the paper be retracted. We quote the following reason for the retraction given in this paper <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;G A F Ismail, Erratum to: &quot;Modified technique for solving advance-delay differential systems\\'\\' &lt;span class=&quot;non-italic&quot;&gt;[&lt;/span&gt;Math. Comput. Modelling &lt;span class=&quot;non-italic&quot;&gt;41(2&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;3)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(2005)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;287&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;299]&lt;/span&gt;, &lt;em&gt;Math. Comput. Modelling&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;44&lt;/span&gt; &lt;/strong&gt;&lt;span class=&quot;non-italic&quot;&gt;(1&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;2)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(2006)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;229&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;230&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>The author has plagiarized part of a paper that had already appeared in \\'J. Math. Biol.\\' <strong><span class=\"non-italic\">24</span></strong> <span class=\"non-italic\">(1986)</span>, <span class=\"non-italic\">583</span>-<span class=\"non-italic\">601</span>. One of the conditions of submission of a paper for publication is that authors declare explicitly that their work is original and has not appeared in a publication elsewhere. Re-use of any data should be appropriately cited. As such this article represents a severe abuse of the scientific publishing system. The scientific community takes a very strong view on this matter and we apologize to readers of the journal that this was not detected during the submission process.</blockquote>\\nAfter this unfortunate publication, sadly Ismail does not appear to have published any further papers.\\n<br/>\\n\\n<br/>\\nLet us end this biography by noting that Ismail is a member of the Egyptian Mathematics Society and gives her other interests as reading, listening to music, tennis and travel.</span>\\n  </div>\\n</div>\\n\\n\\n  \\n\\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>References <span class=\"nonoscript\">(<a href=\"#\" id=\"references-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n  \\n<div class=\"row\" id=\"references-list\">\\n    <div class=\"col-md-12\">\\n      <ol name=\"references\">\\n        \\n        <li id=\"reference-1\"><span class=\"markup\">G A F Ismail and I H Ibrahim, Variable step stiffly stable methods, <em>Int. J. Comput. Math.</em> <strong><span class=\"non-italic\">66</span> </strong><span class=\"non-italic\">(3</span>-<span class=\"non-italic\">4)</span> <span class=\"non-italic\">(1998)</span>, <span class=\"non-italic\">227</span>-<span class=\"non-italic\">240</span>.</span></li>\\n        \\n        <li id=\"reference-2\"><span class=\"markup\">G A F Ismail, Erratum to: \"Modified technique for solving advance-delay differential systems\\'\\' <span class=\"non-italic\">[</span>Math. Comput. Modelling <span class=\"non-italic\">41(2</span>-<span class=\"non-italic\">3)</span> <span class=\"non-italic\">(2005)</span>, <span class=\"non-italic\">287</span>-<span class=\"non-italic\">299]</span>, <em>Math. Comput. Modelling</em> <strong><span class=\"non-italic\">44</span> </strong><span class=\"non-italic\">(1</span>-<span class=\"non-italic\">2)</span> <span class=\"non-italic\">(2006)</span>, <span class=\"non-italic\">229</span>-<span class=\"non-italic\">230</span>.</span></li>\\n        \\n        <li id=\"reference-3\"><span class=\"markup\">A I A Karim and G A Ismail, The stability of multistep formulae for solving differential equations, <em>Internat. J. Comput. Math. </em><strong><span class=\"non-italic\">13</span></strong> <span class=\"non-italic\">(1)</span> <span class=\"non-italic\">(1983)</span>, <span class=\"non-italic\">53</span>-<span class=\"non-italic\">67</span>.</span></li>\\n        \\n        <li id=\"reference-4\"><span class=\"markup\">Profile of Gamal Ali Fouad Ismail, <em>Prabook</em>. <a href=\"https://prabook.com/web/gamal_ali_fouad_ismail/345897\">https://prabook.com/web/gamal_ali_fouad_ismail/<span class=\"non-italic\">345897</span></a></span></li>\\n        \\n      </ol>\\n    </div>\\n  </div>\\n    \\n  \\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>Additional Resources <span class=\"nonoscript\">(<a href=\"#\" id=\"additional-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n\\n  \\n<div class=\"row\" id=\"additional-list\">\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other pages about Gamal Ismail:</p>\\n      <ol name=\"additional\">\\n        \\n        <li><a href=\"../../HistTopics/African_women_1#Ismail\"><span class=\"markup\">Entry in the list of African women PhDs</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other websites about Gamal Ismail:</p>\\n      <ol name=\"otherweb\">\\n        \\n        \\n        <li><a href=\"http://www.ams.org/mathscinet/MRAuthorID/626771\" target=\"_blank\"><span class=\"markup\">MathSciNet Author profile</span></a></li>\\n        \\n        \\n        <li><a href=\"https://zbmath.org/authors/?q=ai:ismail.gamal-a-fouad\" target=\"_blank\"><span class=\"markup\">zbMATH entry</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n  </div>\\n    \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Cross-references\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"xrefs-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"xrefs-list\">\\n  <div class=\"col-md-12\">\\n    <ol name=\"xrefs\">\\n      \\n      <li><a href=\"../../HistTopics/African_women_1/\">History Topics: <span class=\"markup\">African women with a doctorate in mathematics <span class=\"non-italic\">1</span></span></a></li>\\n      \\n    </ol>\\n  </div>\\n</div>\\n \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    Written by <span class=\"markup\">J J O\\'Connor and E F Robertson</span>  \\n    <br/>\\n    Last Update March 2019\\n  </div>\\n</div>\\n\\n\\n\\n<div class=\"row\">\\n          <div class=\"cr-footer col-md-4\">\\n            DJF/JOC/EFR<br/>\\n            <a href=\"../../Miscellaneous/copyright/\">Copyright information</a><br/>\\n            <a href=\"../../Miscellaneous/accessibility/\">Accessibility statement</a>\\n          </div>\\n          <div class=\"links-footer col-md-6\">\\n            <a href=\"https://www.st-andrews.ac.uk/mathematics-statistics/\" target=\"_blank\">School of Mathematics and Statistics</a>\\n            <br/>\\n            <a href=\"http://www.st-andrews.ac.uk/\" target=\"_blank\">University of St Andrews, Scotland</a>\\n          </div>\\n          <div class=\"col-md-2\">\\n            <img src=\"../../static/img/st-andrews-logo.png?h=e46f195e\" alt=\"University of St. Andrews logo\"/>\\n          </div>\\n        </div>\\n        \\n<div class=\"row\">\\n          <div class=\"col-md-12\">\\n            If you have comments, or spot errors, we are always pleased to\\n            <a href=\"../../Miscellaneous/contact_us/\">hear from you</a>.\\n          </div>\\n        </div>\\n      </root>'), (429, '1755-1839', 'Gaspard de Prony', 'https://mathshistory.st-andrews.ac.uk/Biographies/De_Prony/', '<root><div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h1>Gaspard Clair François Marie  Riche de Prony</h1>\\n  </div>\\n</div>\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-8\">\\n    <h3>Quick Info</h3>\\n\\n    \\n    <dt>Born</dt>\\n    <dd>\\n      22 July 1755 <br/>  <a href=\"../../Map/#Villefranche\" target=\"_blank\"> Chamelet, Beaujolais, France </a> \\n    </dd>\\n     \\n    <dt>Died</dt>\\n    <dd>\\n      29 July 1839 <br/> Paris, France\\n    </dd>\\n     \\n    <hr/>\\n    <dt>Summary</dt>\\n    <dd><span class=\"markup\"><strong>Gaspard de Prony</strong> was a French mathematician who produced mathematical tables and texts on mathematical physics.</span></dd>\\n    \\n  </div>\\n\\n   \\n  <div class=\"col-md-4 biography-thumbnail-container\">\\n    \\n    <a href=\"pictdisplay/\" target=\"_blank\">\\n      \\n      <img class=\"biography-thumbnail\" src=\"thumbnail.jpg\" alt=\"Thumbnail of Gaspard de Prony\"/>\\n      \\n      <br/>\\n      View two larger pictures</a>\\n    \\n  </div>\\n  \\n</div>\\n\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Biography</h3>\\n    <span class=\"markup\"><strong>Gaspard de Prony</strong>\\'s family name was Riche, the de Prony title having been bought by his parents. In fact de Prony\\'s younger brother was always known by the name Riche. De Prony was educated at the Benedictine College at Toissei in Doubs. From there he entered the École des Ponts et Chaussés in <span class=\"non-italic\">1776</span> where he studied engineering. He graduated in <span class=\"non-italic\">1779</span> as the top student and remained for a further year in Paris, doing as the head of the École des Ponts et Chaussés told him:-\\n<blockquote>M de Prony ... concern yourself with acquiring a deep knowledge of your art, for you are destined to become head of the École des Ponts et Chaussés.</blockquote>\\nIn <span class=\"non-italic\">1780</span> he became an engineer with the École des Ponts et Chaussés and after three years in a number of different regions of France he returned to the École des Ponts et Chaussés in Paris <span class=\"non-italic\">1783</span>. This was the same year he published his first major work in the <a class=\"aclink\" href=\"../../Societies/Paris/\" rel=\"noreferrer\" target=\"_blank\">Académie des Sciences</a> on the forces on arches. <a class=\"mlink\" data-popup=\"../Monge/popup/\" href=\"../Monge/\">Monge</a> was impressed with this paper and realised that de Prony was someone of great potential.\\n<br/>\\n\\n<br/>\\nIn <span class=\"non-italic\">1785</span> de Prony visited England on a project to obtain an accurate measurement of the relative positions of the Greenwich Observatory and the Paris Observatory. Two years later he was promoted to inspector at the École des Ponts et Chaussés. Around this time he was involved with the work on the Louis XVI Bridge in Paris which is now called the Pont de la Concorde.\\n<br/>\\n\\n<br/>\\nFurther promotion in <span class=\"non-italic\">1790</span> was followed the next year by his being appointed Engineer-in-Chief of the École des Ponts et Chaussés. This promotion was as a result of the opening of the Louis XVI Bridge.\\n<br/>\\n\\n<br/>\\nAlso around <span class=\"non-italic\">1791</span> de Prony was working on geometry with <a class=\"mlink\" data-popup=\"../Girard_Pierre/popup/\" href=\"../Girard_Pierre/\">Pierre Girard</a>. Then in <span class=\"non-italic\">1792</span>, de Prony began a major task of producing logarithmic and trigonometric tables, the <em>Cadastre</em>. With the assistance of <a class=\"mlink\" data-popup=\"../Legendre/popup/\" href=\"../Legendre/\">Legendre</a>, <a class=\"mlink\" data-popup=\"../Carnot/popup/\" href=\"../Carnot/\">Carnot</a> and other mathematicians, and between <span class=\"non-italic\">70</span> to <span class=\"non-italic\">80</span> assistants, the work was undertaken over a period of years, being completed in <span class=\"non-italic\">1801</span>. The tables were, see <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;M M Bradley, Prony the bridge builder : the life and times of Gaspard de Prony, educator and scientist, &lt;em&gt;Centaurus&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;37&lt;/span&gt;&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(1994)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;230&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;268&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>... vast, with values calculated to between fourteen and twenty-nine decimal places. Each copy consisted of eighteen folio volumes together with another volume of mathematical procedures.</blockquote>\\nGetting such a massive work published was another matter. Negotiations went on over a number of years until, in <span class=\"non-italic\">1809</span>, it seemed they would appear. The publisher wrote:-\\n<blockquote>The present generation would never have witnessed the end of this monumental work if M de Prony had not had the fortunate idea of applying the powerful method of division of labour, conceiving methods to reduce the long and laborious part of the production of the tables to simple additions and subtractions...</blockquote>\\nHowever the tables were never published in full and it was near the end of the century before even a part appeared. It was just too expensive to print at a time when France was not in the best of financial states.\\n<br/>\\n\\n<br/>\\nIn <span class=\"non-italic\">1794</span> the École Centrale des Travaux Publics was founded by and was directed by <a class=\"mlink\" data-popup=\"../Carnot/popup/\" href=\"../Carnot/\">Carnot</a> and <a class=\"mlink\" data-popup=\"../Monge/popup/\" href=\"../Monge/\">Monge</a>. It was renamed the École Polytechnique in <span class=\"non-italic\">1795</span> and de Prony was certainly one of the main lectures by this time. He is listed among the first teachers at the university as:-\\n<blockquote>Prony, lecturer in analysis, director of the Cadastre, member of the Institute. Annual salary <span class=\"non-italic\">6</span>,<span class=\"non-italic\">000</span> francs. Accommodation within the school...</blockquote>\\nDe Prony\\'s lectures given at the École Polytechnique were published, including his lectures on hydraulics.\\n<br/>\\n\\n<br/>\\nIn <span class=\"non-italic\">1798</span> de Prony refused Napoleon\\'s request that he join his army of invasion to Egypt. <a class=\"mlink\" data-popup=\"../Fourier/popup/\" href=\"../Fourier/\">Fourier</a>, <a class=\"mlink\" data-popup=\"../Monge/popup/\" href=\"../Monge/\">Monge</a> and <a class=\"mlink\" data-popup=\"../Malus/popup/\" href=\"../Malus/\">Malus</a> had agreed to be part of the expeditionary force and Napoleon was angry that de Prony would not come. It did mean that de Prony was to fail to receive the honours he deserved from Napoleon but de Prony\\'s wife was a close friend of Joséphine and this probably saved de Prony from anything worse.\\n<br/>\\n\\n<br/>\\nIn <span class=\"non-italic\">1798</span> de Prony achieved his ambition of being appointed director of the École des Ponts et Chaussés. His desire for this post was almost certainly a main reason for his refusing to join Napoleon. As director he began producing a number of important texts on mathematical physics. He became a member of the Bureau de Longitude and, in <span class=\"non-italic\">1810</span> and <span class=\"non-italic\">1811</span>, he produced two further major texts from his lectures at the École Polytechnique, namely <em>Leçons de Mécanique Analytique</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Lessons on analytical mechanics&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Lessons on analytical mechanics</span><span class=\"non-italic\">)</span></noscript></span> and <em>Sommaire des Leçons du Cours de Mécanique</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Summary of lessons in a course on mechanics&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Summary of lessons in a course on mechanics</span><span class=\"non-italic\">)</span></noscript></span>.\\n<br/>\\n\\n<br/>\\nAfter Napoleon was defeated the reorganisation in France included a reorganisation of the École Polytechnique which was closed during <span class=\"non-italic\">1816</span>. De Prony lost his position as professor there and was not part of the reorganisation committee. However, as soon as the school reopened, de Prony was asked to be an examiner so he continued his connection yet only had to work one month per year.\\n<br/>\\n\\n<br/>\\nOne of de Prony\\'s most important scientific inventions was the \\'de Prony brake\\' which he invented in <span class=\"non-italic\">1821</span> to measure the performance of machines and engines. It was based on ideas of <a class=\"mlink\" data-popup=\"../Hachette/popup/\" href=\"../Hachette/\">Hachette</a> and was a considerable improvement on a method which <a class=\"mlink\" data-popup=\"../Girard_Pierre/popup/\" href=\"../Girard_Pierre/\">Pierre Girard</a> had used two years earlier.\\n<br/>\\n\\n<br/>\\nThe last part of de Prony\\'s career was more involved with education rather than administration. One battle he fought, without success, was against <a class=\"mlink\" data-popup=\"../Cauchy/popup/\" href=\"../Cauchy/\">Cauchy</a>\\'s move towards pure mathematics and away from the more applied mathematics which de Prony firmly believed in. In <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;M M Bradley, Prony the bridge builder : the life and times of Gaspard de Prony, educator and scientist, &lt;em&gt;Centaurus&lt;/em&gt; &lt;strong&gt;&lt;span class=&quot;non-italic&quot;&gt;37&lt;/span&gt;&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(1994)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;230&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;268&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span> Margaret Bradley writes:-\\n<blockquote>... there had long been an increasing demand for the reform of the École des Ponts et Chaussés and his lack of attention to this attracted severe criticism. He was now showing even less interest in the day to day running of the school, in favour of science. He was disillusioned by the failure of his attempts to reform mathematics teaching at the École Polytechnique, where he had made energetic and determined efforts to combat the emphasis on theory of <a class=\"mlink\" data-popup=\"../Cauchy/popup/\" href=\"../Cauchy/\">A-L Cauchy</a> ... Prony seems to have lost heart for the continuing struggle and to have been less conscientious with regard to his duties as examiner.</blockquote></span>\\n  </div>\\n</div>\\n\\n\\n  \\n\\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>References <span class=\"nonoscript\">(<a href=\"#\" id=\"references-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n  \\n<div class=\"row\" id=\"references-list\">\\n    <div class=\"col-md-12\">\\n      <ol name=\"references\">\\n        \\n        <li id=\"reference-1\"><span class=\"markup\">M M Bradley, <em>Gaspard- Clair- François- Marie- Riche de Prony : his career as educator and scientist</em> <span class=\"non-italic\">(</span>PhD Thesis Coventry <span class=\"non-italic\">(</span>Lanchester<span class=\"non-italic\">)</span> Polytechnic, <span class=\"non-italic\">1984)</span>.</span></li>\\n        \\n        <li id=\"reference-2\"><span class=\"markup\">M M Bradley, Prony the bridge builder : the life and times of Gaspard de Prony, educator and scientist, <em>Centaurus</em> <strong><span class=\"non-italic\">37</span></strong> <span class=\"non-italic\">(1994)</span>, <span class=\"non-italic\">230</span>-<span class=\"non-italic\">268</span>.</span></li>\\n        \\n        <li id=\"reference-3\"><span class=\"markup\">I Grattan-Guinness, Work for the hairdressers : The production of de Prony\\'s logarithmic and trigonometric tables, <em>Annals of the History of Computing</em> <strong><span class=\"non-italic\">12</span></strong> <span class=\"non-italic\">(3)</span> <span class=\"non-italic\">(1990)</span>, <span class=\"non-italic\">177</span>-<span class=\"non-italic\">185</span>.</span></li>\\n        \\n        <li id=\"reference-4\"><span class=\"markup\">M Walckenaer, La Vie de Prony, <em>Bulletin de la Societé pour l\\'Encouragement de l\\'Industrie Nationale</em> <strong><span class=\"non-italic\">139</span></strong> <span class=\"non-italic\">(1940)</span>, <span class=\"non-italic\">68</span>-<span class=\"non-italic\">98</span>.</span></li>\\n        \\n      </ol>\\n    </div>\\n  </div>\\n     \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Honours\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"honours-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"honours-list\">\\n  <div class=\"col-md-12\">\\n    <p>Honours awarded to Gaspard de Prony</p>\\n    <ol name=\"honours\">\\n       <li><a href=\"../../Honours/FRS/\"><span class=\"markup\">Fellow of the Royal Society <span class=\"non-italic\">1818</span></span></a></li>  <li><a href=\"../../Societies/RSE/FRSE/\"><span class=\"markup\">Fellow of the Royal Society of Edinburgh Elected <span class=\"non-italic\">1820</span></span></a></li>  <li><a href=\"../../Honours/ParisNames/\"><span class=\"markup\">Paris street names <strong>Rue de Prony</strong> <span class=\"non-italic\">(17</span>th Arrondissement<span class=\"non-italic\">)</span></span></a></li>  <li><a href=\"../../Honours/Eiffel/\"><span class=\"markup\">Commemorated on the Eiffel Tower</span></a></li> \\n    </ol>\\n  </div>\\n</div>\\n \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Cross-references\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"xrefs-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"xrefs-list\">\\n  <div class=\"col-md-12\">\\n    <ol name=\"xrefs\">\\n      \\n      <li><a href=\"../../Projects/Ayel/chapter-2/\">Student Projects: The French Grandes Écoles: Chapter 2</a></li>\\n      \\n      <li><a href=\"../../Projects/Ayel/chapter-3/\">Student Projects: The French Grandes Écoles: Chapter 3</a></li>\\n      \\n      <li><a href=\"../../Projects/Ayel/chapter-4/\">Student Projects: The French Grandes Écoles: Chapter 4</a></li>\\n      \\n      <li><a href=\"../../Societies/RSE/FRSE2/\">Other: Fellows of the Royal Society of Edinburgh</a></li>\\n      \\n    </ol>\\n  </div>\\n</div>\\n \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    Written by <span class=\"markup\">J J O\\'Connor and E F Robertson</span>  \\n    <br/>\\n    Last Update April 1997\\n  </div>\\n</div>\\n\\n\\n\\n<div class=\"row\">\\n          <div class=\"cr-footer col-md-4\">\\n            DJF/JOC/EFR<br/>\\n            <a href=\"../../Miscellaneous/copyright/\">Copyright information</a><br/>\\n            <a href=\"../../Miscellaneous/accessibility/\">Accessibility statement</a>\\n          </div>\\n          <div class=\"links-footer col-md-6\">\\n            <a href=\"https://www.st-andrews.ac.uk/mathematics-statistics/\" target=\"_blank\">School of Mathematics and Statistics</a>\\n            <br/>\\n            <a href=\"http://www.st-andrews.ac.uk/\" target=\"_blank\">University of St Andrews, Scotland</a>\\n          </div>\\n          <div class=\"col-md-2\">\\n            <img src=\"../../static/img/st-andrews-logo.png?h=e46f195e\" alt=\"University of St. Andrews logo\"/>\\n          </div>\\n        </div>\\n        \\n<div class=\"row\">\\n          <div class=\"col-md-12\">\\n            If you have comments, or spot errors, we are always pleased to\\n            <a href=\"../../Miscellaneous/contact_us/\">hear from you</a>.\\n          </div>\\n        </div>\\n      </root>'), (58, '1412-1486', 'Al-Qalasadi', 'https://mathshistory.st-andrews.ac.uk/Biographies/Al-Qalasadi/', '<root><div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h1>Abu\\'l Hasan ibn Ali al Qalasadi</h1>\\n  </div>\\n</div>\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Quick Info</h3>\\n\\n    \\n    <dt>Born</dt>\\n    <dd>\\n      1412 <br/>  <a href=\"../../Map/#Baza\" target=\"_blank\"> Bastah (now Baza, Spain) </a> \\n    </dd>\\n     \\n    <dt>Died</dt>\\n    <dd>\\n      1486 <br/> Béja, Tunisia\\n    </dd>\\n     \\n    <hr/>\\n    <dt>Summary</dt>\\n    <dd><span class=\"markup\"><strong>Al-Qalasadi</strong> was a Spanish Islamic mathematician who took the first steps toward the introduction of algebraic symbolism by using letters in place of numbers.</span></dd>\\n    \\n  </div>\\n\\n  \\n</div>\\n\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Biography</h3>\\n    <span class=\"markup\"><strong>Al-Qalasadi</strong> <span class=\"non-italic\">(</span>or <strong>al-Kalasadi,</strong> as it is sometimes written<span class=\"non-italic\">)</span> was born in Bastah, a Moorish city in Andalusia, now a part of Spain. Andalusia was derived from the Arabic name al-Andalus which was originally applied by the Muslims to the whole of present day Spain and Portugal, an area which they occupied from the <span class=\"non-italic\">8</span><span class=\"superscript\">th</span>  Century. In the <span class=\"non-italic\">11</span><span class=\"superscript\">th</span>  Century Christians began to retake the area, slowly moving down from the north and east. Andalusia was then the name applied to the region remaining under Muslim rule.\\n<br/>\\n\\n<br/>\\nThe Christian reconquest took four hundred years. Andalusia had prospered during the <span class=\"non-italic\">13</span><span class=\"superscript\">th</span>  century and the Alhambra, a wonderful palace and fortress of the rulers of Granada, was largely completed by <span class=\"non-italic\">1360</span>. The Christian kingdom of Castile to the north had suffered civil strife through the <span class=\"non-italic\">14</span><span class=\"superscript\">th</span>  Century, so Andalusia had prospered but, in <span class=\"non-italic\">1407</span>, five years before al-Qalasadi was born, Castile began a major push to conquer the whole of Spain and Portugal.\\n<br/>\\n\\n<br/>\\nAl-Qalasadi was a Muslim who was brought up in Bastah which is north-east of Granada city. It must have been a difficult period in which to live in Bastah, with a steady, yet intermittent, encroachment of Castile towards the city. Al-Qalasadi began his education in Bastah, studying law, the Qur\\'an and the science of fixed shares in an estate. He moved south, away from the war zone, to Granada where he continued his studies, in particular philosophy, science and Muslim law.\\n<br/>\\n\\n<br/>\\nAl-Qalasadi chose to remain in the Islamic world and he left Granada and travelled widely throughout Islamic territory. In particular he spent much time in the North Africa, living in Islamic countries which had supported Andalusia, both with political and with military aid in its resistance to the Christian attacks. He spent some time in Tlemcen <span class=\"non-italic\">(</span>now in northwestern Algeria, near the Moroccan border<span class=\"non-italic\">)</span> where he studied under teachers who taught him arithmetic and its applications. Form there al-Qalasadi went to Egypt where again he studied with some of the leading scholars. Eventually al-Qalasadi reached Mecca, the purpose of his pilgrimage, and returned to Granada.\\n<br/>\\n\\n<br/>\\nThings were in a bad way when al-Qalasadi returned to Granada. The last remaining parts of the Muslim state were under severe attack from the Christians of Aragon and Castile. However, al-Qalasadi taught and wrote some of his major works during this period but eventually the advancing Christian armies made life impossible for him. Al-Qalasadi <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;C Brockelmann, &lt;em&gt;Geschichte der arabischen literatur&lt;/em&gt; &lt;strong&gt;II&lt;/strong&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Leiden, &lt;span class=&quot;non-italic&quot;&gt;1949)&lt;/span&gt;, &lt;span class=&quot;non-italic&quot;&gt;343&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;344&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-5\"><span class=\"non-italic\">5</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>Courageously ... exerted himself in trying to organise resistance, but he was soon forced to join the Andalusian hordes of refugees that were spreading over the Maghrib.</blockquote>\\nThe defeat of the whole Muslim state in Granada finally took place until <span class=\"non-italic\">1492</span>, six years after al-Qalasadi\\'s death in North Africa, when the city of Granada fell to Christian Castile.\\n<br/>\\n\\n<br/>\\nIn <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;J Samsó, &lt;em&gt;Las ciencias de los antiguos en al-Andalus&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Madrid, &lt;span class=&quot;non-italic&quot;&gt;1992)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span> al-Qalasadi is described as a specialist in the apportioning of inheritances who took the first steps toward the introduction of algebraic symbolism. His contributions to algebraic symbolism were in using short Arabic words, or just their initial letters, as mathematical symbols. In particular he used \\n<blockquote>wa meaning \"and\" for +\\n<br/>\\nilla meaning \"less\" for -\\n<br/>\\nfi meaning \"times\" for ×\\n<br/>\\nala meaning \"over\" for ÷\\n<br/>\\nj from jadah meaning \"root\"\\n<br/>\\nsh from shay meaning \"thing\" <span class=\"non-italic\">(</span><span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>x</mi></mrow><annotation encoding=\"application/x-tex\">x</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"/><span class=\"mord mathdefault\">x</span></span></span></span></span>, the unknown<span class=\"non-italic\">)</span>\\n<br/>\\nm from mal for <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><annotation encoding=\"application/x-tex\">x^{2}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8141079999999999em;vertical-align:0em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">x</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span></span></span></span>\\n<br/>\\nk form kab for <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow><annotation encoding=\"application/x-tex\">x^{3}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8141079999999999em;vertical-align:0em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">x</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span></span></span></span></span>\\n<br/>\\nl from yadilu for =</blockquote>\\nAl-Qalasadi wrote several books on arithmetic and one on algebra. Some of these are commentaries such as his commentary on the <em>Talkhis amal al-hisab</em> <span class=\"non-italic\">(</span>Summary of arithmetical operations<span class=\"non-italic\">)</span> by <a class=\"mlink\" data-popup=\"../Al-Banna/popup/\" href=\"../Al-Banna/\">ibn al-Banna</a>. <a class=\"mlink\" data-popup=\"../Al-Banna/popup/\" href=\"../Al-Banna/\">Ibn al-Banna</a> was a Moroccan who had died over <span class=\"non-italic\">100</span> years before al-Qalasadi wrote his commentary but, perhaps surprisingly, <a class=\"mlink\" data-popup=\"../Al-Banna/popup/\" href=\"../Al-Banna/\">ibn al-Banna</a> himself had written a commentary on his own work.\\n<br/>\\n\\n<br/>\\nCertainly al-Qalasadi wrote original works. His major treatise was <em>al-Tabsira fi\\'lm al-hisab</em> <span class=\"non-italic\">(</span>Clarification of the science of arithmetic<span class=\"non-italic\">)</span>. This was a difficult text and, perhaps to some extent following the example of <a class=\"mlink\" data-popup=\"../Al-Banna/popup/\" href=\"../Al-Banna/\">ibn al-Banna</a>, al-Qalasadi followed it up by writing a simpler version which he called <em>Unveiling the science of arithmetic</em>. Even this he must have considered to be too difficult to be used as a teaching book, for he wrote yet a third version <em>Unfolding the secrets of the use of dust letters</em>.\\n<br/>\\n\\n<br/>\\nThe title of this work needs some explanation. The early methods of calculating with Hindu numerals involved the use of a dust board. A dust board was used because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, <a class=\"mlink\" data-popup=\"../Al-Uqlidisi/popup/\" href=\"../Al-Uqlidisi/\">al-Uqlidisi</a> in the tenth century had showed how to modify arithmetical techniques so that pen and paper could be used instead of the dust board. In his arithmetic texts al-Qalasadi computed <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo>∑</mo><msup><mi>n</mi><mn>2</mn></msup><mo separator=\"true\">,</mo><mo>∑</mo><msup><mi>n</mi><mn>3</mn></msup></mrow><annotation encoding=\"application/x-tex\">\\\\sum n^{2}, \\\\sum n^{3}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.064118em;vertical-align:-0.25001em;\"/><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">∑</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span><span class=\"mpunct\">,</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"/><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">∑</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span></span></span></span></span> and used the method of successive approximation to determine square roots.\\n<br/>\\n\\n<br/>\\nBoth of the simpler versions of al-Qalasadi\\'s arithmetic treatise proved popular in teaching arithmetic in North Africa and the works were in use for over <span class=\"non-italic\">100</span> years. It is now certain that, despite being popular teaching books, there was little original in al-Qalasadi\\'s work. For example, the sequences <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo>∑</mo><msup><mi>n</mi><mn>2</mn></msup></mrow><annotation encoding=\"application/x-tex\">\\\\sum  n^{2}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.064118em;vertical-align:-0.25001em;\"/><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">∑</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span></span></span></span> and <span class=\"math\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo>∑</mo><msup><mi>n</mi><mn>3</mn></msup></mrow><annotation encoding=\"application/x-tex\">\\\\sum  n^{3}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.064118em;vertical-align:-0.25001em;\"/><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">∑</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"/><span class=\"mord\"><span class=\"mord mathdefault\">n</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"/><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3</span></span></span></span></span></span></span></span></span></span></span></span></span> had been studied by <a class=\"mlink\" data-popup=\"../Al-Samawal/popup/\" href=\"../Al-Samawal/\">al-Samawal</a> and <a class=\"mlink\" data-popup=\"../Al-Baghdadi/popup/\" href=\"../Al-Baghdadi/\">al-Baghdadi</a>, and methods for computing square roots were known to the Babylonians.\\n<br/>\\n\\n<br/>\\nHowever, this was poorly understood by the historians of the <span class=\"non-italic\">19</span><span class=\"superscript\">th</span>  century who first tried to understand the contributions to mathematics by the Muslims. The difficulty was that al-Qalasadi, being one of the last of the mathematicians associated with the major mathematical contributions by the Muslims and Arabs, was better known than many of the earlier contributors. Ignorance of the earlier contributions led historians to give too much credit to al-Qalasadi whom in many ways displayed the same characteristics as the later ancient Greek mathematicians.\\n<br/>\\n\\n<br/>\\nOnce established, however, ideas are harder to overturn than one might imagine. J Samso-Moya, reviewing <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;al-Kalasadi, The Encyclopaedia of Islam Vol IV &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Leiden, &lt;span class=&quot;non-italic&quot;&gt;1978)&lt;/span&gt;,&lt;/span&gt;\" href=\"#reference-6\"><span class=\"non-italic\">6</span></a><span class=\"non-italic\">]</span></span>. writes:-\\n<blockquote>The author analyses the work of the mathematicians of the Maghrib as if they were entirely independent of their predecessors in Eastern Islam. This leads him to stress the importance of the algebraic symbolism used by al-Qalasadi <span class=\"non-italic\">(1412</span>-<span class=\"non-italic\">1486)</span> without taking into consideration similar previous attempts both in Eastern and in Western Islam, a fact which was already known - in the second half of the <span class=\"non-italic\">19</span><span class=\"superscript\">th</span>  century - by F Woepcke.</blockquote>\\nThe book <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;J Samsó, &lt;em&gt;Las ciencias de los antiguos en al-Andalus&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Madrid, &lt;span class=&quot;non-italic&quot;&gt;1992)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-2\"><span class=\"non-italic\">2</span></a><span class=\"non-italic\">]</span></span> is a reprint of Woepcke\\'s <span class=\"non-italic\">19</span><span class=\"superscript\">th</span>\\n<br/>\\ncentury treatise refered to by Samso-Moya. Again reviewing <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;F Woepcke, &lt;em&gt;Études sur les mathématiques arabo-islamiques&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(2&lt;/span&gt; Vols.&lt;span class=&quot;non-italic&quot;&gt;)&lt;/span&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;Frankfurt am Main, &lt;span class=&quot;non-italic&quot;&gt;1986)&lt;/span&gt;.&lt;/span&gt;\" href=\"#reference-3\"><span class=\"non-italic\">3</span></a><span class=\"non-italic\">]</span></span> J Samso-Moya writes:-\\n<blockquote>The author seems to believe that algebraic symbolism was first developed in Islam by the Spanish-Arabic mathematicians <a class=\"mlink\" data-popup=\"../al-Banna/@popup/\" href=\"../al-Banna\">Ibn al-Banna</a> <span class=\"non-italic\">(</span>d. <span class=\"non-italic\">1321</span>, a Moroccan<span class=\"non-italic\">)</span> and al-Qalasadi <span class=\"non-italic\">(</span>d. <span class=\"non-italic\">1486)</span>: the extreme rarity of algebraical symbolism in the parts dedicated to algebra in medieval Italian books on the <a class=\"gllink\" data-popup=\"../../Glossary/abacus/\" href=\"../../Glossary/#abacus\">abacus</a> and arithmetic is possibly due to the fact that <a class=\"mlink\" data-popup=\"../Fibonacci/popup/\" href=\"../Fibonacci/\">Leonardo Fibonacci</a> <span class=\"non-italic\">(</span>d. after <span class=\"non-italic\">1240)</span>, whose \"Liber abaci\" was extremely influential in medieval Italy, was not aware of the work of Andalusian mathematicians.</blockquote>\\nCertainly symbols were not the invention of al-Qalasadi. Perhaps even more telling is that the particular symbols he used were not even his own invention since the same ones had been used by other Muslim mathematicians in North Africa <span class=\"non-italic\">100</span> years earlier. Symbols had been used in the east of the Muslim empire even earlier than that. We should not, however, let any of this argument detract from al-Qalasadi\\'s contribution. We must stress that he does not clam originality - this was the incorrect invention of historians <span class=\"non-italic\">400</span> years later.\\n<br/>\\n</span>\\n  </div>\\n</div>\\n\\n\\n  \\n\\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>References <span class=\"nonoscript\">(<a href=\"#\" id=\"references-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n  \\n<div class=\"row\" id=\"references-list\">\\n    <div class=\"col-md-12\">\\n      <ol name=\"references\">\\n        \\n        <li id=\"reference-1\"><span class=\"markup\">A S Saidan, Biography in <em>Dictionary of Scientific Biography</em> <span class=\"non-italic\">(</span>New York <span class=\"non-italic\">1970</span>-<span class=\"non-italic\">1990)</span>.\\n<br/>\\nSee <a href=\"http://www.encyclopedia.com/doc/1G2-2830903548.html\">THIS LINK</a>.</span></li>\\n        \\n        <li id=\"reference-2\"><span class=\"markup\">J Samsó, <em>Las ciencias de los antiguos en al-Andalus</em> <span class=\"non-italic\">(</span>Madrid, <span class=\"non-italic\">1992)</span>.</span></li>\\n        \\n        <li id=\"reference-3\"><span class=\"markup\">F Woepcke, <em>Études sur les mathématiques arabo-islamiques</em> <span class=\"non-italic\">(2</span> Vols.<span class=\"non-italic\">)</span> <span class=\"non-italic\">(</span>Frankfurt am Main, <span class=\"non-italic\">1986)</span>.</span></li>\\n        \\n        <li id=\"reference-4\"><span class=\"markup\">G Arrighi, Review of some mathematical symbols <span class=\"non-italic\">(</span>Italian<span class=\"non-italic\">)</span>, <em>Physis-Riv. Internaz. Storia Sci.</em> <strong><span class=\"non-italic\">27</span></strong> <span class=\"non-italic\">(1</span>-<span class=\"non-italic\">2)</span> <span class=\"non-italic\">(1985)</span>, <span class=\"non-italic\">163</span>-<span class=\"non-italic\">179</span>.</span></li>\\n        \\n        <li id=\"reference-5\"><span class=\"markup\">C Brockelmann, <em>Geschichte der arabischen literatur</em> <strong>II</strong> <span class=\"non-italic\">(</span>Leiden, <span class=\"non-italic\">1949)</span>, <span class=\"non-italic\">343</span>-<span class=\"non-italic\">344</span>.</span></li>\\n        \\n        <li id=\"reference-6\"><span class=\"markup\">al-Kalasadi, The Encyclopaedia of Islam Vol IV <span class=\"non-italic\">(</span>Leiden, <span class=\"non-italic\">1978)</span>,</span></li>\\n        \\n        <li id=\"reference-7\"><span class=\"markup\">M Souissi, L\\'école mathématique maghrébine: quelques exemples de ses travaux et certaines de ses particularités, in <em>Histoire des mathématiques arabes, Algiers, <span class=\"non-italic\">1986</span></em> <span class=\"non-italic\">(</span>Algiers, <span class=\"non-italic\">1988)</span>, <span class=\"non-italic\">9</span>-<span class=\"non-italic\">23</span>.</span></li>\\n        \\n        <li id=\"reference-8\"><span class=\"markup\">M Zarruqi, Fractions in the Morroccan mathematical tradition between the <span class=\"non-italic\">12</span>th and <span class=\"non-italic\">15</span>th centuries A.D. as found in anonymous manuscripts <span class=\"non-italic\">(</span>Arabic<span class=\"non-italic\">)</span>, in <em>Deuxième Colloque Maghrebin sur l\\'Histoire des Mathématiques Arabes, Tunis, <span class=\"non-italic\">1988</span></em> <span class=\"non-italic\">(</span>Maghreb, Tunis, <span class=\"non-italic\">1990)</span>, A<span class=\"non-italic\">97</span>-A<span class=\"non-italic\">109</span>.</span></li>\\n        \\n      </ol>\\n    </div>\\n  </div>\\n    \\n  \\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>Additional Resources <span class=\"nonoscript\">(<a href=\"#\" id=\"additional-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n\\n  \\n<div class=\"row\" id=\"additional-list\">\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other pages about Al-Qalasadi:</p>\\n      <ol name=\"additional\">\\n        \\n        <li><a href=\"../../Timelines/timelineb.html\"><span class=\"markup\">See Al-Qalasadi on a timeline</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other websites about Al-Qalasadi:</p>\\n      <ol name=\"otherweb\">\\n        \\n        \\n        <li><a href=\"http://www.encyclopedia.com/doc/1G2-2830903548.html\" target=\"_blank\"><span class=\"markup\">Dictionary of Scientific Biography</span></a></li>\\n        \\n        \\n        <li><a href=\"http://www.ams.org/mathscinet/MRAuthorID/717540\" target=\"_blank\"><span class=\"markup\">MathSciNet Author profile</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n  </div>\\n    \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Cross-references\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"xrefs-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"xrefs-list\">\\n  <div class=\"col-md-12\">\\n    <ol name=\"xrefs\">\\n      \\n      <li><a href=\"../../HistTopics/Arabic_mathematics/\">History Topics: <span class=\"markup\">Arabic mathematics : forgotten brilliance?</span></a></li>\\n      \\n      <li><a href=\"../../Miller/mathsym/operation/\">Other: Earliest Uses of Symbols of Operation</a></li>\\n      \\n    </ol>\\n  </div>\\n</div>\\n \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    Written by <span class=\"markup\">J J O\\'Connor and E F Robertson</span>  \\n    <br/>\\n    Last Update November 1999\\n  </div>\\n</div>\\n\\n\\n\\n<div class=\"row\">\\n          <div class=\"cr-footer col-md-4\">\\n            DJF/JOC/EFR<br/>\\n            <a href=\"../../Miscellaneous/copyright/\">Copyright information</a><br/>\\n            <a href=\"../../Miscellaneous/accessibility/\">Accessibility statement</a>\\n          </div>\\n          <div class=\"links-footer col-md-6\">\\n            <a href=\"https://www.st-andrews.ac.uk/mathematics-statistics/\" target=\"_blank\">School of Mathematics and Statistics</a>\\n            <br/>\\n            <a href=\"http://www.st-andrews.ac.uk/\" target=\"_blank\">University of St Andrews, Scotland</a>\\n          </div>\\n          <div class=\"col-md-2\">\\n            <img src=\"../../static/img/st-andrews-logo.png?h=e46f195e\" alt=\"University of St. Andrews logo\"/>\\n          </div>\\n        </div>\\n        \\n<div class=\"row\">\\n          <div class=\"col-md-12\">\\n            If you have comments, or spot errors, we are always pleased to\\n            <a href=\"../../Miscellaneous/contact_us/\">hear from you</a>.\\n          </div>\\n        </div>\\n      </root>'), (283, '1677-1750', 'Johann Gabriel Doppelmayr', 'https://mathshistory.st-andrews.ac.uk/Biographies/Doppelmayr/', '<root><div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h1>Johann Gabriel Doppelmayr</h1>\\n  </div>\\n</div>\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-8\">\\n    <h3>Quick Info</h3>\\n\\n    \\n    <dt>Born</dt>\\n    <dd>\\n      27 September 1677 <br/>  <a href=\"../../Map/#Nuremberg\" target=\"_blank\"> Nuremberg, Germany </a> \\n    </dd>\\n     \\n    <dt>Died</dt>\\n    <dd>\\n      1 December 1750 <br/> Nuremberg, Germany\\n    </dd>\\n     \\n    <hr/>\\n    <dt>Summary</dt>\\n    <dd><span class=\"markup\"><strong>Johann Doppelmayr</strong> was a German mathematician who wrote on astronomy, spherical trigonometry, sundials and mathematical instruments.</span></dd>\\n    \\n  </div>\\n\\n   \\n  <div class=\"col-md-4 biography-thumbnail-container\">\\n    \\n    <a href=\"pictdisplay/\" target=\"_blank\">\\n      \\n      <img class=\"biography-thumbnail\" src=\"thumbnail.jpg\" alt=\"Thumbnail of Johann Gabriel Doppelmayr\"/>\\n      \\n      <br/>\\n      View one larger picture</a>\\n    \\n  </div>\\n  \\n</div>\\n\\n\\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>Biography</h3>\\n    <span class=\"markup\"><strong>Johann Gabriel Doppelmayr</strong>\\'s name is sometimes given as Doppelmaier or Doppelmair. His father, Johann Siegmund Doppelmayr, was a merchant but had deep interests in science. Writing about his father later in his life, Doppelmayr explained how his hobby was carrying out experiments in physics. He was the first to introduce a vacuum air pump into Nuremberg.\\n<br/>\\n\\n<br/>\\nJohann Doppelmayr entered the Aegidien <a class=\"gllink\" data-popup=\"../../Glossary/gymnasium/\" href=\"../../Glossary/#gymnasium\">Gymnasium</a> in Nuremberg in <span class=\"non-italic\">1689</span>. The Aegidien Gymnasium had been founded in the <span class=\"non-italic\">16</span><span class=\"superscript\">th</span>  century by the Swiss Protestant reformer Ulrich Zwingli. Doppelmayr was to return to this Gymnasium as a professor later in his career. From Nuremberg, Doppelmayr went to the University of Altdorf in <span class=\"non-italic\">1696</span> where he studied law, mathematics and natural philosophy. In <span class=\"non-italic\">1698</span> he completed a dissertation on the sun, then went on to attend lectures on mathematics and natural philosophy by Johann Christoph Sturm who was considered the leading experimental physicist in Germany at the time. Doppelmayr submitted his dissertation <em>De visionis sensu nobilissimo, ex camerae obscurae tenebris illustrato</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;On the most noble visions illustrated with the \\'camera obscura\\'&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">On the most noble visions illustrated with the \\'camera obscura\\'</span><span class=\"non-italic\">)</span></noscript></span>  in <span class=\"non-italic\">1699</span>. For a short time in <span class=\"non-italic\">1700</span> he studied physics and mathematics at the University of Halle where he also learnt French and Italian, then spent two years travelling in Germany, Holland and England. Until his visit to the University of Halle he had kept his options open of making a career in law or in mathematics and physics, but in <span class=\"non-italic\">1700</span> he made the definite decision to give up his study of law and to concentrate on mathematics and science.\\n<br/>\\n\\n<br/>\\nFirst Doppelmayr went to Berlin in September <span class=\"non-italic\">1700</span> from where he moved on to Franeker and Amsterdam in Holland before arriving in Utrecht. There he spent two months, again studying mathematics and physics, but here also improving his language skills by studying English. From Utrecht, he moved on to Leiden in April <span class=\"non-italic\">1701</span> where he was welcomed by Lothar Zumbach von Koesfeld, the professor of astronomy, who invited him to live in his home during his visit. Doppelmayr made good use of his time, as he did in every place he visited, learning instrument making skills in Leiden such as how to make telescopes and how to grind lenses. Having quickly mastered these new skills, he moved on again, going this time to Rotterdam before crossing to England in May <span class=\"non-italic\">1701</span> where he visited Oxford and London. Before the end of <span class=\"non-italic\">1701</span> he was back in Holland, returning to Leiden for a five month visit to attend astronomy lectures by Lothar Zumbach von Koesfeld. Leaving Leiden he returned to Nuremberg but took a long route which involved visits to Utrecht, Deventer, Osnabrück, Hannover, Kassel, Marburg, Giessen, Wetzlar and Frankfurt. By August <span class=\"non-italic\">1702</span> he was back in Nuremberg having learnt  awide range of mathematical and scientific skills which at that time were not available in Germany.\\n<br/>\\n\\n<br/>\\nHe clearly made a good impression on people during these visits since he was later elected to membership of a number of scientific societies including the <a class=\"aclink\" href=\"../../Societies/Berlin/\" rel=\"noreferrer\" target=\"_blank\">Berlin Academy</a>, the <a class=\"aclink\" href=\"../../Societies/German_Academy/\" rel=\"noreferrer\" target=\"_blank\">German Academy of Scientists Leopoldina</a> <span class=\"non-italic\">(</span>the Kaiserlich Leopoldinische Akademie der Naturforscher<span class=\"non-italic\">)</span> in Halle <span class=\"non-italic\">(1715)</span>, the <a class=\"aclink\" href=\"../../Societies/RS/\" rel=\"noreferrer\" target=\"_blank\">Royal Society</a> <span class=\"non-italic\">(6</span> December <span class=\"non-italic\">1733)</span>, and the <a class=\"aclink\" href=\"../../Societies/Russian/\" rel=\"noreferrer\" target=\"_blank\">St Petersburg Academy</a> <span class=\"non-italic\">(1740)</span>.\\n<br/>\\n\\n<br/>\\nDoppelmayr was appointed professor of mathematics at the Aegidien Gymnasium in Nuremberg in <span class=\"non-italic\">1704</span> and he remained there for the rest of his life. In February <span class=\"non-italic\">1716</span> he married Susanna Maria Kellner who was eighteen years old at the time <span class=\"non-italic\">(</span>Doppelmayr was <span class=\"non-italic\">38</span> years old by this time<span class=\"non-italic\">)</span>. They had four children, although only one survived beyond infancy, and Susanna died at the age of <span class=\"non-italic\">31</span> in <span class=\"non-italic\">1728</span>. Although Doppelmayr was to remain at the Aegidien Gymnasium in Nuremberg for the rest of his life, this was very much his choice since he had opportunities to move to much more prestigious positions. In <span class=\"non-italic\">1723</span> he was honoured with the offer of the chair of mechanics at the Academy of St Petersburg. He turned down this offer, however, suggesting instead that <a class=\"mlink\" data-popup=\"../Bernoulli_Nicolaus(II)/popup/\" href=\"../Bernoulli_Nicolaus(II)/\">Nicolaus <span class=\"non-italic\">(</span>II<span class=\"non-italic\">)</span> Bernoulli</a> be offered the post. Indeed <a class=\"mlink\" data-popup=\"../Bernoulli_Nicolaus(II)/popup/\" href=\"../Bernoulli_Nicolaus(II)/\">Bernoulli</a> did accept the chair at the Academy of St Petersburg.\\n<br/>\\n\\n<br/>\\nDoppelmayr wrote on astronomy, spherical trigonometry, sundials and mathematical instruments. He used his language skills to translate a number of texts on astronomy, geography and scientific instrument into German or Latin. For example he translated the English text <em>Astronomia Carolina: A New Theorie of the Coelestial Motions</em>  by Thomas Streete into Latin, publishing his translation of the <span class=\"non-italic\">1665</span> original in <span class=\"non-italic\">1705</span>. The French mathematics text <em>Traité de la construction et des principaux usages des instrumens de mathématiques</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Treatise on the making and the main uses of mathematical instruments&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Treatise on the making and the main uses of mathematical instruments</span><span class=\"non-italic\">)</span></noscript></span> by Nicolas Bion, published in Paris in <span class=\"non-italic\">1709</span>, was translated in German by Doppelmayr in <span class=\"non-italic\">1712</span> as <em>Neu-eröffnete mathematische Werck-Schule Nicolai Bion</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;New mathematical works of Nicolai Bion.&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">New mathematical works of Nicolai Bion.</span><span class=\"non-italic\">)</span></noscript></span>. As a final example, Doppelmayr translated the English text <em>Discovery of a new World in the Moon</em>  by <a class=\"mlink\" data-popup=\"../Wilkins/popup/\" href=\"../Wilkins/\">John Wilkins</a> <span class=\"non-italic\">(</span>which had been published in London in <span class=\"non-italic\">1638</span> and was a vigorous defence of the ideas of <a class=\"mlink\" data-popup=\"../Copernicus/popup/\" href=\"../Copernicus/\">Copernicus</a><span class=\"non-italic\">)</span> into German publishing it as <em>Johannes Wilkins, des fürtrefflichen Englischen Bischoffs zu Chester Vertheidigter Copernicus, oder Curioser und gründlicher Beweiss der Copernicanischen Grundsätze</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;A German translation of the Discovery of a new Worlde in the Moone by John Wilkins.&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">A German translation of the Discovery of a new Worlde in the Moone by John Wilkins.</span><span class=\"non-italic\">)</span></noscript></span> in <span class=\"non-italic\">1713</span>.\\n<br/>\\n\\n<br/>\\nDoppelmayr also wrote a book of tremendous value giving biographical details of <span class=\"non-italic\">360</span> mathematicians and instrument makers of Nuremberg from the <span class=\"non-italic\">15</span><span class=\"superscript\">th</span>  to the <span class=\"non-italic\">18</span><span class=\"superscript\">th</span>  century. This had the lengthy title <em>Historische Nachricht von den Nürnbergischen Mathematicis und Künstlern, welche fast von dreyen Seculis her durch ihre Schriften und Kunst-Bemühungen die Mathematic und mehrere Künste in Nürnberg vor andern trefflich befördert und sich um solche sehr wohl verdient gemacht zu einem guten Exempel, und zur weitern rühmlichen Nachahmung</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Past news of the Nuremberg mathematicians and artists ...&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Past news of the Nuremberg mathematicians and artists ...</span><span class=\"non-italic\">)</span></noscript></span> and was published in <span class=\"non-italic\">1730</span>.\\n<br/>\\n\\n<br/>\\nPerhaps the most famous of all of the works by Doppelmayr is the <em>Atlas Coelestis</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Atlas of the heavens&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Atlas of the heavens</span><span class=\"non-italic\">)</span></noscript></span> which he published in Nuremberg in <span class=\"non-italic\">1742</span>. The full Latin title is closer to a summary of the text than to a title so let us quote it in full: <em>Atlas Coelestis in quo Mundus Spectabilis et in eodem Stellarum omnium Phoenomena notabilia, circa ipsarum Lumen, Figuram, Faciem, Motum, Eclipses, Occultationes, Transitus, Magnitudines, Distantias, aliaque secundum Nic. Copernici et ex parte Tychonis de Brahe Hipothesin. Nostri intuitu, specialiter, respectu vero ad apparentias planetarum indagatu possibiles e planetis primariis, et e luna habito, generaliter celeberrimorum astronomorum observationibus graphice descripta exhibentur, cum tabulis majoribus XXX</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Of all things  visible in the world of the stars in the Atlas Coelestis, and their notable phenomena, with regard to the shape of their light, the face of a motion, eclipses, occultations, transits, magnitudes, distances, and other, according to Nic. Copernicus and Tycho Brahe. Our view, in particular, with respect to possible appearances of the planets researched from the various planets, and the moon, having been described in general terms by the most celebrated astronomers. Observations are graphically presented, with &lt;span class=&quot;non-italic&quot;&gt;30&lt;/span&gt; maps of the stars.&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Of all things  visible in the world of the stars in the Atlas Coelestis, and their notable phenomena, with regard to the shape of their light, the face of a motion, eclipses, occultations, transits, magnitudes, distances, and other, according to Nic. Copernicus and Tycho Brahe. Our view, in particular, with respect to possible appearances of the planets researched from the various planets, and the moon, having been described in general terms by the most celebrated astronomers. Observations are graphically presented, with <span class=\"non-italic\"><span class=\"non-italic\">30</span></span> maps of the stars.</span><span class=\"non-italic\">)</span></noscript></span> <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;C A Wilson, Biography in &lt;em&gt;Dictionary of Scientific Biography&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;New York &lt;span class=&quot;non-italic&quot;&gt;1970&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;1990)&lt;/span&gt;. See &lt;a href=&quot;http://www.encyclopedia.com/doc/1G2-2830901213.html&quot;&gt;THIS LINK&lt;/a&gt;.&lt;/span&gt;\" href=\"#reference-1\"><span class=\"non-italic\">1</span></a><span class=\"non-italic\">]</span></span>:-\\n<blockquote>Besides star charts and a selenographic map, the Atlas includes diagrams illustrating the planetary systems of <a class=\"mlink\" data-popup=\"../Copernicus/popup/\" href=\"../Copernicus/\">Copernicus</a>, <a class=\"mlink\" data-popup=\"../Brahe/popup/\" href=\"../Brahe/\">Tycho Brahe</a>, and Riccioli; the elliptic theories of <a class=\"mlink\" data-popup=\"../Kepler/popup/\" href=\"../Kepler/\">Kepler</a>, <a class=\"mlink\" data-popup=\"../Boulliau/popup/\" href=\"../Boulliau/\">Boulliau</a>, Seth Ward, and <a class=\"mlink\" data-popup=\"../Mercator_Nicolaus/popup/\" href=\"../Mercator_Nicolaus/\">Nicolaus Mercator</a>; the lunar theories of <a class=\"mlink\" data-popup=\"../Brahe/popup/\" href=\"../Brahe/\">Tycho Brahe</a>, <a class=\"mlink\" data-popup=\"../Horrocks/popup/\" href=\"../Horrocks/\">Horrocks</a>, and <a class=\"mlink\" data-popup=\"../Newton/popup/\" href=\"../Newton/\">Newton</a>; and <a class=\"mlink\" data-popup=\"../Halley/popup/\" href=\"../Halley/\">Halley</a>\\'s cometary theory.</blockquote>\\nWe mentioned above Doppelmayr\\'s translation of a mathematics text. He also wrote several mathematics texts himself, including one on spherical trigonometry and <em>Summa geometricae practicae</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Summary of practical geometry&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Summary of practical geometry</span><span class=\"non-italic\">)</span></noscript></span>. He was an enthusiastic experimental physicist and he published <em>Physica experimentis illustrata</em> <span><a class=\"translation nonoscript non-italic\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;Illustrated physics experiments&lt;/span&gt;\">Ⓣ</a><noscript><span class=\"non-italic\">(</span><span class=\"markup\">Illustrated physics experiments</span><span class=\"non-italic\">)</span></noscript></span> in <span class=\"non-italic\">1731</span> which describes <span class=\"non-italic\">700</span> experiments which Doppelmayr had carried out himself.\\n<br/>\\n\\n<br/>\\nCurtis Wilson <span><span class=\"non-italic\">[</span><a class=\"reference\" data-popup=\"&lt;span class=&quot;markup&quot;&gt;C A Wilson, Biography in &lt;em&gt;Dictionary of Scientific Biography&lt;/em&gt; &lt;span class=&quot;non-italic&quot;&gt;(&lt;/span&gt;New York &lt;span class=&quot;non-italic&quot;&gt;1970&lt;/span&gt;-&lt;span class=&quot;non-italic&quot;&gt;1990)&lt;/span&gt;. See &lt;a href=&quot;http://www.encyclopedia.com/doc/1G2-2830901213.html&quot;&gt;THIS LINK&lt;/a&gt;.&lt;/span&gt;\" href=\"#reference-1\"><span class=\"non-italic\">1</span></a><span class=\"non-italic\">]</span></span> writes:-\\n<blockquote>Doppelmayr\\'s electrical investigations continued until his death, which followed a severe shock suffered while experimenting with one of the newly invented condensers.</blockquote>\\nIn this description Wilson follows a number of reports written shortly after his death which made these claims. However this cause of death is not universally accepted by historians and more recent research has led to several making the claim that Doppelmayr\\'s electrical experiments were completed several years before his death so, these sources claim, could not have been the cause of his death.</span>\\n  </div>\\n</div>\\n\\n\\n  \\n\\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>References <span class=\"nonoscript\">(<a href=\"#\" id=\"references-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n  \\n<div class=\"row\" id=\"references-list\">\\n    <div class=\"col-md-12\">\\n      <ol name=\"references\">\\n        \\n        <li id=\"reference-1\"><span class=\"markup\">C A Wilson, Biography in <em>Dictionary of Scientific Biography</em> <span class=\"non-italic\">(</span>New York <span class=\"non-italic\">1970</span>-<span class=\"non-italic\">1990)</span>. See <a href=\"http://www.encyclopedia.com/doc/1G2-2830901213.html\">THIS LINK</a>.</span></li>\\n        \\n        <li id=\"reference-2\"><span class=\"markup\">M Cantor, Johann Gabriel Doppelmayr, <em>Allgemeine deutsche Biographie</em> <strong>V</strong> <span class=\"non-italic\">(</span>Duncker &amp; Humblot, Leipzig, <span class=\"non-italic\">1877)</span>, <span class=\"non-italic\">344</span>-<span class=\"non-italic\">345</span>.</span></li>\\n        \\n        <li id=\"reference-3\"><span class=\"markup\">H Gaab, Johann Gabriel Doppelmayr <span class=\"non-italic\">(1677</span>-<span class=\"non-italic\">1750)</span>, in W R Dick and J Hamel <span class=\"non-italic\">(</span>eds.<span class=\"non-italic\">)</span>, <em>Beiträge zur Astronomiegeschichte</em> <strong><span class=\"non-italic\">4</span></strong> <span class=\"non-italic\">(</span>Harri Deutsch, Frankfurt am Main, <span class=\"non-italic\">2001)</span>, <span class=\"non-italic\">46</span>-<span class=\"non-italic\">99</span>.</span></li>\\n        \\n        <li id=\"reference-4\"><span class=\"markup\">K Pilz, <em><span class=\"non-italic\">600</span> Jahre Astronomie in Nürnberg</em> <span class=\"non-italic\">(</span>Verlag Hans Carl, Nuremberg, <span class=\"non-italic\">1977)</span>, <span class=\"non-italic\">312</span>-<span class=\"non-italic\">318</span>.</span></li>\\n        \\n        <li id=\"reference-5\"><span class=\"markup\">A Wissner, Johann Gabriel Doppelmayr, in <em>Neue Deutsche Biographie</em> <strong><span class=\"non-italic\">4</span></strong> <span class=\"non-italic\">(</span>Duncker &amp; Humblot, Berlin, <span class=\"non-italic\">1971)</span>, <span class=\"non-italic\">76</span>.</span></li>\\n        \\n      </ol>\\n    </div>\\n  </div>\\n    \\n  \\n<div class=\"row\">\\n    <div class=\"col-md-12\">\\n      <h3>Additional Resources <span class=\"nonoscript\">(<a href=\"#\" id=\"additional-toggle\">show</a>)</span></h3>\\n    </div>\\n  </div>\\n\\n  \\n<div class=\"row\" id=\"additional-list\">\\n    \\n\\n    \\n    <div class=\"col-md-6\">\\n      <p>Other websites about Johann Gabriel Doppelmayr:</p>\\n      <ol name=\"otherweb\">\\n        \\n        \\n        <li><a href=\"http://www.encyclopedia.com/doc/1G2-2830901213.html\" target=\"_blank\"><span class=\"markup\">Dictionary of Scientific Biography</span></a></li>\\n        \\n        \\n        <li><a href=\"http://galileo.rice.edu/Catalog/NewFiles/doplmayr.html\" target=\"_blank\"><span class=\"markup\">The Galileo Project</span></a></li>\\n        \\n        \\n        <li><a href=\"http://www.genealogy.math.ndsu.nodak.edu/id.php?id=127727\" target=\"_blank\"><span class=\"markup\">Mathematical Genealogy Project</span></a></li>\\n        \\n      </ol>\\n    </div>\\n    \\n  </div>\\n   \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    <h3>\\n      Honours\\n      <span class=\"nonoscript\">(<a href=\"#\" id=\"honours-toggle\">show</a>)</span>\\n    </h3>\\n  </div>\\n</div>\\n\\n<div class=\"row\" id=\"honours-list\">\\n  <div class=\"col-md-12\">\\n    <p>Honours awarded to Johann Gabriel Doppelmayr</p>\\n    <ol name=\"honours\">\\n       <li><a href=\"../../Honours/FRS/\"><span class=\"markup\">Fellow of the Royal Society <span class=\"non-italic\">1733</span></span></a></li>  <li><a href=\"../../Honours/LunarFeatures0/\"><span class=\"markup\">Lunar features <strong>Crater Doppelmayr</strong> and <strong>Rimae Doppelmayer</strong></span></a></li> \\n    </ol>\\n  </div>\\n</div>\\n  \\n\\n<div class=\"row\">\\n  <div class=\"col-md-12\">\\n    Written by <span class=\"markup\">J J O\\'Connor and E F Robertson</span>  \\n    <br/>\\n    Last Update August 2006\\n  </div>\\n</div>\\n\\n\\n\\n<div class=\"row\">\\n          <div class=\"cr-footer col-md-4\">\\n            DJF/JOC/EFR<br/>\\n            <a href=\"../../Miscellaneous/copyright/\">Copyright information</a><br/>\\n            <a href=\"../../Miscellaneous/accessibility/\">Accessibility statement</a>\\n          </div>\\n          <div class=\"links-footer col-md-6\">\\n            <a href=\"https://www.st-andrews.ac.uk/mathematics-statistics/\" target=\"_blank\">School of Mathematics and Statistics</a>\\n            <br/>\\n            <a href=\"http://www.st-andrews.ac.uk/\" target=\"_blank\">University of St Andrews, Scotland</a>\\n          </div>\\n          <div class=\"col-md-2\">\\n            <img src=\"../../static/img/st-andrews-logo.png?h=e46f195e\" alt=\"University of St. Andrews logo\"/>\\n          </div>\\n        </div>\\n        \\n<div class=\"row\">\\n          <div class=\"col-md-12\">\\n            If you have comments, or spot errors, we are always pleased to\\n            <a href=\"../../Miscellaneous/contact_us/\">hear from you</a>.\\n          </div>\\n        </div>\\n      </root>')]\n"
     ]
    }
   ],
   "source": [
    "result = sql_explore(q)\n",
    "print(f'Lines count: {len(result[0])}, errors count: {len(result[1])}, \\nFirst lines: {result[0][:5]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Muliple cards per name ?\n",
    "## Result:\n",
    "# Lines count: 4, errors count: 0, \n",
    "# First lines: [('Gustav von Escherich', [894, 895]), ('John Wilson', [875, 396]), ('Lloyd Williams', [1537, 2536]), ('William Thomson', [700, 992])]\n",
    "# Deleted one line: https://mathshistory.st-andrews.ac.uk/Biographies/Esterich/ — see below\n",
    "\n",
    "q4 = \"\"\"\n",
    "select \"name\", array_agg(pk_mathshistory) \n",
    "from espace_intellectuel.astronomers.mathshistory m\n",
    "group by \"name\" \n",
    "having count(*) > 1;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "qu = \"\"\"with tw1 as (\n",
    "SELECT pk_mathshistory, name, substr(dates, 1, 4)::INTEGER birth_year,\n",
    "array_to_string(xpath('//div[./h3/text()=\"Biography\"]//a[contains(text(), \"THIS LINK\")]/@href[contains(., \"ocieties\")]', page_html), ',') as links\n",
    "FROM astronomers.mathshistory)\n",
    "select *\n",
    "from tw1\n",
    "where length(links) > 5;\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "with conn.cursor() as curs:\n",
    "    try:   \n",
    "        ### Décommenter pour nouvelle exécution\n",
    "        curs.execute(qu)\n",
    "        conn.commit()\n",
    "    except Exception as e:\n",
    "        print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = \"\"\"\n",
    "select * from astronomers.mathshistory m where length(page_html::text) = 0;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lines count: 0, errors count: 0, \n",
      "First lines: []\n"
     ]
    }
   ],
   "source": [
    "result = sql_explore(q)\n",
    "print(f'Lines count: {len(result[0])}, errors count: {len(result[1])}, \\nFirst lines: {result[0][:5]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = \"\"\"\n",
    "SELECT pk_mathshistory, name, substr(dates, 1, 4)::INTEGER birth_year,\n",
    "array_to_string(xpath('//dt[text()=\"Summary\"]/following-sibling::dd/descendant-or-self::*/text()', page_html), ' ') as summary\n",
    "FROM astronomers.mathshistory\n",
    "limit 10;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lines count: 10, errors count: 0, \n",
      "First lines: [(135, 'Johannes Kepler', 1571, 'Johannes Kepler  was a German mathematician and astronomer who discovered that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. He also did important work in optics and geometry.'), (21, 'Michael Scot', 1175, 'Michael Scot   ( or  Scotus )  helped in the transmission of Islamic mathematics from Spain to the rest of Europe.'), (22, 'Li Zhi', 1192, 'Li Zhi  was a Chinese mathematician who described methods for solving equations.'), (23, 'John Sacrobosco', 1195, 'John of Holywood  or  Johannes de Sacrobosco  was an English scholar who wrote an important text on astronomy and promoted Arabic methods of arithmetic and algebra.'), (24, 'Albertus', 1200, \"Albert   ( or  Albertus Magnus )  was a German Dominican who wrote a commentary on Euclid's  Elements . He was made a Saint in  1931  and, in  1941 , was made patron of natural scientists.\")]\n"
     ]
    }
   ],
   "source": [
    "result = sql_explore(q)\n",
    "print(f'Lines count: {len(result[0])}, errors count: {len(result[1])}, \\nFirst lines: {result[0][:5]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1 = \"\"\"\n",
    "UPDATE astronomers.mathshistory SET summary = array_to_string(xpath('//dt[text()=\"Summary\"]/following-sibling::dd/descendant-or-self::*/text()', page_html), ' ');\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "errors_list = []\n",
    "elem = []\n",
    "with conn.cursor() as curs:\n",
    "    try:   \n",
    "        ### Décommenter pour nouvelle exécution\n",
    "        curs.execute(q1)\n",
    "        ## conn.commit()\n",
    "    except Exception as e:\n",
    "        print(e)\n",
    "conn.commit()        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = \"\"\"\n",
    "select length(summary) l_summary, summary, name, dates, pk_mathshistory from astronomers.mathshistory ;\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lines count: 3010, errors count: 0, \n",
      "First lines: [(114, 'Michael Scot   ( or  Scotus )  helped in the transmission of Islamic mathematics from Spain to the rest of Europe.', 'Michael Scot', '1175-1235', 21), (164, 'John of Holywood  or  Johannes de Sacrobosco  was an English scholar who wrote an important text on astronomy and promoted Arabic methods of arithmetic and algebra.', 'John Sacrobosco', '1195-1256', 23), (188, \"Albert   ( or  Albertus Magnus )  was a German Dominican who wrote a commentary on Euclid's  Elements . He was made a Saint in  1931  and, in  1941 , was made patron of natural scientists.\", 'Albertus', '1200-1280', 24), (193, 'Nasir al-Tusi  was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.', 'Nasir al-Din al-Tusi', '1201-1274', 25), (141, 'Qin Jiushao  was a Chinese mathematician who wrote an important study  Shushu Jiuzang  on equations, including the Chinese Remainder Theorem.', 'Qin Jiushao', '1202-1261', 26)]\n"
     ]
    }
   ],
   "source": [
    "result = sql_explore(q)\n",
    "print(f'Lines count: {len(result[0])}, errors count: {len(result[1])}, \\nFirst lines: {result[0][:5]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(237,\n",
       "  \"John Napier  was a Scottish scholar who is best known for his invention of logarithms, but other mathematical contributions include a mnemonic for formulas used in solving spherical triangles and two formulas known as Napier's analogies.\",\n",
       "  'John Napier',\n",
       "  '1550-1617',\n",
       "  116),\n",
       " (107,\n",
       "  \"Michael Mästlin  was a German astronomer who was Kepler's teacher and who publicised the Copernican system.\",\n",
       "  'Michael Mästlin',\n",
       "  '1550-1631',\n",
       "  117)]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result[0][100:102]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploration of summaries' sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(result[0])\n",
    "df.columns = ['txt_len','summary', 'name', 'dates', 'pk']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>txt_len</th>\n",
       "      <th>summary</th>\n",
       "      <th>name</th>\n",
       "      <th>dates</th>\n",
       "      <th>pk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>114</td>\n",
       "      <td>Michael Scot   ( or  Scotus )  helped in the t...</td>\n",
       "      <td>Michael Scot</td>\n",
       "      <td>1175-1235</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>164</td>\n",
       "      <td>John of Holywood  or  Johannes de Sacrobosco  ...</td>\n",
       "      <td>John Sacrobosco</td>\n",
       "      <td>1195-1256</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>188</td>\n",
       "      <td>Albert   ( or  Albertus Magnus )  was a German...</td>\n",
       "      <td>Albertus</td>\n",
       "      <td>1200-1280</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>193</td>\n",
       "      <td>Nasir al-Tusi  was an Islamic astronomer and m...</td>\n",
       "      <td>Nasir al-Din al-Tusi</td>\n",
       "      <td>1201-1274</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>141</td>\n",
       "      <td>Qin Jiushao  was a Chinese mathematician who w...</td>\n",
       "      <td>Qin Jiushao</td>\n",
       "      <td>1202-1261</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   txt_len                                            summary  \\\n",
       "0      114  Michael Scot   ( or  Scotus )  helped in the t...   \n",
       "1      164  John of Holywood  or  Johannes de Sacrobosco  ...   \n",
       "2      188  Albert   ( or  Albertus Magnus )  was a German...   \n",
       "3      193  Nasir al-Tusi  was an Islamic astronomer and m...   \n",
       "4      141  Qin Jiushao  was a Chinese mathematician who w...   \n",
       "\n",
       "                   name      dates  pk  \n",
       "0          Michael Scot  1175-1235  21  \n",
       "1       John Sacrobosco  1195-1256  23  \n",
       "2              Albertus  1200-1280  24  \n",
       "3  Nasir al-Din al-Tusi  1201-1274  25  \n",
       "4           Qin Jiushao  1202-1261  26  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    3010.000000\n",
       "mean      137.818937\n",
       "std        58.516013\n",
       "min         0.000000\n",
       "25%        99.000000\n",
       "50%       123.000000\n",
       "75%       160.000000\n",
       "max       470.000000\n",
       "Name: txt_len, dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tl = df['txt_len']\n",
    "tl.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 470.0)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1400x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Violinplot : rend visible la différente densité de la distribution\n",
    "#  https://mode.com/blog/violin-plot-examples/\n",
    "#  https://seaborn.pydata.org/generated/seaborn.violinplot.html#seaborn.violinplot\n",
    "\n",
    "sns.set_theme(style=\"whitegrid\")\n",
    "\n",
    "sns.set(rc={\"figure.figsize\":(14, 7)})\n",
    "\n",
    "a = tl\n",
    "lim_left=min(a)\n",
    "lim_right=max(a)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax = sns.violinplot(x=a)\n",
    "\n",
    "### Noter que au delà des limites les valeurs sont coupées car postulées\n",
    "ax.set_xlim(left=lim_left, right=lim_right)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    const data = [[438, 37, \"William Morgan  was an early actuary.\", \"William Morgan\", \"1750-1833\", 419], [2398, 46, \"Bill Boone  worked on word problems in Groups.\", \"Bill Boone\", \"1920-1983\", 2387], [730, 47, \"Zacharias Dase  was a German mental calculator.\", \"Zacharias Dase\", \"1824-1861\", 701], [1338, 47, \"Ernst Steinitz  worked on the theory of fields.\", \"Ernst Steinitz\", \"1871-1928\", 1232], [1265, 51, \"Ernest Brown  worked on lunar and planetary motion.\", \"Ernest Brown\", \"1866-1938\", 1155], [2160, 52, \"Doris Hellman  was an American historian of Science.\", \"Doris Hellman\", \"1910-1973\", 2117], [572, 53, \"Jules Bienaym\\u00e9  worked on statistics and probability.\", \"Jules Bienaym\\u00e9\", \"1796-1878\", 552], [349, 53, \"Kurt Hirsch  worked in various areas of Group Theory.\", \"Kurt Hirsch\", \"1906-1986\", 2002], [757, 53, \"Moritz Cantor  was a German historian of mathematics.\", \"Moritz Cantor\", \"1829-1920\", 726], [604, 54, \"J\\u00e1nos Bolyai  was a pioneer of non-Euclidean geometry.\", \"J\\u00e1nos Bolyai\", \"1802-1860\", 579], [658, 54, \"Fernando Pio Rosellini  was an Italian educationalist.\", \"Fernando Pio Rosellini\", \"1814-1872\", 632], [712, 54, \"Rudolf Clausius  did important work in thermodynamics.\", \"Rudolf Clausius\", \"1822-1888\", 685], [505, 54, \"Joz\\u00e9f Wronski  wrote on the philosophy of mathematics.\", \"Joz\\u00e9f Ho\\u00ebn\\u00e9 Wronski\", \"1778-1853\", 485], [766, 55, \"Georg Sidler  was a Swiss mathematician and astronomer.\", \"Georg Sidler\", \"1831-1907\", 735], [855, 55, \"Robert Ball  was an Irish mathematician and astronomer.\", \"Robert Ball\", \"1840-1913\", 806], [1118, 55, \"Ernst Fiedler  was a German born Swiss  school teacher.\", \"Ernst Fiedler\", \"1861-1954\", 1047], [1937, 56, \"Howard Aiken  was a pioneer designer of early computers.\", \"Howard Aiken\", \"1900-1973\", 1790], [1880, 57, \"John Wishart  made important contributions to Statistics.\", \"John Wishart\", \"1898-1956\", 1746], [824, 57, \"Theodor Reye  worked in Geometry and Projective Geometry.\", \"Theodor Reye\", \"1838-1919\", 784], [2159, 58, \"Dan Pedoe  was an English-born mathematician and geometer.\", \"Daniel Pedoe\", \"1910-1998\", 2116], [1249, 58, \"Clarence Lewis  was an American philosopher and  logician.\", \"Clarence Lewis\", \"1883-1964\", 1429], [912, 58, \"Victor B\\u00e4cklund  wasa Swedish physicist and mathematician.\", \"Victor B\\u00e4cklund\", \"1845-1922\", 856], [1328, 59, \"Helge von Koch  is best known for the fractal Koch curve.\\\\n \", \"Helge von Koch\", \"1870-1924\", 1222], [574, 60, \"Sadi Carnot  is best known for his theory of thermodynamics.\", \"Sadi Carnot\", \"1796-1832\", 554], [782, 60, \"Fran\\u00e7ois Folie   was a Belgian mathematician and astronomer.\", \"Fran\\u00e7ois Folie\", \"1833-1905\", 751], [557, 60, \"Michel Chasles  worked on algebraic and projective geometry.\", \"Michel Chasles\", \"1793-1880\", 536], [849, 60, \"Emory McClintock  was an American mathematician and actuary.\", \"Emory McClintock\", \"1840-1916\", 800], [632, 60, \"Johann Listing  wrote one of the earliest texts on Topology.\", \"Johann Benedict Listing\", \"1808-1882\", 607], [248, 61, \"Siguenza y Gongora  was a Mexican astronomer and philosopher.\", \"Siguenza y Gongora\", \"1645-1700\", 242], [1289, 61, \"Alessandro Padoa   was an Italian mathematician and logician.\", \"Alessandro Padoa\", \"1868-1937\", 1179], [575, 61, \"F\\u00e9lix Savary  worked on electromagnetism and electrodynamics.\", \"F\\u00e9lix Savary\", \"1797-1841\", 555], [1034, 61, \"Karl Rohn   was a German mathematician, who studied geometry.\", \"Karl Rohn\", \"1855-1920\", 972], [644, 62, \"Andrew Hart  was an Irish mathematician who wrote on geometry.\", \"Andrew Hart\", \"1811-1890\", 618], [2082, 62, \"Carl Benjamin Boyer  was an American historian of mathematics.\", \"Carl Boyer\", \"1906-1976\", 1980], [2080, 62, \"Viggo Brun  was a Norwegian mathematician and number theorist.\", \"Viggo Brun\", \"1885-1978\", 1487], [1650, 62, \"Georges Darmois   was a French mathematician and statistician.\", \"Georges Darmois\", \"1888-1960\", 1530], [2145, 62, \"Gheorghe Mihoc  was a Romanian mathematician and statistician.\", \"Gheorghe Mihoc\", \"1906-1981\", 1992], [1127, 62, \"Gheorghe Pic  was a Czech mathematician who worked in algebra.\", \"Gheorghe Pic\", \"1907-1984\", 2027], [2583, 62, \"Rex Tims  was an English mathematician and university teacher.\", \"Rex Tims\", \"1926-1971\", 2575], [2396, 62, \"Anne Cobb  was an English mathematician who worked in algebra.\", \"Anne Cobbe\", \"1920-1971\", 2385], [794, 63, \"Howard Van Amringe  was an American educator and mathematician.\", \"Howard Van Amringe\", \"1835-1915\", 763], [2326, 63, \"Beno Eckmann  was a Swiss mathematician who worked in topology.\", \"Beno Eckmann\", \"1917-2008\", 2307], [2083, 63, \"David Champernowne  was an English economist and mathematician.\", \"David Champernowne\", \"1912-2000\", 2176], [1462, 63, \"Jan A Schouten  worked on tensor analysis and its applications.\", \"Jan A Schouten\", \"1883-1971\", 1438], [882, 64, \"James Stuart  was a Scottish educational pioneer and politician.\", \"James Stuart\", \"1843-1913\", 832], [1879, 64, \"Helmut Hasse  did fundamental work in algebra and number theory.\", \"Helmut Hasse\", \"1898-1979\", 1745], [2207, 64, \"Zassenhaus  did important work on Group Theory and Lie algebras.\", \"Hans Zassenhaus\", \"1912-1991\", 2184], [844, 64, \"Joseph-\\u00c9mile Barbier  was a French astronomer and mathematician.\", \"Joseph-\\u00c9mile Barbier\", \"1839-1889\", 795], [858, 65, \"Rudolf Sturm   was a German mathematician who worked in geometry.\", \"Rudolf Sturm\", \"1841-1919\", 809], [806, 65, \"Josef Stefan  was an Austrian physicist, mathematician, and poet.\", \"Josef Stefan\", \"1835-1893\", 766], [857, 65, \"Hermann Laurent  was a Luxembourg mathematician and statistician.\", \"Hermann Laurent\", \"1841-1908\", 808], [1136, 65, \"Heawood  made important contributions to the four colour theorem.\", \"P J Heawood\", \"1861-1955\", 1058], [1532, 65, \"Severi 's most important contributions are to algebraic geometry.\", \"Francesco Severi\", \"1879-1961\", 1369], [1442, 65, \"Ludwig Prandtl  was a German engineer who worked on aerodynamics.\", \"Ludwig Prandtl\", \"1875-1953\", 1298], [442, 65, \"Edward Troughton  was an English maker of scientific instruments.\", \"Edward Troughton\", \"1753-1835\", 423], [821, 66, \"Frank Baldwin  was an American who invented a pinwheel calculator.\", \"Frank Baldwin\", \"1838-1925\", 781], [812, 66, \"Hugh MacColl  was a Scottish mathematician, logician and novelist.\", \"Hugh MacColl\", \"1837-1909\", 772], [1890, 66, \"Jim Wiegold  was a Welsh mathematician who worked in group theory.\", \"James Wiegold\", \"1934-2009\", 2754], [2026, 66, \"Kenjiro Shoda  was a Japanese mathematician who worked in algebra.\", \"Kenjiro Shoda\", \"1902-1977\", 1846], [2375, 67, \"Erwin Hiebert  was a Canadian historian and philosopher of science.\", \"Erwin Hiebert\", \"1919-2012\", 2364], [2721, 67, \"Sripati  was an Indian who wrote works on astronomy and arithmetic.\", \"Sripati\", \"1019-1066\", 4], [2304, 67, \"Sheila Power  was an Irish mathematician and theoretical physicist.\", \"Sheila Power Tinney\", \"1918-2010\", 2355], [1697, 67, \"Ralph Jeffery  was a Canadian mathematician who worked on analysis.\", \"Ralph Jeffery\", \"1889-1975\", 1569], [1579, 68, \"Heinrich Scholz   was a German logician, philosopher and theologian.\", \"Heinrich Scholz\", \"1884-1956\", 1457], [750, 68, \"Giuseppe Bruno  was an Italian mathematician who worked in geometry.\", \"Giuseppe Bruno\", \"1828-1893\", 719], [1012, 68, \"Christian Beyel  was a Swiss mathematician who taught at ETH Z\\u00fcrich.\", \"Christian Beyel\", \"1854-1941\", 954], [754, 68, \"Heinrich Schr\\u00f6ter  was a German mathematician, who studied geometry.\", \"Heinrich Schr\\u00f6ter\", \"1829-1892\", 723], [2084, 68, \"Errett Bishop  was an American mathematician who worked in analysis.\", \"Errett Bishop\", \"1928-1983\", 2618], [573, 68, \"Nikolai Brashman  was a Czech mathematician who worked on mechanics.\", \"Nikolai Dmetrievich Brashman\", \"1796-1866\", 553], [114, 68, \"Thomas Fincke  was a Danish doctor who wrote a textbook on geometry.\", \"Thomas Fincke\", \"1561-1656\", 130], [1586, 68, \"Lefschetz  was the main source of the algebraic aspects of topology.\", \"Solomon Lefschetz\", \"1884-1972\", 1462], [1951, 68, \"Wolfgang Pauli  won a Nobel prize for his work on quantum mechanics.\", \"Wolfgang Pauli\", \"1900-1958\", 1799], [2241, 68, \"Johannes de Groot  was a Dutch mathematician who worked in topology.\", \"Johannes de Groot\", \"1914-1972\", 2238], [1551, 69, \"Pierre Boutroux  was a French mathematician and historian of science.\", \"Pierre Boutroux\", \"1880-1922\", 1388], [1255, 69, \"Gordon Whyburn  was an American mathematician who worked on topology.\", \"Gordon Whyburn\", \"1904-1969\", 1914], [1016, 69, \"Hjalmar Mellin   was a Finnish mathematician and functional theorist.\", \"Hjalmar Mellin\", \"1854-1933\", 958], [1057, 69, \"Luigi Bianchi  made important contributions to differential geometry.\", \"Luigi Bianchi\", \"1856-1928\", 987], [1690, 69, \"Henry Forder  was a New Zealand mathematician who worked in geometry.\", \"Henry Forder\", \"1889-1981\", 1562], [1392, 69, \"Maxime B\\u00f4cher  worked on differential equations, series, and algebra.\", \"Maxime B\\u00f4cher\", \"1867-1918\", 1177], [808, 69, \"Stanley Jevons  was an English mathematician, economist and logician.\", \"Stanley Jevons\", \"1835-1882\", 768], [1029, 69, \"Christian Juel  was a Danish mathematician, specializing in geometry.\", \"Christian Juel\", \"1855-1935\", 967], [144, 70, \"Paul Tur\\u00e1n  was a Hungarian mathematician who worked in number theory.\", \"Paul Tur\\u00e1n\", \"1910-1976\", 2139], [2158, 70, \"Charles Pisot  was a French mathematician who worked in number theory.\", \"Charles Pisot\", \"1910-1984\", 2115], [2301, 70, \"Leonard Jimmie Savage  was an American mathematician and statistician.\", \"Leonard Jimmie Savage\", \"1917-1971\", 2321], [2508, 70, \"Thomas Flett  was an Eglish mathematician who worked in Real analysis.\", \"Thomas Flett\", \"1923-1976\", 2487], [1982, 70, \"Horst Sachs  was a German mathematician and an expert in graph theory.\", \"Horst Sachs\", \"1927-2016\", 2596], [1872, 70, \"B\\u00e9la Ker\\u00e9kj\\u00e1rt\\u00f3  was a Hungarian mathematician who worked in topology.\", \"B\\u00e9la Ker\\u00e9kj\\u00e1rt\\u00f3\", \"1898-1946\", 1737], [288, 70, \"Eustachio Manfredi  was an Italian mathematician, astronomer and poet.\", \"Eustachio Manfredi\", \"1674-1739\", 278], [986, 70, \"Julius Gysel  was a Swiss school-teacher with an interest in geometry.\", \"Julius Gysel\", \"1851-1935\", 926], [1083, 70, \"William Johnson  was an English mathematician, logician and economist.\", \"William Johnson\", \"1858-1931\", 1013], [1237, 70, \"Giuseppe Bagnera  was an Italian mathematician who worked in geometry.\", \"Giuseppe Bagnera\", \"1865-1927\", 1139], [1571, 70, \"D\\u00e9nes K\\u00f6nig  was a Hungarian mathematician who worked in graph theory.\", \"D\\u00e9nes K\\u00f6nig\", \"1884-1944\", 1449], [1063, 70, \"Adolf Kiefer  was a Swiss mathematician who worked mainly in geometry.\", \"Adolf Kiefer\", \"1857-1929\", 993], [2243, 71, \"Wassily Hoeffding  was a Finnish statistician and probability theorist.\", \"Wassily Hoeffding\", \"1914-1991\", 2255], [2213, 71, \"Martin Eichler  was a German matnematician who worked in number theory.\", \"Martin Eichler\", \"1912-1992\", 2190], [1368, 71, \"Georgii Pfeiffer  did important work on partial differential equations.\", \"Georgii Vasilovich Pfeiffer\", \"1872-1946\", 1251], [2581, 71, \"Peter Lax  is a Hungarian mathematician who works on scattering theory.\", \"Peter Lax\", \"1926-\", 2573], [2366, 71, \"Leon Mirsky  worked in Number Theory, Linear Algebra and Combinatorics.\", \"Leon Mirsky\", \"1918-1983\", 2349], [719, 71, \"Corrado Gini  was an Italian statistician, demographer and sociologist.\", \"Corrado Gini\", \"1884-1965\", 1447], [2809, 71, \"David Hayes  was an American mathematician who worked in number theory.\", \"David Hayes\", \"1937-2011\", 2803], [2161, 72, \"Ernests Fogels  was a Latvian mathematician who worked in number theory.\", \"Ernests Fogels\", \"1910-1985\", 2118], [1446, 72, \"Takagi  worked on class field theory, building on Heinrich Weber's work.\", \"Teiji Takagi\", \"1875-1960\", 1302], [1523, 72, \"Wilhelm Oseen  was a Swedish mathematician who worked in fluid dynamics.\", \"C Wilhelm Oseen\", \"1879-1944\", 1364], [2745, 72, \"Vivienne Malone-Mayes  was an American mathematician and educationalist.\", \"Vivienne Malone-Mayes\", \"1932-1995\", 2733], [2330, 72, \"Elizabeth Scott  was an American mathematician who worked in statistics.\", \"Elizabeth Scott\", \"1917-1988\", 2310], [1426, 72, \"Mih\\u00e1ly Bauer  was a Hungarian mathematician who worked in number theory.\", \"Mih\\u00e1ly Bauer\", \"1874-1945\", 1283], [2623, 72, \"L\\u00e1szl\\u00f3 Kov\\u00e1cs  was a Hungarian mathematician who worked in group theory.\", \"L\\u00e1szl\\u00f3 Kov\\u00e1cs\", \"1936-2013\", 2788], [1399, 72, \"Louis Karpinski  was an American mathematician and historian of science.\", \"Louis Karpinski\", \"1878-1956\", 1353], [2654, 73, \"Paulo Ribenboim  is a Brazilian mathematician who works in number theory.\", \"Paulo Ribenboim\", \"1928-\", 2638], [1427, 73, \"Ren\\u00e9 Baire  worked on the theory of functions and the concept of a limit.\", \"Ren\\u00e9 Baire\", \"1874-1932\", 1284], [1247, 73, \"Brian Kuttner  was an English mathematician who worked on Fourier Series.\", \"Brian Kuttner\", \"1908-1992\", 2052], [2453, 73, \"Ron Mitchell  was a Scottish applied mathematician and numerical analyst.\", \"Ronald Mitchell\", \"1921-2007\", 2436], [2454, 73, \"Shimshon Amitsur  was an Israeli mathematician who worked in ring theory.\", \"Shimshon Amitsur\", \"1921-1994\", 2437], [1145, 73, \"Adolf Kneser  was a German mathematician who wrote on integral equations.\", \"Adolf Kneser\", \"1862-1930\", 1066], [1569, 73, \"Charles Weatherburn  worked on vector analysis and differential geometry.\", \"Charles Weatherburn\", \"1884-1974\", 1446], [209, 73, \"Ren\\u00e9 de Sluze  is best known for the curves called the  Pearls of Sluze .\", \"Ren\\u00e9 de Sluze\", \"1622-1685\", 207], [2368, 73, \"Mario Fiorentini  is an Italian partisan, secret agent and mathematician.\", \"Mario Fiorentini\", \"1918-2022\", 2351], [119, 73, \"Christoph Scheiner  was a German Jesuit priest, physicist and astronomer.\", \"Christoph Scheiner\", \"1573-1650\", 136], [262, 73, \"Jean Le F\\u00e8vre  was a French astronomer who published astronomical tables.\", \"Jean Le F\\u00e8vre\", \"1652-1706\", 252], [2233, 73, \"Bob Dilworth  was an American mathematician who worked in lattice theory.\", \"Robert Dilworth\", \"1914-1993\", 2249], [848, 73, \"\\u00c9mile  Lemoine   was a French civil engineer, mathematician and geometer.\", \"\\u00c9mile Lemoine\", \"1840-1912\", 799], [543, 74, \"Al\\u00e9xis Petit  was a French mathematician who worked on the theory of heat.\", \"Alexis Petit\", \"1791-1820\", 522], [1895, 74, \"Helge Tverberg  was a Norwegian mathematician who worked in combinatorics.\", \"Helge Tverberg\", \"1935-2020\", 2766], [2025, 74, \"Kazimierz Zarankiewicz  was a Polish mathematician who worked in topology.\", \"Kazimierz Zarankiewicz\", \"1902-1959\", 1845], [2260, 74, \"Andr\\u00e1s Rapcs\\u00e1k  was a Hungarian mathematician who specialised in geometry.\", \"Andr\\u00e1s Rapcs\\u00e1k\", \"1914-1993\", 2226], [1425, 74, \"Dickson  is known for his contributions to number theory and group theory.\", \"Leonard Dickson\", \"1874-1954\", 1282], [1528, 74, \"Nikolai Chudakov  was a Russian mathematician who worked in number theory.\", \"Nikolai Grigor'evich Chudakov\", \"1904-1986\", 1927], [56, 74, \"Thomas Wren  was an English mathematician whose main work was in geometry.\", \"Thomas Lancaster Wren\", \"1889-1972\", 1573], [2901, 74, \"Dusa McDuff  is an English mathematician who works on symplectic geometry.\", \"Dusa McDuff\", \"1945-\", 2889], [388, 74, \"John Hellins  was an English mathematician, astronomer and country parson.\", \"John Hellins\", \"1749-1827\", 412], [2234, 75, \"Rufus Isaacs  was an American mathematician who specialised in game theory.\", \"Rufus Isaacs\", \"1914-1981\", 2250], [261, 75, \"Alexander Dinghas  was a Greek mathematician who worked in function theory.\", \"Alexander Dinghas\", \"1908-1974\", 2048], [1547, 75, \"Michele Cipolla   was an Italian mathematician who worked in number theory.\", \"Michele Cipolla\", \"1880-1947\", 1384], [286, 75, \"Guido Grandi  was a Camaldolese monk who worked on geometry and hydraulics.\", \"Guido Grandi\", \"1671-1742\", 276], [2079, 75, \"Ebenezer Cunningham  was an English mathematician who worked in relativity.\", \"Ebenezer Cunningham\", \"1881-1977\", 1393], [1386, 75, \"Andrea Tacquet  was a Flemish Jesuit who wrote some popular teaching works.\", \"Andrea Tacquet\", \"1612-1660\", 188], [207, 75, \"Adrien Auzout   was a French astronomer who improved measuring instruments.\", \"Adrien Auzout\", \"1622-1691\", 205], [804, 75, \"James Moriarty  is best known as the criminal adversary of Sherlock Holmes.\", \"James Moriarty\", \"1835-1891\", 764], [1387, 75, \"Jakob Steiner  was one of the greatest contributors to projective geometry.\", \"Jakob Steiner\", \"1796-1863\", 551], [2635, 75, \"Fran\\u00e7ois Bruhat  was a French mathematician who worked on algebraic groups.\", \"Fran\\u00e7ois Bruhat\", \"1929-2007\", 2649], [1573, 75, \"Francesco Cecioni  was an Italian mathematician who specialised in algebra.\", \"Francesco Cecioni\", \"1884-1968\", 1451], [1062, 75, \"Tadeusz Banachiewicz  was a Polish astronomer, mathematician and geodesist.\", \"Tadeusz Banachiewicz\", \"1882-1954\", 1423], [1805, 75, \"G\\u00e1bor Szeg\\u0151  worked in the area of extremal problems and Toeplitz matrices.\", \"G\\u00e1bor Szeg\\u0151\", \"1895-1985\", 1678], [2837, 75, \"Hideo Tanaka  wasa Japanese mathematician known for his work on fuzzy sets.\", \"Hideo Tanaka\", \"1938-2012\", 2830], [1813, 75, \"R Buckminster Fuller  is best known for the invention of the geodesic dome.\", \"R Buckminster Fuller\", \"1895-1983\", 1686], [2516, 75, \"Attia Ashour  was an Egyptian mathematician who worked in electromagnetism.\", \"Attia Ashour\", \"1924-2017\", 2495], [344, 75, \"Vincenzo Riccati  was an Italian Jesuit who worked on hyperbolic functions.\", \"Vincenzo Riccati\", \"1707-1775\", 335], [2923, 75, \"Rufus Bowen  was an American mathematician who worked on dynamical systems.\", \"Robert Edward Bowen\", \"1947-1978\", 2917], [1370, 75, \"Gustave Dumas   was a Swiss mathematician who worked in algebraic geometry.\", \"Gustave Dumas\", \"1872-1955\", 1253], [2133, 75, \"Gelfond  developed basic techniques in the study of transcendental numbers.\", \"Aleksandr Osipovich Gelfond\", \"1906-1968\", 1975], [616, 76, \"Pierre Verhulst  was a Belgian statistician who worked on population growth.\", \"Pierre Verhulst\", \"1804-1849\", 591], [296, 76, \"Jakob Hermann  was a Swiss mathematician who made contributions to dynamics.\", \"Jakob Hermann\", \"1678-1733\", 286], [2724, 76, \"Gian-Carlo Rota  was an Italian-born American mathematician and philosopher.\", \"Gian-Carlo Rota\", \"1932-1999\", 2712], [2928, 76, \"Gerard Murphy  was an Irish mathematician who worked in functional analysis.\", \"Gerard Murphy\", \"1948-2006\", 2922], [1559, 76, \"Hilda Hudson  was an English mathematician who worked on algebraic geometry.\", \"Hilda Hudson\", \"1881-1965\", 1397], [415, 76, \"Charles Hutton  was an English mathematician who wrote arithmetic textbooks.\", \"Charles Hutton\", \"1737-1823\", 389], [1457, 76, \"Heinrich Jung  was a German mathematician who worked on algebraic functions.\", \"Heinrich Jung\", \"1876-1953\", 1314], [1474, 76, \"Schieffelin Claytor  was an American mathematician specialising in topology.\", \"Schieffelin Claytor\", \"1908-1967\", 2075], [2679, 76, \"Goro Shimura  was a Japanese mathematician who worked on algebraic geometry.\", \"Goro Shimura\", \"1930-2019\", 2669], [434, 76, \"Aida Yasuaki  was a Japanese mathematician who published about  2000  works.\", \"Aida Yasuaki\", \"1747-1817\", 407], [1507, 76, \"Leonard Roth  was an English mathematician who worked on Algebraic Geometry.\", \"Leonard Roth\", \"1904-1968\", 1925], [854, 76, \"Olaus  Henrici  was a German mathematician who became a professor in London.\", \"Olaus Henrici\", \"1840-1918\", 805], [2805, 76, \"Barry Johnson  was an English mathematician who worked on operator algebras.\", \"Barry Johnson\", \"1937-2002\", 2799], [123, 76, \"Benedetto Castelli  was an Italian Benedictine who was a student of Galileo.\", \"Benedetto Castelli\", \"1578-1643\", 140], [1380, 76, \"John Meiklejohn  graduated from Edinburgh and taught at Dundee High School. \", \"John Meiklejohn\", \"1872-1951\", 1254], [2878, 76, \"Pat Keast  was Scottish mathematician who specialised in numerical analysis.\", \"Patrick Keast\", \"1942-2016\", 2873], [13, 76, \"Eddington  made important contributions to the theory of general relativity.\", \"Arthur Eddington\", \"1882-1944\", 1406], [362, 76, \"Giovanni Fagnano  was an Italian priest who worked on geometry and calculus.\", \"Giovanni Fagnano\", \"1715-1797\", 349], [2936, 76, \"Fritz Grunewald  was a German mathematician who specialised in group theory.\", \"Fritz Grunewald\", \"1949-2010\", 2932], [2208, 76, \"Hugh Dowker  was an English mathematician known for his work on knot theory.\", \"Hugh Dowker\", \"1912-1982\", 2185], [738, 76, \"William Spottiswoode  was an English mathematician, physicist and publisher.\", \"William Spottiswoode\", \"1825-1883\", 708], [502, 77, \"Daniel Hecht  was a German mathematician who wrote several high school texts.\", \"Daniel Hecht\", \"1777-1833\", 482], [241, 77, \"Bernard Lamy  was a French mathematician who wrote on geometry and mechanics.\", \"Bernard Lamy\", \"1640-1715\", 235], [1864, 77, \"Otakar Boruvka  was a Czech mathematician known for his work in graph theory.\", \"Otakar Boruvka\", \"1899-1995\", 1768], [2220, 77, \"Shigeo Sasaki  was a Japanese mathematician working on differential geometry.\", \"Shigeo Sasaki\", \"1912-1987\", 2197], [2369, 77, \"Naum Il'ich Feldman  was a Russian mathematician who worked in number theory.\", \"Naum Il'ich Feldman\", \"1918-1994\", 2352], [2276, 77, \"John Crank  was an English numerical analyst who worked on the heat equation.\", \"John Crank\", \"1916-2006\", 2298], [630, 77, \"Moritz Abraham Stern  was a German mathematician who worked in number theory.\", \"Moritz Abraham Stern\", \"1807-1894\", 605], [1722, 77, \"Ivan Privalov   was a Russian mathematician who worked on analytic functions.\", \"Ivan Ivanovich Privalov\", \"1891-1941\", 1598], [2090, 77, \"Demetrios Kappos  was a Greek mathematician who worked in probability theory.\", \"Demetrios Kappos\", \"1904-1985\", 1905], [1694, 77, \"Oscar Chisini  was an Italian mathematician who worked in algebraic geometry.\", \"Oscar Chisini\", \"1889-1967\", 1566], [2731, 77, \"John Lewis  was a Welsh applied mathematican who worked on quantum mechanics.\", \"John Lewis\", \"1932-2004\", 2719], [679, 77, \"William Ferrel  was an American astronomer who worked on the theory of tides.\", \"William Ferrel\", \"1817-1891\", 652], [684, 77, \"George Salmon  made many discoveries about ruled surfaces and other surfaces.\", \"George Salmon\", \"1819-1904\", 657], [2588, 77, \"Alexander Skopin  was a Russian mathematician who worked in abstract algebra.\", \"Alexander Ivanovich Skopin\", \"1927-2003\", 2581], [693, 77, \"Siegfried Aronhold  made important contributions to the theory of invariants.\", \"Siegfried Aronhold\", \"1819-1884\", 666], [2990, 77, \"Richard Askey  was an American mathematician who worked in special functions.\", \"Richard Askey\", \"1933-2019\", 2748], [1388, 77, \"Gomes Teixeira   was a Portuguese mathematician and historian of mathematics.\", \"Gomes Teixeira\", \"1851-1933\", 922], [2382, 77, \"Jim Wilkinson  was an English mathematician who worked in numerical analysis.\", \"Jim Wilkinson\", \"1919-1986\", 2371], [919, 77, \"M\\u00f3r R\\u00e9thy  was a Hungarian mathematician. He became an expert on the Bolyais.\", \"M\\u00f3r R\\u00e9thy\", \"1846-1925\", 863], [905, 77, \"F\\u00e9lix Tisserand  was a French astronomer who updated Laplace's standard work.\", \"F\\u00e9lix Tisserand\", \"1845-1896\", 849], [269, 78, \"William Molyneux  was an Irish scientist and philosopher who worked on optics.\", \"William Molyneux\", \"1656-1698\", 259], [1974, 78, \"Ott\\u00f3 Varga  was a Hungarian mathematician who worked in differential geometry.\", \"Ott\\u00f3 Varga\", \"1909-1969\", 2104], [1418, 78, \"Zo\\u00e1rd Ge\\u00f6cze  was a Hungarian mathematician famous for his theory of surfaces.\", \"Zo\\u00e1rd Ge\\u00f6cze\", \"1873-1916\", 1275], [239, 78, \"Erich Bessel-Hagen  was a German mathematician and a historian of mathematics.\", \"Erich Bessel-Hagen\", \"1898-1946\", 1741], [2604, 78, \"John Stewart Bell  was an Irish mathematician who worked in quantum mechanics.\", \"John Bell\", \"1928-1990\", 2625], [805, 78, \"John Purser  was an Irish mathematician who taught at Queen's College Belfast.\", \"John Purser\", \"1835-1903\", 765], [459, 78, \"James Ivory  was a Scottish mathematician who wrote on mathematical astronomy.\", \"James Ivory\", \"1765-1842\", 439], [1188, 78, \"Henri Pad\\u00e9  made important contributions to the theory of continued fractions.\", \"Henri Pad\\u00e9\", \"1863-1953\", 1100], [2367, 78, \"Leslie Fox  was a British mathematician who specialised in numerical analysis.\", \"Leslie Fox\", \"1918-1992\", 2350], [588, 78, \"Karl von Staudt  was a German mathematician who worked on projective geometry.\", \"Karl von Staudt\", \"1798-1867\", 563], [277, 78, \"Takebe  was a Japanese mathematician who wrote most of Seki's  Encyclopaedia .\", \"Takebe Katahiro\", \"1664-1739\", 267], [2631, 78, \"Yuri Prokhorov  was a Russian mathematician who worked in probability theory. \", \"Yurii Vasilevich Prokhorov\", \"1929-2013\", 2661], [1882, 78, \"Leopold Infeld  was a Polish physicist who worked in the theory of relativity.\", \"Leopold Infeld\", \"1898-1968\", 1748], [985, 78, \"James Taylor  was a Scottish mathematics teacher who taught at Dollar Academy.\", \"James Taylor\", \"1851-1910\", 925], [2738, 78, \"Mary Warner  was a Welsh mathematician who was a pioneer in fuzzy mathematics.\", \"Mary Warner\", \"1932-1998\", 2726], [2149, 78, \"Hans Bethe  was a mathematician and physicist who worked on quantum mechanics.\", \"Hans Bethe\", \"1906-2005\", 1996], [2842, 78, \"Alan Baker  was an English mathematician, known for his work in number theory.\", \"Alan Baker\", \"1939-2018\", 2835], [1455, 78, \"Gaetano Scorza  was an Italian mathematician who worked in algebraic geometry.\", \"Gaetano Scorza\", \"1876-1939\", 1312], [2694, 78, \"Satoshi Suzuki  wa a Japanese mathematician who worked in algrabraic geometry.\", \"Satoshi Suzuki\", \"1930-1991\", 2684], [623, 78, \"Ferdinand Minding  worked in differential geometry and the theory of surfaces.\", \"Ferdinand Minding\", \"1806-1885\", 598], [811, 78, \"Hermann Bleuler  was a Swiss engineer and artillery officer in the Swiss army.\", \"Hermann Bleuler\", \"1837-1912\", 771], [411, 79, \"Harry Vandiver  was an American mathematician, known for work in number theory.\", \"Harry Vandiver\", \"1882-1973\", 1413], [847, 79, \"Carl Johannes Thomae  was a German mathematician who worked in function theory.\", \"Carl Johannes Thomae\", \"1840-1921\", 798], [2817, 79, \"Leonid Pastur  is a Ukrainian mathematical physicist and theoretical physicist.\", \"Leonid Andreevich Pastur\", \"1937-\", 2811], [419, 79, \"Anders Lexell  made major contributions to spherical geometry and trigonometry.\", \"Anders Lexell\", \"1740-1784\", 393], [418, 79, \"Georg Kl\\u00fcgel  was a German mathematician who wrote a Dictionary of Mathematics.\", \"Georg Kl\\u00fcgel\", \"1739-1812\", 392], [2116, 79, \"John Todd  was an Irish-born numerical analyst. He was married to Olga Taussky.\", \"Jack Todd\", \"1911-2007\", 2153], [2210, 79, \"Kentaro Yano  was a Japanese mathematician who worked on differential geometry.\", \"Kentaro Yano\", \"1912-1993\", 2187], [1851, 79, \"Jesse Douglas  worked on geometry, group theory and the calculus of variations.\", \"Jesse Douglas\", \"1897-1965\", 1723], [377, 79, \"Johann Lambert  was the first to provide a rigorous proof that \\u03c0 is irrational.\", \"Johann Heinrich Lambert\", \"1728-1777\", 364], [1744, 79, \"Alfred Brauer  was a German-American mathematician who worked in number theory.\", \"Alfred Brauer\", \"1894-1985\", 1650], [2537, 79, \"James Eells  was an American mathematician who worked in mathematical analysis.\", \"James Eells\", \"1926-2007\", 2559], [2237, 79, \"Vladimir Potapov  was a Ukrainian mathematician who worked on matrix functions.\", \"Vladimir Potapov\", \"1914-1980\", 2253], [550, 79, \"Victor-Am\\u00e9d\\u00e9e Lebesgue  was a French mathematician who worked on number theory.\", \"Victor Am\\u00e9d\\u00e9e Lebesgue\", \"1791-1875\", 529], [2439, 79, \"Iacopo Barsotti  was an Italian mathematician who worked in algebraic geometry.\", \"Iacopo Barsotti\", \"1921-1987\", 2425], [2536, 79, \"James Clunie  was a Scottish-born mathematician who worked in complex analysis.\", \"James Clunie\", \"1926-2013\", 2558], [1374, 79, \"Hans Schubert  was a German mathematician who worked on differential equations.\", \"Hans Schubert\", \"1908-1987\", 2062], [2472, 80, \"Rimhak Ree  was a Korean-born Canadian mathematician who worked in group theory.\", \"Rimhak Ree\", \"1922-2005\", 2456], [2440, 80, \"Elena Popoviciu  was a Romanian mathematician who worked in functional analysis.\", \"Elena Moldovan Popoviciu\", \"1924-2009\", 2499], [1038, 80, \"Thomas Craig  was an American mathematician who worked on differential geometry.\", \"Thomas Craig\", \"1855-1900\", 976], [330, 80, \"William Emerson  published textbooks which popularised the work of Isaac Newton.\", \"William Emerson\", \"1701-1782\", 321], [252, 80, \"Emil Grosswald  was a Romanian mathematician who worked mainly in number theory.\", \"Emil Grosswald\", \"1912-1989\", 2180], [2615, 80, \"Karl Gruenberg  was an Austrian mathematician who worked in finite group theory.\", \"Karl Gruenberg\", \"1928-2007\", 2629], [602, 80, \"Mikhail Ostrogradski  worked on hydrodynamics, elasticity, heat and electricity.\", \"Mikhail Vasilevich Ostrogradski\", \"1801-1862\", 577], [1734, 80, \"Arnold Walfisz  was a Polish mathematician who worked in analytic number theory.\", \"Arnold Walfisz\", \"1892-1962\", 1610], [435, 80, \"Charles Tinseau  was a French mathematician who wrote on the theory of surfaces.\", \"Charles Tinseau\", \"1748-1822\", 408], [2965, 80, \"Robert Thomason  was an American mathematician who worked on algebraic K-theory.\", \"Bob Thomason\", \"1952-1995\", 2949], [221, 80, \"J\\u00e1nos Ap\\u00e1czai  was born in Transylvania and wrote the  Hungarian Encyclopaedia .\", \"J\\u00e1nos Ap\\u00e1czai\", \"1625-1659\", 217], [1100, 80, \"August Gutzmer  was a German mathematician who worked on differential equations.\", \"August Gutzmer\", \"1860-1924\", 1030], [1889, 80, \"Zyoiti Suetuna  was a Japanese mathematician who worked mainly in number theory.\", \"Zyoiti Suetuna\", \"1898-1970\", 1758], [2163, 80, \"Floyd Burton Jones  was an American mathematician who worked mainly in topology.\", \"Floyd Burton Jones\", \"1910-1999\", 2120], [600, 80, \"Joseph Raabe  is mostly remembered for  Raabe's Test  for convergence of series.\", \"Joseph Raabe\", \"1801-1859\", 575], [1372, 80, \"Li Zhi  was a Chinese mathematician who described methods for solving equations.\", \"Li Zhi\", \"1192-1279\", 22], [742, 80, \"Gabriel Koenigs  was a French mathematician who worked on analysis and geometry.\", \"Gabriel Koenigs\", \"1858-1931\", 1008], [1930, 80, \"Edward Collingwood  was an English mathematician who worked in complex analysis.\", \"Edward Collingwood\", \"1900-1970\", 1783], [174, 80, \"Maria Cunitz  was an astronomer who published simpler versions of Kepler's work.\", \"Maria Cunitz\", \"1607-1664\", 180], [1980, 81, \"Abe Gelbart  was an American mathematician who worked in complex function theory.\", \"Abraham Gelbart\", \"1911-1994\", 2143], [2792, 81, \"Don Ornstein  is an American mathematician working in the area of ergodic theory.\", \"Donald Ornstein\", \"1934-\", 2750], [1965, 81, \"Johannes Haantjes  was a Dutch mathematician who worked in differential geometry.\", \"Johannes Haantjes\", \"1909-1956\", 2098], [2630, 81, \"Manuel Valdivia  was a Spanish mathematician who worked in topology and analysis.\", \"Manuel Valdivia\", \"1928-2014\", 2632], [1804, 81, \"Erich Hans Rothe  was a German mathematician who worked in the field of analysis.\", \"Erich Hans Rothe\", \"1895-1988\", 1677], [275, 81, \"John Craig  was a Scottish mathematician who published three important textbooks.\", \"John Craig\", \"1663-1731\", 265], [1344, 81, \"Hans Heilbronn  was a German mathematician who worked in algebraic number theory.\", \"Hans Heilbronn\", \"1908-1975\", 2060], [1291, 81, \"Aleksei Vasilevich Pogorelov  was a Russian mathematician who worked in geometry.\", \"Aleksei Vasilevich Pogorelov\", \"1919-2002\", 2360], [1055, 81, \"Giacinto Morera  was an Italian mathematician who made contributions to dynamics.\", \"Giacinto Morera\", \"1856-1907\", 985], [2873, 81, \"David Crighton  was a Welsh mathematician who worked on fluid flow and acoustics.\", \"David Crighton\", \"1942-2000\", 2868], [272, 81, \"Joseph Saurin  was a French mathematician who made contributions to the calculus.\", \"Joseph Saurin\", \"1659-1737\", 262], [1922, 81, \"Tom\\u00e1s Bachiller  was a Chinese-born Spanish mathematician who worked in topology.\", \"Tom\\u00e1s Rodr\\u00edguez Bachiller\", \"1899-1980\", 1775], [1280, 81, \"Derrick Norman Lehmer  was an American mathematician who worked in number theory.\", \"Derrick Norman Lehmer\", \"1867-1938\", 1171], [2723, 81, \"Gene Golub  was an Amercian mathematician who worked in numerical linear algebra.\", \"Gene Golub\", \"1932-2007\", 2711], [504, 81, \"William Spence  was a Scottish mathematician who worked on logarithmic functions.\", \"William Spence\", \"1777-1815\", 484], [1461, 81, \"Paul Montel  was a French mathematician who worked on complex analytic functions.\", \"Paul Montel\", \"1876-1975\", 1318], [2223, 81, \"Adriaan Cornelis Zaanen  was a Dutch mathematician who worked mainly in analysis.\", \"Adriaan Cornelis Zaanen\", \"1913-2003\", 2200], [558, 81, \"Th\\u00e9odore Olivier  was a French geometer who made string models of ruled surfaces.\", \"Th\\u00e9odore Olivier\", \"1793-1853\", 537], [1649, 81, \"Dunham Jackson  was an American mathematician who worked in approximation theory.\", \"Dunham Jackson\", \"1888-1946\", 1529], [580, 81, \"Alexander Doniphan Wallace  was an American mathematician who worked in topology.\", \"Alexander Doniphan Wallace\", \"1905-1985\", 1938], [1060, 81, \"Wilhelm Meyer  studied algebraic geometry, algebraic curves and invariant theory.\", \"Wilhelm Meyer\", \"1856-1934\", 991], [10, 81, \"Ramon Llull  was a Majorcan philosopher whose logical methods influenced Leibniz.\", \"Ramon Llull\", \"1235-1316\", 32], [1318, 81, \"Virgil Snyder  was an American mathematician, specializing in algebraic geometry.\", \"Virgil Snyder\", \"1869-1950\", 1214], [1496, 81, \"Edward Kasner  was an American mathematician who worked on differential geometry.\", \"Edward Kasner\", \"1878-1955\", 1343], [2106, 82, \"John Hildebrant  was an American mathematician and specialist in semigroup theory.\", \"John Hildebrant\", \"1935-2003\", 2769], [833, 82, \"Samuel Wilks  was an American mathematician who worked in mathematical statistics.\", \"Samuel Wilks\", \"1906-1964\", 2013], [2511, 82, \"Wim Cohen  was a Dutch mathematician who worked in queueing theory and statistics.\", \"Wim Cohen\", \"1923-2000\", 2490], [593, 82, \"Karl Feuerbach  was a geometer who discovered the nine point circle of a triangle.\", \"Karl Feuerbach\", \"1800-1834\", 568], [1933, 82, \"Gertrude Mary Cox  was an American statistician who worked in experimental design.\", \"Gertrude Cox\", \"1900-1978\", 1786], [2487, 82, \"Dionisio Gallarati  was an Italian mathematician who worked in algebraic geometry.\", \"Dionisio Gallarati\", \"1923-2019\", 2467], [921, 82, \"Platon Sergeevich Poretsky  was a Russian astronomer, mathematician, and logician.\", \"Platon Sergeevich Poretsky\", \"1846-1907\", 865], [1109, 82, \"Mathias Lerch  was a Czech mathematician who worked in analysis and number theory.\", \"Maty\\u00e1\\u0161 Lerch\", \"1860-1922\", 1039], [2395, 82, \"Ambrose Rogers  wrote extensively on Number Theory and on Sphere-packing problems.\", \"Ambrose Rogers\", \"1920-2005\", 2384], [1391, 82, \"Georg Scheffers  was a German mathematician specializing in differential geometry.\", \"Georg Scheffers\", \"1866-1945\", 1159], [1477, 82, \"Paul Kelly  was an American mathematician who worked in geometry and graph theory.\", \"Paul Kelly\", \"1915-1995\", 2277], [1443, 82, \"Max Abraham  was a German physicist who worked on electromagnetism and relativity.\", \"Max Abraham\", \"1875-1922\", 1299], [1041, 82, \"Ei\\u017eens Leimanis  was a Latvian mathematician who worked on the three-body problem.\", \"Ei\\u017eens Leimanis\", \"1905-1992\", 1944], [725, 82, \"Delfino Codazzi  was an Italian mathematician who worked in differential geometry.\", \"Delfino Codazzi\", \"1824-1873\", 696], [722, 82, \"Oscar Schl\\u00f6milch   was a German mathematician who worked in mathematical analysis.\", \"Oscar Schl\\u00f6milch\", \"1823-1901\", 694], [718, 82, \"Jakob Amsler-Laffon   was a Swiss mathematician, physicist, engineer and inventor.\", \"Jacob Amsler\", \"1823-1912\", 691], [853, 82, \"Joseph  Neuberg   was a Luxembourg mathematician who worked primarily in geometry.\", \"Joseph Neuberg\", \"1840-1926\", 804], [813, 82, \"Joseph Tilly  was a Belgian soldier who published works on non-Euclidean geometry.\", \"Joseph Tilly\", \"1837-1906\", 773], [1472, 82, \"Marceli Stark  was a Polish mathematician who published many important text-books.\", \"Marceli Stark\", \"1908-1974\", 2073], [1182, 82, \"Dmitry Grave  was a Russian mathematician who worked in algebra and number theory.\", \"Dmitry Aleksandrovich Grave\", \"1863-1939\", 1094], [243, 82, \"Jacques Ozanam  was a French mathematician who was a popular writer of text-books.\", \"Jacques Ozanam\", \"1640-1718\", 237], [165, 82, \"Richard Delamain  was an English mathematician who invented a circular slide rule.\", \"Richard Delamain\", \"1600-1644\", 171], [2779, 82, \"Graham Allan  was an English mathematician who specialised in functional analysis.\", \"Graham Allan\", \"1936-2007\", 2782], [133, 82, \"Wilhelm Ljunggren  was a Norwegian mathematician who specialised in number theory.\", \"Wilhelm Ljunggren\", \"1905-1973\", 1971], [2832, 82, \"Don Carlson  was an American mathematician who worked in mechanics and elasticity.\", \"Don Carlson\", \"1938-2010\", 2825], [2345, 83, \"Moshe Livsic  was a Ukrainian-born mathematician who worked in functional analysis.\", \"Moshe Livsic\", \"1917-2007\", 2323], [2447, 83, \"Leo Moser  was an Austrian-born Canadian mathematician who worked in number theory.\", \"Leo Moser\", \"1921-1970\", 2430], [313, 83, \"Samuel Molyneux  was an English astronomer who produced some new telescope designs.\", \"Samuel Molyneux\", \"1689-1728\", 304], [2954, 83, \"David Broomhead  was an English mathematician who specialised in dynamical systems.\", \"David Broomhead\", \"1950-2014\", 2938], [1871, 83, \"Arend Heyting  is important in the development of intuitionistic logic and algebra.\", \"Arend Heyting\", \"1898-1980\", 1736], [1885, 83, \"Escher  is an artist whose works have included a considerable mathematical content.\", \"Maurits Escher\", \"1898-1972\", 1751], [177, 83, \"Honor\\u00e9 Fabri  was a French Jesuit who worked on astronomy, physics and mathematics.\", \"Honor\\u00e9 Fabri\", \"1608-1688\", 183], [1444, 83, \"Michele de Franchis  was an Italian mathematician who worked in algebraic geometry.\", \"Michele de Franchis\", \"1875-1946\", 1300], [1757, 83, \"Olli Lehto  was a Finnish mathematician who worked in in geometric function theory.\", \"Olli Lehto\", \"1925-2020\", 2541], [615, 83, \"George Jerrard  was an English mathematician who worked on the theory of equations.\", \"George Jerrard\", \"1804-1863\", 590], [1583, 83, \"Nicolae Abramescu  was a Romanian mathematician who worked in descriptive geometry.\", \"Nicolae Abramescu\", \"1884-1947\", 1459], [360, 83, \"Alexander Wilson  was a Scottish astronomer who published observations on sunspots.\", \"Alexander Wilson\", \"1714-1786\", 347], [775, 83, \"Nathan Fine  was an American mathematician who worked on the hypergeometric series.\", \"Nathan Fine\", \"1916-1994\", 2300], [404, 83, \"Jesse Ramsden  was an English instrument maker who made improvements to telescopes.\", \"Jesse Ramsden\", \"1735-1800\", 383], [495, 83, \"Farkas Bolyai  was a mathematics teacher, best known as the father of J\\u00e1nos Bolyai.\", \"Farkas Bolyai\", \"1775-1856\", 475], [2777, 83, \"Dmitri Anosov  was a  Russian mathematician who worked in dynamical systems theory.\", \"Dmitrii Viktorovich Anosov\", \"1936-2014\", 2780], [257, 83, \"Tommaso Ceva  was an Italian Jesuit who worked in geometry, gravity and arithmetic.\", \"Tommaso Ceva\", \"1648-1737\", 250], [2381, 83, \"Jaap Seidel  was a Dutch mathematician who who worked in geometry and graph theory.\", \"Jaap Seidel\", \"1919-2001\", 2370], [1973, 83, \"Henri Cartan  was a French mathematiician who was one of the original Bourbakistes.\", \"Henri Cartan\", \"1904-2008\", 1917], [122, 83, \"Paul Guldin  was a Swiss mathematician who wrote on volumes and centres of gravity.\", \"Paul Guldin\", \"1577-1643\", 139], [673, 83, \"Johann  Rosenhain  was a German mathematician who introduced theta characteristics.\", \"Johann Rosenhain\", \"1816-1887\", 646], [2819, 83, \"Ron Book  was an American mathematician who worked in theoretical computer science.\", \"Ron Book\", \"1937-1997\", 2813], [1184, 83, \"Edvard Phragm\\u00e9n  was a Swedish mathematician who worked on the theory of functions.\", \"Edvard Phragm\\u00e9n\", \"1863-1937\", 1096], [1552, 83, \"Rudolf Fueter  was a Swiss mathematician, best known for his work on number theory.\", \"Rudolf Fueter\", \"1880-1950\", 1389], [2081, 84, \"Harry  Carver   was an American mathematician who worked in mathematical statistics.\", \"Harry Carver\", \"1890-1977\", 1581], [1093, 84, \"J\\u00e9r\\u00f4me Franel   was a Swiss mathematician who specialised in analytic number theory.\", \"J\\u00e9r\\u00f4me Franel\", \"1859-1939\", 1023], [2883, 84, \"Vitaly Fedorchuk  was a Russian mathematician who worked various areas of topology. \", \"Vitaly Vitalievich Fedorchuk\", \"1942-2012\", 2878], [1913, 84, \"Edward Titchmarsh  was an English mathematician best known for his work in analysis.\", \"Edward Titchmarsh\", \"1899-1963\", 1760], [364, 84, \"Matthew Stewart  was a Scottish geometer who wrote on geometry and planetary motion.\", \"Matthew Stewart\", \"1717-1785\", 351], [383, 84, \"Francis Maseres  was an English mathematician who wrote some influential text-books.\", \"Francis Maseres\", \"1731-1824\", 370], [2403, 84, \"Frank Bonsall  was a English mathematician who worked mainly in functional analysis.\", \"Frank Bonsall\", \"1920-2011\", 2392], [421, 84, \"Carl Friedrich Hindenburg  published a series of works on combinatorial mathematics.\", \"Carl Friedrich Hindenburg\", \"1741-1808\", 395], [2456, 84, \"Yozo Matsushima  was a Japanese mathematician who worked in Lie groups and algebras.\", \"Yozo Matsushima\", \"1921-1983\", 2439], [1214, 84, \"J\\u00f3zsef K\\u00fcrsch\\u00e1k  was a Hungarian mathematician who founded the theory of valuations.\", \"J\\u00f3zsef K\\u00fcrsch\\u00e1k\", \"1864-1933\", 1122], [1793, 84, \"Norbert Wiener  was an American mathematician who did important work on probability.\", \"Norbert Wiener\", \"1894-1964\", 1663], [14, 84, \"Clement V Durell  was an English schoolmaster famous for his mathematical textbooks.\", \"Clement Durell\", \"1882-1968\", 1407], [2529, 84, \"Wilhelm Klingenberg  was a German mathematician who worked on differential geometry.\", \"Wilhelm Klingenberg\", \"1924-2010\", 2519], [2350, 84, \"Roger Lyndon  was an American mathematician who worked in topology and group theory.\", \"Roger Lyndon\", \"1917-1988\", 2328], [210, 84, \"Vincenzo Viviani  was an Italian engineer who worked on the geometry of the cycloid.\", \"Vincenzo Viviani\", \"1622-1703\", 208], [1270, 84, \"Fredholm  is best remembered for his work on integral equations and spectral theory.\", \"Ivar Fredholm\", \"1866-1927\", 1162], [991, 84, \"Andrei Petrovich Kiselev  wasa Russian mathematician known mainly for his textbooks.\", \"Andrei Petrovich Kiselev\", \"1852-1940\", 931], [2179, 84, \"Sheila Scott Macintyre  taught at the University of Aberdeen and worked in analysis.\", \"Sheila Scott Macintyre\", \"1910-1960\", 2140], [215, 84, \"Guarino Guarini  was an Italian mathematician who worked in geometry and philosophy.\", \"Guarino Guarini\", \"1624-1683\", 212], [200, 84, \"Gabriel Mouton  was a French clergyman who worked on interpolation and on astronomy.\", \"Gabriel Mouton\", \"1618-1694\", 198], [2068, 85, \"Taro Morishima  was a Japanese mathematician who worked in algebra and number theory.\", \"Taro Morishima\", \"1903-1989\", 1893], [2343, 85, \"Kenkichi Iwasawa  was a Japanese mathematician who worked in algebraic number theory.\", \"Kenkichi Iwasawa\", \"1917-1998\", 2319], [773, 85, \"Eug\\u00e8ne Rouch\\u00e9  was a French geometer best known for his theorem on complex functions.\", \"Eug\\u00e8ne Rouch\\u00e9\", \"1832-1910\", 743], [256, 85, \"Henry Aldrich  was an English mathematician who published an important work on logic.\", \"Henry Aldrich\", \"1648-1710\", 249], [2680, 85, \"Gregory Maxwell Kelly  was an Australian mathematician who worked in category theory.\", \"Gregory Maxwell Kelly\", \"1930-2007\", 2670], [55, 85, \"Charles de Bouvelles  was a French priest who wrote works on geometry and philosophy.\", \"Charles de Bouvelles\", \"1471-1553\", 73], [1069, 85, \"Hermann Wiener  was a German mathematician who worked on the foundations of geometry.\", \"Hermann Wiener\", \"1857-1939\", 999], [2814, 85, \"Johannes Boersma  was a Dutch mathematician who specialised in mathematical analysis.\", \"Johannes Boersma\", \"1937-2004\", 2808], [334, 85, \"Alexis Fontaine  was a French mathematician who worked on the calculus of variations.\", \"Alexis Fontaine\", \"1704-1771\", 326], [1428, 85, \"Robert d'Adh\\u00e9mar  was a French mathematician and philosopher of science and religion.\", \"Robert d'Adh\\u00e9mar\", \"1874-1941\", 1285], [1814, 85, \"Rolf Nevanlinna  was a Finnish mathematician famous for his work on complex analysis.\", \"Rolf Nevanlinna\", \"1895-1980\", 1687], [584, 85, \"Christoph Gudermann  worked on geometry and special functions. He taught Weierstrass.\", \"Christoph Gudermann\", \"1798-1852\", 559], [1637, 85, \"Otto Haupt  was a German mathematician who specialised in geometry and real analysis.\", \"Otto Haupt\", \"1887-1988\", 1518], [2252, 85, \"Oswald Teichm\\u00fcller 's main contribution was in the area of geometric function theory.\", \"Oswald Teichm\\u00fcller\", \"1913-1943\", 2218], [1686, 85, \"Enrico Bompiani  was an Italian mathematician, specializing in differential geometry.\", \"Enrico Bompiani\", \"1889-1975\", 1558], [2768, 85, \"Sharaf al-Tusi  was an Islamic mathematician who wrote a treatise on cubic equations.\", \"Sharaf al-Din al-Tusi\", \"1135-1213\", 17], [472, 86, \"Fran\\u00e7ois-Joseph Servois  was a French mathematician who worked on projective geometry.\", \"Fran\\u00e7ois-Joseph Servois\", \"1768-1847\", 452], [1042, 86, \"Emanuel Sperner  was a German mathematician who worked in the foundations of geometry.\", \"Emanuel Sperner\", \"1905-1980\", 1945], [763, 86, \"Am\\u00e9d\\u00e9e Mannheim  was a French mathematician and the inventor of the modern slide rule.\", \"Am\\u00e9d\\u00e9e Mannheim\", \"1831-1906\", 732], [2595, 86, \"Frank Levin  was an American mathematician who worked mainly in infinite group theory.\", \"Frank Levin\", \"1927-2011\", 2588], [2560, 86, \"Keith Stewartson  was an English mathematician who worked in the theory of fluid flow.\", \"Keith Stewartson\", \"1925-1983\", 2534], [1996, 86, \"Werner Heisenberg  did important work in Quantum Mechanics as well as nuclear physics.\", \"Werner Heisenberg\", \"1901-1976\", 1828], [1537, 86, \"Philip Jourdain   was an English logician who worked on the foundations of set theory.\", \"Philip Jourdain\", \"1879-1919\", 1374], [498, 86, \"Peter Barlow  was an English mathematician who produced important mathematical tables.\", \"Peter Barlow\", \"1776-1862\", 478], [2056, 86, \"Jean Delsarte  was a French mathematician known for his work in mathematical analysis.\", \"Jean Delsarte\", \"1903-1968\", 1883], [1267, 86, \"Cosserat  studied the deformation of surfaces which led him to a theory of elasticity.\", \"Eug\\u00e8ne Cosserat\", \"1866-1931\", 1157], [1379, 86, \"Karol Borsuk  was a Polish mathematician who made important contributions to topology.\", \"Karol Borsuk\", \"1905-1982\", 1955], [2524, 86, \"Mary Ellen Rudin  was an American mathematician known for herwork in general topology.\", \"Mary Ellen Rudin\", \"1924-2013\", 2513], [1292, 86, \"Sewall Green Wright   was an American geneticist who worked on on evolutionary theory.\", \"Sewall Green Wright\", \"1889-1988\", 1572], [583, 86, \"Pierre-Joseph-\\u00c9tienne Finck  wrote books on algebra, mechanics, geometry and analysis.\", \"Pierre-Joseph-\\u00c9tienne Finck\", \"1797-1870\", 558], [2848, 86, \"L\\u00e1szl\\u00f3 Filep  was a Hungarian mathematician who specialised in history of mathematics.\", \"L\\u00e1szl\\u00f3 Filep\", \"1941-2004\", 2864], [2184, 86, \"Chow Wei-Liang  was a Chinese mathematician  known for his work in algebraic geometry.\", \"Wei-Liang Chow\", \"1911-1995\", 2167], [2719, 86, \"Donald Solitar  was a Canadian mathematician who worked in combinatorial group theory.\", \"Donald Solitar\", \"1932-2008\", 2709], [1615, 86, \"Annibale Comessatti  was an Italian mathematician who worked in in algebraic geometry.\", \"Annibale Comessatti\", \"1886-1945\", 1491], [2332, 86, \"David Kendall  was a leading world authority on applied probability and data analysis.\", \"David Kendall\", \"1918-2007\", 2335], [2576, 86, \"Claude Berge  was a French mathematician who worked in combinatorics and graph theory.\", \"Claude Berge\", \"1926-2002\", 2550], [861, 86, \"Agnes Mary Clerke  was an Irish astronomer and writer on both astronomy and biography.\", \"Agnes Mary Clerke\", \"1842-1907\", 812], [42, 86, \"Piero Borgi  was the author of the best known  15 th Century Italian arithmetic books.\", \"Piero Borgi\", \"1424-1494\", 61], [426, 87, \"Johann ( III )  Bernoulli  wrote a number of works on astronomy and probability theory.\", \"Johann(III) Bernoulli\", \"1744-1807\", 399], [2265, 87, \"Evgeny Sergeevich Lyapin  was a Ukranian mathematician who worked in algebraic systems.\", \"Evgeny Sergeevich Lyapin\", \"1914-2005\", 2231], [686, 87, \"Hippolyte Fizeau   was a French physicist, best known for measuring the speed of light.\", \"Hippolyte Fizeau\", \"1819-1896\", 659], [591, 87, \"Fox Talbot  was a pioneer English photographer who also did work on elliptic functions.\", \"Henry Fox Talbot\", \"1800-1877\", 566], [2373, 87, \"Clifford Truesdell  was an American mathematician best known as a historian of science.\", \"Clifford Ambrose Truesdell III\", \"1919-2000\", 2362], [2085, 87, \"Fan Chung  is a Taiwanese-born American mathematician who works mainly in graph theory.\", \"Fan Chung\", \"1949-\", 2931], [400, 87, \"Achille-Pierre Dionis du S\\u00e9jour  was a French mathematician, astronomer and politician.\", \"Achille-Pierre Dionis du S\\u00e9jour\", \"1734-1794\", 379], [2744, 87, \"Tom Whiteside  was an English historian of mathematics who specialised in Isaac Newton.\", \"Tom Whiteside\", \"1932-2008\", 2732], [514, 87, \"Charles-Julien Brianchon  was a French mathematician who worked on projective geometry.\", \"Charles-Julien Brianchon\", \"1783-1864\", 494], [2186, 87, \"Alan Turing 's work was fundamental in the theoretical foundations of computer science.\", \"Alan Turing\", \"1912-1954\", 2169], [146, 87, \"Benjamin Bramer  was a German architect who published work on the calculation of sines.\", \"Benjamin Bramer\", \"1588-1652\", 152], [142, 87, \"Claude Mydorge  was a French geometer who published books on optics and conic sections.\", \"Claude Mydorge\", \"1585-1647\", 149], [220, 87, \"Jan de Witt  was a Dutch mathematician and statesman who wrote on geometry and finance.\", \"Jan de Witt\", \"1625-1672\", 216], [893, 87, \"Paul Tannery  was a French mathematician who was famous as an historian of mathematics.\", \"Paul Tannery\", \"1843-1904\", 837], [2527, 87, \"Ott\\u00f3 Steinfeld  was a Hungarian mathematician who worked in Rings and Semigroup theory.\", \"Ott\\u00f3 Steinfeld\", \"1924-1990\", 2516], [1226, 87, \"Aleksandr Kotelnikov  was a Russian mathematician who worked on non-Euclidean geometry.\", \"Aleksandr P Kotelnikov\", \"1865-1944\", 1128], [2959, 87, \"Viktor Gorbunov  was a Russian mathematician who worked in universal algebra and logic.\", \"Viktor Aleksandrovich Gorbunov\", \"1950-1999\", 2943], [1187, 87, \"Giovanni Vailati  was an Italian  philosopher, historian of science, and mathematician.\", \"Giovanni Vailati\", \"1863-1909\", 1099], [1676, 87, \"Janiszewski  produced important results in topology and the foundations of mathematics.\", \"Zygmunt Janiszewski\", \"1888-1920\", 1551], [1540, 87, \" Evgeny Slutsky  was important in the application of mathematical methods in economics.\", \"Evgeny Evgenievich Slutsky\", \"1880-1948\", 1377], [46, 87, \"Nicolas Chuquet  was a French mathematician who wrote the earliest French algebra book.\", \"Nicolas Chuquet\", \"1445-1488\", 65], [2966, 87, \"Emilio Cafaro  was an Italian mathematician who was an expert on thermo fluid dynamics.\", \"Emilio Cafaro\", \"1952-2015\", 2950], [2840, 87, \"Robion Kirby  is an American mathematician who specialises in low-dimensional topology.\", \"Robion Kirby\", \"1938-\", 2833], [1735, 87, \"Carlo Emilio Bonferroni  was an Italian mathematician who worked on probability theory.\", \"Carlo Bonferroni\", \"1892-1960\", 1611], [984, 87, \"Jacques Bertillon  was a French statistician who applied statistics to social sciences.\", \"Jacques Bertillon\", \"1851-1922\", 924], [964, 87, \"Alfred Pringsheim  was a German mathematician who worked on real and complex functions.\", \"Alfred Pringsheim\", \"1850-1941\", 903], [2816, 87, \"John Knopfmacher  was a South African mathematician who worked mainly in number theory.\", \"John Knopfmacher\", \"1937-1999\", 2810], [1036, 87, \"Paul Appell  was a French mathematician who worked in analysis, geometry and mechanics.\", \"Paul Appell\", \"1855-1930\", 974], [1463, 87, \"John Maynard Keynes  published works on probability, but is best known as an economist.\", \"John Maynard Keynes\", \"1883-1946\", 1439], [736, 87, \"Helmut Wielandt  worked on finite groups and on finite and infinite permutation groups.\", \"Helmut Wielandt\", \"1910-2001\", 2124], [2404, 87, \"George Batchelor  was an Australian applied mathematician who worked in fluid dynamics.\", \"George Batchelor\", \"1920-2000\", 2393], [382, 87, \"Benjamin Banneker  was a black American who is best-known for his Astronomical Almanac.\", \"Benjamin Banneker\", \"1731-1806\", 369], [1724, 87, \"James Cassels  graduated from Edinburgh University and became a teacher at Ayr Academy.\", \"James Cassels\", \"1891-1980\", 1600], [1273, 87, \"Mineo Chini  was an Italian mathematician who worked on the foundations of mathematics.\", \"Mineo Chini\", \"1866-1933\", 1165], [1048, 87, \"\\u00c9mile Picard  worked in algebraic geometry as well as elasticity, heat and electricity.\", \"\\u00c9mile Picard\", \"1856-1941\", 982], [110, 87, \"Bartholomeo Pitiscus  was a Polish theologian who first coined the word  Trigonometry .\", \"Bartholomeo Pitiscus\", \"1561-1613\", 126], [2178, 88, \"Pao-Lu Hsu  was a Chinese mathematician who worked in probability theory and statistics.\", \"Pao Lu Hsu\", \"1910-1970\", 2138], [2169, 88, \"Joseph Doob  was an American mathematician who worked in probability and measure theory.\", \"Joseph Doob\", \"1910-2004\", 2128], [179, 88, \"Jan Stampioen  was a Dutch mathematician who published a work on spherical trigonometry.\", \"Jan Stampioen\", \"1610-1690\", 185], [697, 88, \"John Casey   was an Irish geometer best kown for his work on the geometry of the circle.\", \"John Casey\", \"1820-1891\", 670], [1224, 88, \"Wilhelm Wien  was a German physicist who won the Nobel prize for discovering the proton.\", \"Wilhelm Wien\", \"1864-1928\", 1126], [2566, 88, \"Adelard  was an English philosopher who translated Arabic mathematical works into Latin.\", \"Adelard\", \"1075-1160\", 10], [507, 88, \"August Crelle  was a German mathematician who founded an important mathematical journal.\", \"August Crelle\", \"1780-1855\", 487], [1513, 88, \"Marcel Grossmann   was a Swiss mathematician and a friend and collaborator  of Einstein.\", \"Marcel Grossmann\", \"1878-1936\", 1354], [1031, 88, \"Giovanni Battista Guccia  was an Italian mathematician who worked in algebraic geometry.\", \"Giovanni Guccia\", \"1855-1914\", 969], [1040, 88, \"Arnold Droz-Farny  was a Swiss mathematician best known for the Droz-Farny line theorem.\", \"Arnold Droz-Farny\", \"1856-1912\", 978], [2315, 88, \"Douglas Northcott  was an English mathematician best known for his work on ideal theory.\", \"Douglas Northcott\", \"1916-2005\", 2288], [1354, 88, \"Jurjen Ferdinand Koksma  was a Dutch mathematician who worked in analytic number theory.\", \"Jurjen Koksma\", \"1904-1964\", 1923], [974, 88, \"Adolf Weiler  was a Swiss mathematician. His research interests lay in Steiner geometry.\", \"Adolf Weiler\", \"1851-1916\", 912], [586, 88, \"Franz Neumann  worked on crystallography and other physical applications of mathematics.\", \"Franz Neumann\", \"1798-1895\", 561], [2156, 88, \"Cahit Arf  was a Turkish mathematician. He is known for the  Arf invariant  in topology.\", \"Cahit Arf\", \"1910-1997\", 2113], [2060, 88, \"Emanuels Grinbergs  was a Russian mathematician who worked in geometry and graph theory.\", \"Emanuels Grinbergs\", \"1911-1982\", 2147], [263, 88, \"Michel Rolle  was a French mathematician best known for the so-called  Rolle's theorem .\", \"Michel Rolle\", \"1652-1719\", 253], [1842, 88, \"Philip Franklin   was an American mathematician who worked in analysis and graph theory.\", \"Philip Franklin\", \"1898-1965\", 1753], [2089, 88, \"Arnold Scholz  was a German mathematician who proved important results in number theory.\", \"Arnold Scholz\", \"1904-1942\", 1904], [371, 88, \"Richard Price  was a Welsh congregational minister who made contributions to statistics.\", \"Richard Price\", \"1723-1791\", 358], [1381, 88, \"Marian Smoluchowski  was an Austrian physicist who was a pioneer of statistical physics.\", \"Marian Smoluchowski\", \"1872-1917\", 1255], [2919, 88, \"Jean-Louis Loday  wasa French mathematician whoo worked in the field of cyclic homology.\", \"Jean-Louis Loday\", \"1946-2012\", 2906], [638, 88, \"John Pratt  worked in India as a chaplain. He published works on the shape of the earth.\", \"John Pratt\", \"1809-1871\", 613], [850, 88, \"Ernst Abbe  was a German instument maker who made important improvements in lens design.\", \"Ernst Abbe\", \"1840-1905\", 801], [2109, 88, \"Marek Kuczma  was a Polish mathematician who worked in the area of functional equations.\", \"Marek Kuczma\", \"1935-1991\", 2772], [2749, 88, \"Frederick Almgren  was an American mathematician who worked in geometric measure theory.\", \"Frederick Justin Almgren\", \"1933-1997\", 2737], [1807, 88, \"Joseph Leonard Walsh  was an American mathematician who worked in the field of analysis.\", \"Joseph Walsh\", \"1895-1973\", 1680], [2911, 88, \"Saharon Shelah  is an Israeli mathematician who worked in America on mathematical logic.\", \"Saharon Shelah\", \"1945-\", 2898], [2609, 88, \"Joan Birman  is an American mathematician who worked in in braid theory and knot theory.\", \"Joan Sylvia Lyttle Birman\", \"1927-\", 2598], [336, 88, \"Johann Castillon  was an Italian mathematician and astronomer who wrote on the cardioid.\", \"Johann Castillon\", \"1704-1791\", 328], [595, 88, \"Antoine Cournot  was a French mathematician who was a pioneer of mathematical economics.\", \"Augustin Cournot\", \"1801-1877\", 570], [2055, 88, \"Jan Tinbergen  was a Dutch economist who was awarded the first Nobel Prize in Economics.\", \"Jan Tinbergen\", \"1903-1994\", 1882], [2592, 88, \"Benjamin Carlos de Lyra  was a Brazilian mathematician who worked in algebraic topology.\", \"Carlos Benjamin de Lyra\", \"1927-1974\", 2585], [1723, 88, \"Vinogradov  used trigonometric series to attack deep problems in analytic number theory.\", \"Ivan Matveevich Vinogradov\", \"1891-1983\", 1599], [2475, 88, \"Aleksei Dezin  was a Russian mathematician who worked on partial differential equations.\", \"Aleksei Alekseevich Dezin\", \"1923-2008\", 2459], [120, 89, \"Simon Mayr  was a German astronomer who may have observed Jupiter's moons before Galileo.\", \"Simon Mayr\", \"1573-1624\", 137], [694, 89, \"Ernest de Jonqui\\u00e8res  was a French naval officer who discovered many results in geometry.\", \"Ernest de Jonqui\\u00e8res\", \"1820-1901\", 667], [2753, 89, \"Ludvig Faddeev  was a  Russian mathematical physicist who worked in quantum field theory.\", \"Ludwig Faddeev\", \"1934-2017\", 2755], [1698, 89, \"Ren\\u00e9 Eug\\u00e8ne Gateaux  was a French mathematician who worked in the calculus of variations.\", \"Ren\\u00e9 Eug\\u00e8ne Gateaux\", \"1889-1914\", 1570], [206, 89, \"Claude Dechales  was a French Jesuit who published a widely used textbook on mathematics.\", \"Claude Dechales\", \"1621-1678\", 204], [2121, 89, \"Margaret Boyle  graduated from St Andrews and taught mathematics at Dalkeith High School.\", \"Margaret E Boyle\", \"1905-1995\", 1960], [2696, 89, \"Stephen Smale  received the Fields medal in  1966  for his work on differential geometry.\", \"Stephen Smale\", \"1930-\", 2686], [183, 89, \"Henry More  was an English philosopher of science whose ideas may have influenced Newton.\", \"Henry More\", \"1614-1687\", 190], [1999, 89, \"Mary Simpson  graduated from Edinburgh and then took up a post at Queen's College Dundee.\", \"Mary Simpson\", \"1901-1985\", 1814], [107, 89, \"Joao Baptista Lavanha  was a Portuguese engineer who wrote on mathematics and navigation.\", \"Jo\\u00e3o Baptista Lavanha\", \"1555-1624\", 123], [25, 89, \"Al-Khalili  was an Islamic astronomer who compiled extensive tables for astronomical use.\", \"Al-Khalili\", \"1320-1380\", 44], [2227, 89, \"C\\u00e2ndido Silva Dias  was a Brazilian mathematician who worked in analytic function theory.\", \"C\\u00e2ndido Silva Dias\", \"1913-1998\", 2204], [458, 89, \"Ruan Yuan  was a Chinese scholar who wrote biographies of astronomers and mathematicians.\", \"Ruan Yuan\", \"1764-1849\", 438], [2521, 89, \"Karl Aubert  was a Norwegian mathematician who researched mainly in the field of algebra.\", \"Karl Aubert\", \"1924-1990\", 2510], [2645, 89, \"Heinz Bauer  was a German mahematician who worked in measure theory and potential theory.\", \"Heinz Bauer\", \"1928-2002\", 2620], [378, 89, \"Paolo Frisi  was an Italian mathematician who wrote on geometry, mechanics and cosmology.\", \"Paolo Frisi\", \"1728-1784\", 365], [2964, 90, \"Stein Stromme  was a Norwegian mathematician best known for his work in algebraic geometry\", \"Stein Arild Stromme\", \"1951-2014\", 2948], [2863, 90, \"Linda Keen  is an American mathematician who is known for her work in hyperbolic geometry.\", \"Linda Goldway Keen\", \"1940-\", 2855], [2866, 90, \"Alan Day  was a Canadian mathematician who worked in lattice theory and universal algebra.\", \"Alan Day\", \"1941-1990\", 2858], [2189, 90, \"Boris Gnedenko  was a Soviet mathematician  best known for his work in probability theory.\", \"Boris Vladimirovich Gnedenko\", \"1912-1995\", 2172], [497, 90, \"Robert Adrain  was an Irishman who was one of the first mathematicians to work in America.\", \"Robert Adrain\", \"1775-1843\", 477], [2707, 90, \"Herbert Wilf  was an American mathematician who worked in combinatorics and graph theory. \", \"Herbert Wilf\", \"1931-2012\", 2697], [995, 90, \"Johann Heinrich Graf  was a Swiss mathematician who worked mainly on the Bessel functions.\", \"Johann Heinrich Graf\", \"1852-1918\", 939], [2154, 90, \"Werner Romberg  was a German mathematician and physicist. He worked in numerical analysis.\", \"Werner Romberg\", \"1909-2003\", 2111], [233, 90, \"Hendrik van Heuraet  was a Dutch mathematician who made some contributions to integration.\", \"Hendrik van Heuraet\", \"1634-1660\", 229], [1517, 90, \"Oliver Kellogg  was an American mathematician best known for his work on potential theory.\", \"Oliver Kellogg\", \"1878-1932\", 1358], [2391, 90, \"Wen-Tsun Wu  was a  Chinese mathematician who worked in topology and computer mathematics.\", \"Wen-Tsun Wu\", \"1919-2017\", 2380], [310, 90, \"Louis Castel  was a French mathematician who was a strong opponent of Newton's philosophy.\", \"Louis Castel\", \"1688-1757\", 301], [1840, 90, \"Yurii Dmitrievich Sokolov  was a Russian mathematician who worked on the  n -body problem.\", \"Yurii Sokolov\", \"1896-1971\", 1713], [1720, 90, \"Hans Reichenbach  was a German philosopher of science and proponent of logical empiricism.\", \"Hans Reichenbach\", \"1891-1953\", 1596], [1577, 90, \"Georges Valiron  was a French mathematician, best known for his contributions to analysis.\", \"Georges Valiron\", \"1884-1955\", 1455], [2950, 90, \"Zolt\\u00e1n Balogh  was a Hungarian-born mathematician, specialising in set-theoretic topology.\", \"Zolt\\u00e1n Balogh\", \"1953-2002\", 2954], [1942, 90, \"Brahmadeva  was an Indian mathematician who wrote a commentary on the work of Aryabhata I.\", \"Brahmadeva\", \"1060-1130\", 8], [2214, 90, \"Noel Slater  was an English mathematician who worked on the theory of chemical reactions. \", \"Noel Slater\", \"1912-1973\", 2191], [1297, 90, \"Charles Shirra Dougall  was a Scottish school teacher who became Rector of Dollar Academy.\", \"Charles Shirra Dougall\", \"1868-1930\", 1185], [2394, 90, \"Alfred Goldie  was an English mathematician who proved an important result in Ring Theory.\", \"Alfred Goldie\", \"1920-2005\", 2383], [373, 90, \"Franz Aepinus  was a German scientist who did important work on electricity and magnetism.\", \"Franz Aepinus\", \"1724-1802\", 360], [265, 90, \"Pierre Varignon  was a French mathematician who worked on graphical statics and mechanics.\", \"Pierre Varignon\", \"1654-1722\", 255], [2980, 90, \"Akos Seress  was a Hungarian mathematician specialising in combinatorics and group theory.\", \"Akos Seress\", \"1958-2013\", 2972], [1681, 90, \"Andrea Razmadze  was a Georgian mathematician who worked in in the calculus of variations.\", \"Andrei Razmadze\", \"1889-1929\", 1553], [1682, 90, \"Anton Sushkevich   was a Russian mathematician who worked on  group theory and semigroups.\", \"Anton Kazimirovich Suschkevich\", \"1889-1961\", 1554], [2488, 90, \"Enrico Magenes  was an Italian mathematician who worked on partial differential equations.\", \"Enrico Magenes\", \"1923-2010\", 2468], [1071, 90, \"Oskar Bolza  worked on function theory, integral equations and the calculus of variations.\", \"Oskar Bolza\", \"1857-1942\", 1002], [1902, 90, \"Timothy Gowers  won a Fields medal for his important contributions to functional analysis.\", \"Timothy Gowers\", \"1963-\", 2988], [2289, 90, \"John Tukey  introduced the Fast Fourier Transform and worked in other areas of Statistics.\", \"John Tukey\", \"1915-2000\", 2268], [646, 90, \"John James Waterston   was a Scottish physicist who worked in the kinetic theory of gases.\", \"John Waterston\", \"1811-1883\", 620], [1721, 90, \"Harold Jeffreys  was an English mathematician, statistician, geophysicist, and astronomer.\", \"Harold Jeffreys\", \"1891-1989\", 1597], [287, 90, \"John Keill  was a Scottish mathematician who acted as a propagator of Newton's philosophy.\", \"John Keill\", \"1671-1721\", 277], [352, 91, \"Thomas Fuller  was an African-born slave in America who was a prodigious mental calculator.\", \"Thomas Fuller\", \"1710-1790\", 338], [312, 91, \"Willem 'sGravesande  was a Dutch mathematician who expounded Newton's philosophy in Europe.\", \"Willem 'sGravesande\", \"1688-1742\", 303], [394, 91, \"Simon Lhuilier  was a Swiss mathematician who worked on analysis, topology and probability.\", \"Simon Lhuilier\", \"1750-1840\", 418], [2239, 91, \"Harry Pitt  was an Engish mathematician who worked in real analysis and probability theory.\", \"Harry Pitt\", \"1914-2005\", 2236], [202, 91, \"Michelangelo Ricci  was an Italian churchman who made some early applications of induction.\", \"Michelangelo Ricci\", \"1619-1682\", 200], [831, 91, \"Samarendra Nath Roy  was an Indian-born American mathematician and an applied statistician.\", \"Samarendra Nath Roy\", \"1906-1964\", 2011], [1312, 91, \"Benjamin Kagan  was a Russian and Soviet mathematician who woked on non-Euclidean geometry.\", \"Benjamin Fedorovich Kagan\", \"1869-1953\", 1206], [2087, 91, \"Alfred Leon Foster  was an American mathematician who worked on Boolean rings and algebras.\", \"Alfred Foster\", \"1904-1994\", 1902], [1909, 91, \"Al-Nasawi  was an Islamic mathematician who wrote summaries of some of Euclid's  Elements .\", \"al-Nasawi\", \"1010-1075\", 1], [2716, 91, \"Valentina Borok  was a Ukranian mathematician who worked in partial differential equations.\", \"Valentina Mikhailovna Borok\", \"1931-2004\", 2706], [2741, 91, \"Siobh\\u00e1n Vernon  was the first Irish-born woman to get a PhD in pure mathematics in Ireland.\", \"Siobh\\u00e1n Vernon\", \"1932-2002\", 2729], [1164, 91, \"Ruth Gentry   was a pioneering American woman mathematician. She worked mainly in geometry.\", \"Ruth Gentry\", \"1862-1917\", 1084], [2662, 91, \"Douglas Munn  was a Scottish mathematician who made important progress in semigroup theory.\", \"Douglas Munn\", \"1929-2008\", 2646], [2987, 91, \"Mikhail Lesokhin  wasa Russion mathematician whose research was mostly in semigroup theory.\", \"Mikhail Moiseevich Lesokhin\", \"1933-1998\", 2745], [1271, 91, \"James Pierpont  was an American mathematician who worked on the Galois theory of equations.\", \"James Pierpont\", \"1866-1938\", 1163], [1549, 91, \"Veblen  made important contributions to projective and differential geometry, and topology.\", \"Oswald Veblen\", \"1880-1960\", 1386], [1358, 91, \"Paul Epstein  was a German mathematician best-known for his contributions to number theory.\", \"Paul Epstein\", \"1871-1939\", 1241], [1685, 91, \"Edwin Hubble  was an American astronomer who first detected that the universe is expanding.\", \"Edwin Hubble\", \"1889-1953\", 1557], [141, 91, \"Pierre Vernier  was a French engineer best known for inventing the Vernier measuring scale.\", \"Pierre Vernier\", \"1584-1638\", 148], [2134, 91, \"Andr\\u00e9 Weil  was a French mathematician who worked on algebraic geometry and  number theory.\", \"Andr\\u00e9 Weil\", \"1906-1998\", 1976], [1829, 91, \"Heinz Pr\\u00fcfer  was a German mathematician who proved important results about abelian groups.\", \"Heinz Pr\\u00fcfer\", \"1896-1934\", 1700], [2656, 91, \"Alexei Kostrikin  was a Russian mathematician who worked in algebra and algebraic geometry.\", \"Aleksei Kostrikin\", \"1929-2000\", 2640], [2002, 91, \"Nina Karlovna Bari  was a Russian mathematician known for her work on trigonometric series.\", \"Nina Bari\", \"1901-1961\", 1817], [413, 91, \"Johannes Tetens  was a Danish physicist who made contributions to philosophy and insurance.\", \"Johannes Tetens\", \"1736-1807\", 387], [1353, 91, \"John Semple  was a Irish mathematician whose most important work was in Algebraic geometry.\", \"John Semple\", \"1904-1985\", 1922], [1967, 91, \"Kosaku Yosida  was a Japanese mathematician who worked in the field of functional analysis.\", \"Kosaku Yosida\", \"1909-1990\", 2100], [2650, 91, \"Martin Davis  was an American mathematician, known for his work on Hilbert's tenth problem.\", \"Martin Davis\", \"1928-2023\", 2634], [2774, 92, \"Yakov Grigorevich Sinai  is a Russian mathematician known for his work on dynamical systems.\", \"Yakov Grigorevich Sinai\", \"1935-\", 2777], [2358, 92, \"Irving Segal  was an American mathematician known for work on theoretical quantum mechanics.\", \"Irving Segal\", \"1918-1998\", 2341], [585, 92, \"\\u00c9tienne Bobillier  is best known for his work on polars of curves and of algebraic surfaces.\", \"\\u00c9tienne Bobillier\", \"1798-1840\", 560], [659, 92, \"Franc Mo\\u010dnik  was a Slovenian mathematician, pedagogue and writer of mathematical textbooks.\", \"Franc Mocnik\", \"1814-1892\", 633], [564, 92, \"Bernt Holmboe  was a Norwegian mathematician best known as the teacher of Niels Henrik Abel.\", \"Bernt Holmboe\", \"1795-1850\", 543], [1658, 92, \"Louis Antoine   was a French mathematician famous for his invention of  Antoine's necklace .\", \"Louis Antoine\", \"1888-1971\", 1538], [1242, 92, \"Niels Nielsen  was a Danish mathematician who worked on special functions and number theory.\", \"Niels Nielsen\", \"1865-1931\", 1145], [447, 92, \"Antoine Parseval  was a French mathematician best known for his theorem in Fourier analysis.\", \"Antoine Parseval\", \"1755-1836\", 428], [2014, 92, \"Edna Ernestine Kramer Lassar  was an American mathematician and author of mathematics books.\", \"Edna Kramer\", \"1902-1984\", 1834], [649, 92, \"Urbain Le Verrier  is best known for the calculations which led to the discovery of Neptune.\", \"Urbain Le Verrier\", \"1811-1877\", 623], [2743, 92, \"Taira Honda  was a Japanese mathematician who made important contributions to number theory.\", \"Taira Honda\", \"1932-1975\", 2731], [2544, 92, \"Henry Dye  was an American mathematician who worked in operator algebras and ergodic theory.\", \"Henry Dye\", \"1926-1986\", 2555], [1035, 92, \"Louis Raffy  was a French mathematician who published extensively on infinitesimal geometry.\", \"Louis Raffy\", \"1855-1910\", 973], [478, 92, \"Jean Nicolas Pierre Hachette  was a French mathematician who worked on descriptive geometry.\", \"Jean Nicolas Pierre Hachette\", \"1769-1834\", 458], [2074, 92, \"W\\u0142adys\\u0142aw Orlicz  was a Polish mathematician who worked in functional analysis and topology.\", \"W\\u0142adys\\u0142aw Orlicz\", \"1903-1990\", 1898], [803, 92, \"D R Kaprekar  was a largely self-taught Indian mathematician who worked in in number theory.\", \"D R Kaprekar\", \"1905-1986\", 1942], [698, 92, \"Victor Puiseux  worked on elliptic functions and studied computational methods in astronomy.\", \"Victor Puiseux\", \"1820-1883\", 671], [1504, 92, \"Willard Van Orman Quine  was an American philosopher and logician in the analytic tradition.\", \"Willard Van Quine\", \"1908-2000\", 2081], [2861, 92, \"Franciszek Szafraniec  is a Polish mathematician best known for his work in operator theory.\", \"Franciszek Szafraniec\", \"1940-\", 2853], [1857, 92, \"         Joseph Larmor  worked on electricity, dynamics and\\\\n          thermodynamics.       \", \"Joseph Larmor\", \"1857-1942\", 1000], [204, 92, \"Nicolaus Mercator  was a German mathematician best known for his series for log (1  +  x ) .\", \"Nicolaus Mercator\", \"1620-1687\", 202], [452, 92, \"Jean Chazy   was a French mathematician and astronomer who worked on the three body problem.\", \"Jean Chazy\", \"1882-1955\", 1415], [433, 92, \"William Trail  was a Scottish mathematician who became Professor of Mathematics at Aberdeen.\", \"William Trail\", \"1746-1831\", 406], [2466, 92, \"Jan Kalicki  was a Polish mathematician who worked on logical matrices and equational logic.\", \"Jan Kalicki\", \"1922-1953\", 2450], [976, 92, \"Axel Harnack  was an Estonian-born German mathematician who contributed to potential theory.\", \"Axel Harnack\", \"1851-1888\", 914], [2515, 92, \"Arnljot H\\u00f8yland  was a Norwegian mathematical statistician who worked in reliability theory.\", \"Arnljot H\\u00f8yland\", \"1924-2002\", 2494], [2762, 92, \"Hemchandra  was a Sanskrit scholar who published works on science, languages and philosophy.\", \"Hemchandra\", \"1089-1173\", 11], [1601, 92, \"John McWhan  studied at Glasgow and G\\u00f6ttingen. He returned to a post at Glasgow University. \", \"John McWhan\", \"1885-1943\", 1476], [386, 92, \"J\\u00e9r\\u00f4me Lalande  was a French astronomer who made important measurements of the Solar System.\", \"J\\u00e9r\\u00f4me Lalande\", \"1732-1807\", 373], [2103, 93, \"Hubert Linfoot  was a British mathematician who worked in optics as well as pure mathematics.\", \"Hubert Linfoot\", \"1905-1982\", 1951], [1905, 93, \"Friedrich Bachmann   was a German mathematician who specialised in geometry and group theory.\", \"Friedrich Bachmann\", \"1909-1982\", 2092], [1818, 93, \"Tibor Rad\\u00f3  was a Hungarian mathematician best known for his solution to the Plateau Problem.\", \"Tibor Rad\\u00f3\", \"1895-1965\", 1691], [170, 93, \"John Greaves  was an English mathematician who was interested in measuring ancient monuments.\", \"John Greaves\", \"1602-1652\", 176], [2419, 93, \"Roman Ingarden  was a Polish physicist who worked mainly in optics and statistical mechanics.\", \"Roman Ingarden\", \"1920-2011\", 2405], [884, 93, \"B\\u00f8rge Jessen  was a Danish mathematician best known for his work in analysis and in geometry.\", \"B\\u00f8rge Jessen\", \"1907-1993\", 2019], [1092, 93, \"Ivan Vsevolodovich Meshchersky  was a Russian mathematician famous for his work on mechanics.\", \"Ivan Vsevolodovich Meshchersky\", \"1859-1935\", 1022], [1350, 93, \"Jacob Levitzk  was a Ukrainian-born Israeli mathematician who worked on noncommutative rings.\", \"Jacob Levitzki\", \"1904-1956\", 1919], [2600, 93, \"Heinrich-Wolfgang Leopoldt  was a German mathematician who worked in algebraic number theory.\", \"Heinrich-Wolfgang Leopoldt\", \"1927-2011\", 2594], [2717, 93, \"Vera Pless  was an American mathematician who specialized in combinatorics and coding theory.\", \"Vera Pless\", \"1931-2020\", 2707], [1832, 93, \"Leopold \\\"Alan\\\" Pars  was a British applied mathematician who is best known for his textbooks.\", \"Leopold Pars\", \"1896-1985\", 1703], [1277, 93, \"William McFadden Orr  was an Irish mathematician who worked on thermodynamics and fluid flow.\", \"William McFadden Orr\", \"1866-1934\", 1168], [2438, 93, \"Horst Tietz  was a German mathematician who worked primarily in the field of function theory.\", \"Horst Tietz\", \"1921-2012\", 2424], [1846, 93, \"Douglas Hartree  was an English mathematician and physicist who worked in numerical analysis.\", \"Douglas Hartree\", \"1897-1958\", 1718], [2305, 93, \"Tibor Szele  was a  Hungarian mathematician who worked in combinatorics and abstract algebra.\", \"Tibor Szele\", \"1918-1955\", 2356], [560, 93, \"Franz Taurinus  was a German mathematician best known for his work on non-Euclidean geometry.\", \"Franz Adolph Taurinus\", \"1794-1874\", 539], [9, 93, \"Guo Shoujing  was a Chinese astronomer who worked on spherical trigonometry and the calendar.\", \"Guo Shoujing\", \"1231-1316\", 31], [1448, 93, \"Ugo Amaldi  was an Italian mathematician who worked in the fields of geometry and Lie groups.\", \"Ugo Amaldi\", \"1875-1957\", 1304], [203, 93, \"Jean Picard  was a French astronomer who increased the accuracy of astronomical observations.\", \"Jean Picard\", \"1620-1682\", 201], [1634, 93, \"Johann Radon  worked on the calculus of variations, differential geometry and measure theory.\", \"Johann Radon\", \"1887-1956\", 1515], [1609, 93, \"Pauline Sperry  was an American mathematician who worked in projective differential geometry.\", \"Pauline Sperry\", \"1885-1967\", 1484], [2653, 93, \"Paul Butzer  is a German mathematician working in approximation theory and harmonic analysis.\", \"Paul Butzer\", \"1928-\", 2637], [2240, 93, \"Jacques Feldbau  was a French mathematician who worked on differential geometry and topology.\", \"Jacques Feldbau\", \"1914-1945\", 2237], [1281, 93, \"Gury Vasilievich Kolosov  was a Russian mathematician who worked on the theory of elasticity.\", \"Gury Vasilievich Kolosov\", \"1867-1936\", 1173], [2349, 93, \"Phyllis Nicolson  was an English mathematician best known for her work in numerical analysis.\", \"Phyllis Nicolson\", \"1917-1968\", 2327], [1647, 93, \"Bibhutibhushan Datta , born in what is now Banglsdesh, was a historian of Indian mathematics.\", \"Bibhutibhushan Datta\", \"1888-1958\", 1527], [1205, 93, \"Paul Painlev\\u00e9  worked on differential equations. He served twice as prime-minister of France.\", \"Paul Painlev\\u00e9\", \"1863-1933\", 1113], [2647, 93, \"Ioan James  is an English mathematician who works in topology and the history of mathematics.\", \"Ioan James\", \"1928-\", 2622], [1901, 94, \"Richard Taylor  is a British mathematician who works in America in the field of number theory.\", \"Richard Taylor\", \"1962-\", 2987], [1641, 94, \"Thoralf Skolem  was a Norwegian mathematician who worked in mathematical logic and set theory.\", \"Thoralf Skolem\", \"1887-1963\", 1522], [2754, 94, \"Michael Artin  is an American mathematician known for his contributions to algebraic geometry.\", \"Michael Artin\", \"1934-\", 2756], [464, 94, \"Timofei Fedorovic Osipovsky  was a Russian mathematician who wrote some influential textbooks.\", \"Timofei Fedorovic Osipovsky\", \"1765-1832\", 444], [1952, 94, \"         Jan Popken  was a Dutch mathematician specialising in\\\\n          number theory.       \", \"Jan Popken\", \"1905-1970\", 1952], [568, 94, \"Louis Richard  was a French mathematician who is best-known as the teacher of Evariste Galois.\", \"Louis Richard\", \"1795-1849\", 547], [2612, 94, \"Masayoshi Nagata  was a Japanese mathematician who worked in the field of commutative algebra.\", \"Masayoshi Nagata\", \"1927-2008\", 2601], [2876, 94, \"Lenore Blum  is an American mathematician who has made important advances in computer science.\", \"Lenore Blum\", \"1942-\", 2871], [650, 94, \"Adolph G\\u00f6pel   was a German mathematician who wrote an early paper on hyperelliptic functions.\", \"Adolph G\\u00f6pel\", \"1812-1847\", 624], [1116, 94, \"Boris Yakovlevich Levin  was a Soviet mathematician who made contributions to function theory.\", \"Boris Yakovlevich Levin\", \"1906-1993\", 1978], [1903, 94, \"Art\\u016bras Dubickas  is a Lithuanian mathematician who proved important results in number theory.\", \"Art\\u016bras Dubickas\", \"1964-\", 2989], [2547, 94, \"Friedrich Hirzebruch  was a German mathematician who made important contributions to topology.\", \"Friedrich Hirzebruch\", \"1927-2012\", 2589], [480, 94, \"Martin Bartels  was a German mathematician best known as the teacher of Gauss and Lobachevsky.\", \"Martin Bartels\", \"1769-1836\", 460], [796, 94, \"Ott-Heinrich Keller  was a German mathematician who worked on algebraic geometry and topology.\", \"Ott-Heinrich Keller\", \"1906-1990\", 2007], [2596, 94, \"Friedrich Horn  was an Austrian mathematician who applied mathematics to chemical engineering.\", \"Friedrich Horn\", \"1927-1978\", 2590], [2500, 94, \"Kuo-Tsai Chen  was a Chinese-born mathematician who worked in algebraic topology and analysis.\", \"Kuo-Tsai Chen\", \"1923-1987\", 2480], [2829, 94, \"C P Ramanujam  was an Indian mathematician who worked in number theory and algebraic geometry.\", \"Chidambaram Padmanabhan Ramanujam\", \"1938-1974\", 2822], [2684, 94, \"Jacques Tits  was a Belgium-born French mathematician who worked on group theory and geometry.\", \"Jacques Tits\", \"1930-2021\", 2674], [2715, 94, \"Stanis\\u0142aw Knapowski  was a Polish mathematician who worked on prime numbers and number theory.\", \"Stanis\\u0142aw Knapowski\", \"1931-1967\", 2705], [425, 94, \"Anast\\u00e1cio da Cunha  was a Portuguese mathematician who wrote an  encyclopaedia of mathematics.\", \"Anast\\u00e1cio da Cunha\", \"1744-1787\", 398], [878, 94, \"Enrico D'Ovidio  was an Italian mathematician and politician who worked in algebraic geometry.\", \"Enrico D'Ovidio\", \"1843-1933\", 828], [2756, 94, \"Paul-Andr\\u00e9 Meyer  was a French mathematician who worked in the theory of stochastic processes.\", \"Paul-Andr\\u00e9 Meyer\", \"1934-2003\", 2758], [916, 94, \"Eugenio Bertini  was an Italian mathematician who worked in projective and algebraic geometry.\", \"Eugenio Bertini\", \"1846-1933\", 860], [1683, 94, \"Balthasar van der Pol  was a Dutch physicist famous for the non-linear  van der Pol equation .\", \"Balthasar van der Pol\", \"1889-1959\", 1555], [2166, 94, \"G\\u00e9za Gr\\u00fcnwald  was a Hungarian mathematician who worked on analysis. He died in the Holocaust.\", \"G\\u00e9za Gr\\u00fcnwald\", \"1910-1942\", 2123], [2549, 95, \"John Shepherdson  was a English mathematician who worked in ring theory and mathematical logic.\", \"John Shepherdson\", \"1926-2015\", 2567], [1385, 95, \"Wilhelm Ahrens  was a German mathematician best known for his work on recreational mathematics.\", \"Wilhelm Ahrens\", \"1872-1927\", 1259], [980, 95, \"Emanuel Czuber  was a Czech mathematician who studied was probability theory and related areas.\", \"Emanuel Czuber\", \"1851-1925\", 918], [1703, 95, \"Georg Feigl  was a German mathematician who worked in the foundations of geometry and topology.\", \"Georg Feigl\", \"1890-1945\", 1578], [2321, 95, \"George Mackey  was an American mathematician who worked on the representation theory of groups.\", \"George Mackey\", \"1916-2006\", 2294], [2311, 95, \"Albrecht Fr\\u00f6hlich  was a German mathematician who made important contributions to group theory.\", \"Albrecht Fr\\u00f6hlich\", \"1916-2001\", 2284], [696, 95, \"Isaac Todhunter  is best known for his textbooks and his writing on the history of mathematics.\", \"Isaac Todhunter\", \"1820-1884\", 669], [1021, 95, \"Percy MacMahon  was a Maltese-born mathematician who worked in number theory and combinatorics.\", \"Percy MacMahon\", \"1854-1929\", 963], [636, 95, \"Hermann Grassmann  is chiefly remembered for his development of a general calculus for vectors.\", \"Hermann Grassmann\", \"1809-1877\", 611], [1028, 95, \"Charles Boys  was an English physicist, known for his careful and innovative experimental work.\", \"Charles Boys\", \"1855-1944\", 966], [462, 95, \"Pierre-Simon Girard  was a French mathematician and engineer. He published works on fluid flow.\", \"Pierre-Simon Girard\", \"1765-1836\", 442], [1493, 95, \"Arthur Coble   was an American mathematician who worked  on finite geometries and group theory.\", \"Arthur Coble\", \"1878-1966\", 1340], [1707, 95, \"Jakob Nielsen  was a Danish mathematician best known for his work on automorphisms of surfaces.\", \"Jakob Nielsen\", \"1890-1959\", 1583], [1231, 95, \"Charles Cailler  was a Swiss mathematician who worked on differential equations and kinematics.\", \"Charles Cailler\", \"1865-1922\", 1133], [2585, 95, \"Walter Hayman  was a German born British mathematician best known for work in complex analysis.\", \"Walter Hayman\", \"1926-2020\", 2577], [1384, 95, \"Volodymyr Levytsky   was a Ukrainian mathematician who studied functions of a complex variable.\", \"Volodymyr Levytsky\", \"1872-1956\", 1258], [2468, 95, \"Lazar Gluskin  was a Ukranian mathematician who worked on semigroups of linear transformations.\", \"Lazar Matveevich Gluskin\", \"1922-1985\", 2452], [1948, 95, \"Pedro Puig Adam  was a Spanish mathematician and engineer who worked in relativistic mechanics.\", \"Pedro Puig Adam\", \"1900-1960\", 1796], [1786, 95, \"Einar Carl Hille  was an American mathematician who worked on analysis and functional analysis.\", \"Einar Carl Hille\", \"1894-1980\", 1654], [2224, 95, \"Alessandro Faedo  was an Italian mathematician and politician who worked in numerical analysis.\", \"Alessandro Faedo\", \"1913-2001\", 2201], [674, 95, \"Rudolf Wolf   was a Swiss astronomer and mathematician best known for his research on sunspots.\", \"Rudolf Wolf\", \"1816-1893\", 647], [969, 95, \"Ovide Arino  was a French mathematician who worked in differential equations and Banach spaces.\", \"Ovide Arino\", \"1947-2003\", 2915], [1662, 95, \"Deane Montgomery  was an American mathematician who worked in algebraic and geometric topology.\", \"Deane Montgomery\", \"1909-1992\", 2087], [2800, 95, \"Richard Schelp  was an American mathematician who researched in graph theory and combinatorics.\", \"Richard Schelp\", \"1936-2010\", 2793], [2216, 96, \"Pierre Lelong  was a French mathematician who worked in the theory of several complex variables.\", \"Pierre Lelong\", \"1912-2011\", 2193], [2791, 96, \"Wolfgang Schmidt  is an Austrian mathematician who did his most important work in number theory.\", \"Wolfgang Schmidt\", \"1933-\", 2749], [2492, 96, \"Gloria Olive  was an American mathematician who worked on on applications of generalised powers.\", \"Gloria Olive\", \"1923-2006\", 2472], [537, 96, \"Georg Simon Ohm  was a German mathematician best known for  Ohm's Law  on electrical resistance.\", \"Georg Simon Ohm\", \"1789-1854\", 516], [1796, 96, \"Satyendranath Bose  was an Indian mathematician who did important work in statistical mechanics.\", \"Satyendranath Bose\", \"1894-1974\", 1666], [64, 96, \"Oronce Fine  was a French mathematician who published a major work on mathematics and astronomy.\", \"Oronce Fine\", \"1494-1555\", 81], [728, 96, \"Kirchhoff  was a mathematical physicist best known for his laws on the flow of electric current.\", \"Gustav Kirchhoff\", \"1824-1887\", 699], [2295, 96, \"Lee  Lorch  was an American mathematician who was an early civil rights activist, and communist.\", \"Lee Lorch\", \"1915-2014\", 2274], [1484, 96, \"James Jeans  worked on astronomy as well as thermodynamics, heat and other aspects of radiation.\", \"James Jeans\", \"1877-1946\", 1331], [2029, 96, \"Pascual Jordan  was a German scientist who worked in quantum mechanics and quantum field theory.\", \"Pascual Jordan\", \"1902-1980\", 1849], [1395, 96, \"Isabel Maddison  was an English mathematician best known for her work on differential equations.\", \"Isabel Maddison\", \"1869-1950\", 1210], [1984, 96, \"Kiyoshi Oka  was a Japanese mathematician who worked in the theory of several complex variables.\", \"Kiyoshi Oka\", \"1901-1978\", 1809], [279, 96, \"Giovanni Saccheri  was an Italian Jesuit who did important early work on non-euclidean geometry.\", \"Giovanni Saccheri\", \"1667-1733\", 269], [2613, 96, \"Mikhail Postnikov  was a Soviet mathematician who worked in algebraic and differential topology.\", \"Mikhail Mikhailovich Postnikov\", \"1927-2004\", 2602], [556, 96, \"Jakob Kulik  was a Ukranian-born mathematician who wrote textbooks on mathematics and mechanics.\", \"Jakob Kulik\", \"1793-1863\", 535], [1568, 96, \"Denjoy  was a French mathematician who did outstanding work on the functions of a real variable.\", \"Arnaud Denjoy\", \"1884-1974\", 1445], [28, 96, \"Narayana  was an Indian mathematician who wrote on arithmetic following the work of Bhaskara II.\", \"Narayana\", \"1340-1400\", 47], [2249, 96, \"Mary Cannell  was an English mathematician and historian who worked extensively on George Green.\", \"Mary Cannell\", \"1913-2000\", 2215], [1132, 96, \"Hermann Arthur Jahn  was an English scientist who worked  on quantum mechanics and group theory.\", \"Hermann Arthur Jahn\", \"1907-1979\", 2032], [1004, 96, \"Richard Fuchs  was a German mathematician who worked on differential equations and aerodynamics.\", \"Richard Fuchs\", \"1873-1944\", 1273], [879, 96, \"Gaston Tarry  was a French combinatorialist whose best-known work is a method for solving mazes.\", \"Gaston Tarry\", \"1843-1913\", 829], [1090, 96, \"Georges Humbert   was a French mathematician who worked on geometry and hyperelliptic functions.\", \"Georges Humbert\", \"1859-1921\", 1020], [2067, 96, \"Sydney Goldstein  was a British mathematician best known for his contribution to fluid dynamics.\", \"Sydney Goldstein\", \"1903-1989\", 1892], [2880, 96, \"Stephen Rallis  was an American mathematician who worked on the theory of group representations.\", \"Steve Rallis\", \"1942-2012\", 2875], [370, 96, \"Nicole-Reine Lepaute  was a French noblewoman who helped Lalande with astronomical calculations.\", \"Nicole-Reine Etable de Labri\\u00e8re\", \"1723-1788\", 357], [195, 96, \"Wilhelm Specht  was a German mathematician who in worked group theory and representation theory.\", \"Wilhelm Specht\", \"1907-1985\", 2045], [294, 96, \"Privat de Moli\\u00e8res  was a French mathematician who argued against Newton in favour of Descartes.\", \"Joseph Privat de Moli\\u00e8res\", \"1677-1742\", 284], [2808, 97, \"David Fowler  was an English mathematician who is best known as a historian of Greek mathematics.\", \"David Fowler\", \"1937-2004\", 2802], [396, 97, \"Naonobu Ajima  was a Japanese mathematician and astronomer who developed a theory of integration.\", \"Naonobu Ajima\", \"1732-1798\", 375], [1966, 97, \"Karl-Heinrich Weise  was a German mathematician who worked on differential geometry and topology.\", \"Karl Heinrich Weise\", \"1909-1990\", 2099], [1990, 97, \"Theodor Estermann   was a German mathematician who worked in the field of analytic number theory.\", \"Theodor Estermann\", \"1902-1991\", 1855], [2557, 97, \"Hans-J\\u00fcrgen Hoehnke  was a German mathematician, born in what is now Poland, who studied algebra.\", \"Hans-J\\u00fcrgen Hoehnke\", \"1925-2007\", 2531], [2846, 97, \"Carlo Cercignani  was an Italian mathematician known for his work on the kinetic theory of gases.\", \"Carlo Cercignani\", \"1939-2010\", 2839], [188, 97, \"Seth Ward  was an English mathematician and astronomer and a founder-member of the Royal Society.\", \"Seth Ward\", \"1617-1689\", 195], [2569, 97, \"Richard Kadison  was an American mathematician who contributed to the study of operator algebras.\", \"Richard Kadison\", \"1925-2018\", 2543], [2935, 97, \"Daniel Rudolph  was an American mathematician who worked in ergodic theory and dynamical systems.\", \"Daniel Rudolph\", \"1949-2010\", 2930], [2948, 97, \"Vaughan Jones  is a New Zealand mathematician who won a Fields Medal for his work on Knot theory.\", \"Vaughan Jones\", \"1952-2020\", 2952], [1639, 97, \"Simion Stoilow  was a Romanian mathematician, creator of the Romanian school of complex analysis.\", \"Simion Stoilow\", \"1887-1961\", 1520], [958, 97, \"John Hopkinson  was an English mathematician and engineer who applied mathematics to electricity.\", \"John Hopkinson\", \"1849-1898\", 897], [576, 97, \"Jean Claude Saint-Venant  worked mainly on mechanics, elasticity, hydrostatics and hydrodynamics.\", \"Jean Claude Saint-Venant\", \"1797-1886\", 556], [1584, 97, \"Otto Sz\\u00e1sz  was a Hungarian mathematician who worked on real analysis, especially Fourier series.\", \"Otto Sz\\u00e1sz\", \"1884-1952\", 1460], [1557, 97, \"George Waddel Snedecor  was an American mathematician and statistician who worked on correlation.\", \"George Waddel Snedecor\", \"1881-1974\", 1395], [2539, 97, \"Jaroslav H\\u00e1jek  was a Czech mathematician who worked in theoretical and nonparametric statistics.\", \"Jaroslav H\\u00e1jek\", \"1926-1974\", 2561], [1531, 97, \"Edwin Wilson   was an American mathematician and statistician who worked in many different areas.\", \"Edwin Wilson\", \"1879-1964\", 1368], [297, 97, \"Pierre R\\u00e9mond de Montmort  was a French mathematician who wrote an important work on probability.\", \"Pierre R\\u00e9mond de Montmort\", \"1678-1719\", 287], [469, 97, \"Am\\u00e9lie Harlay  was a French astronomer who published navigational tables and catalogues of stars.\", \"Am\\u00e9lie Harlay\", \"1768-1832\", 449], [2655, 97, \"Richard Varga  was an American mathematician who worked in numerical analysis and linear algebra.\", \"Richard Varga\", \"1928-2022\", 2639], [35, 97, \"Al-Umawi  was a Spanish-born Islamic mathematician who wrote works on mensuration and arithmetic.\", \"Al-Umawi\", \"1400-1489\", 54], [1764, 97, \"Frank Harary  was an American mathematician known as one of the \\\"fathers\\\" of modern graph theory.\", \"Frank Harary\", \"1921-2005\", 2421], [1435, 97, \"Ernst Fischer  is best known for the Riesz-Fischer theorem in the theory of Lebesgue integration.\", \"Ernst Fischer\", \"1875-1954\", 1291], [66, 97, \"Christoff Rudolff  was a German mathematician whose book  Coss  is the first German algebra book.\", \"Christoff Rudolff\", \"1499-1543\", 83], [2727, 97, \"Hyman Bass  is an American mathematician, known for work in algebra and in mathematics education.\", \"Hyman Bass\", \"1932-\", 2715], [1830, 97, \"Ivo Lah  was a Slovenian mathematician and actuary who worked in both mathematics and statistics.\", \"Ivo Lah\", \"1896-1979\", 1701], [621, 97, \"William Rowan Hamilton  was an Irish astronomer and mathematician who discovered the quaternions.\", \"William Rowan Hamilton\", \"1805-1865\", 596], [2128, 97, \"Sigekatu Kuroda  was a Japanese mathematician who worked in number theory and mathematical logic.\", \"Sigekatu Kuroda\", \"1905-1972\", 1967], [2139, 97, \"Edwin Ford Beckenbach  was an American mathematician best known for for his work on inequalities.\", \"Edwin Beckenbach\", \"1906-1982\", 1985], [705, 97, \"Philipp  von Seidel  was a German mathematician who worked on dioptics and mathematical analysis.\", \"Philipp von Seidel\", \"1821-1896\", 678], [1788, 97, \"Harry Schmidt  was a German mathematician who wrote on the application of mathematics to physics.\", \"Harry Schmidt\", \"1894-1951\", 1656], [1780, 97, \"Petre Sergescu  was a Romanian mathematician important in the development of sciences in Romania.\", \"Petre Sergescu\", \"1893-1954\", 1644], [2414, 98, \"Jean-Louis Koszul  was a French mathematician who worked in geometry. He was a member of Bourbaki.\", \"Jean-Louis Koszul\", \"1921-2018\", 2426], [1250, 98, \"David Gibb  graduated from Edinburgh University and went on to become a lecturer and reader there.\", \"David Gibb\", \"1883-1946\", 1430], [1798, 98, \"Jacques Dixmier  is a French mathematician who worked on  C*-algebras and other operator algebras.\", \"Jacques Dixmier\", \"1924-\", 2505], [1585, 98, \"Philipp Frank  was an Austrian-born physicist, mathematician and philosopher who moved to America.\", \"Philipp Frank\", \"1884-1966\", 1461], [1774, 98, \"Jakov Il'ich Frenkel  was a Russian physicist who worked in the field of condensed matter physics.\", \"Jacov Il'ich Frenkel\", \"1894-1952\", 1659], [346, 98, \"Alfred H Clifford  was an American mathematician who worked in group theory and  semigroup theory.\", \"Alfred Hoblitzelle Clifford\", \"1908-1992\", 2049], [994, 98, \"Giovanni Frattini  was an Italian mathematician who made important  contributions to group theory.\", \"Giovanni Frattini\", \"1852-1925\", 938], [1306, 98, \"Louis Couturat  was a French mathematician who worked on logic and the foundations of mathematics.\", \"Louis Couturat\", \"1868-1914\", 1200], [1826, 98, \"William Moser  was a Canadian mathematician who worked in combinatorial geometry and group theory.\", \"William Moser\", \"1927-2009\", 2606], [299, 98, \"Gabriele Manfredi  was an Italian mathematician who was an early worker on differential equations.\", \"Gabriele Manfredi\", \"1681-1761\", 290], [2503, 98, \"Peter Henrici  was a Swiss mathematician best known who worked in the field of numerical analysis.\", \"Peter Henrici\", \"1923-1987\", 2483], [2445, 98, \"Jonas Kubilius  was a Lithuanian mathematician who worked in probability theory and number theory.\", \"Jonas Kubilius\", \"1921-2011\", 2428], [1797, 98, \"Warren Weaver  was an American mathematician famous as one of the pioneers of machine translation.\", \"Warren Weaver\", \"1894-1978\", 1668], [874, 98, \"Otto Stolz   was an Austrian mathematician who worked on mathematical analysis and infinitesimals.\", \"Otto Stolz\", \"1842-1905\", 824], [1106, 98, \"Herman Hollerith  was the inventor of the punched card system which predated electronic computers.\", \"Herman Hollerith\", \"1860-1929\", 1036], [487, 98, \"Nathaniel Bowditch  was an American mathematician who published works on navigation and astronomy.\", \"Nathaniel Bowditch\", \"1773-1838\", 467], [2105, 98, \"Hitoshi Kumano-Go  was a Japanese mathematician who specialised in partial differential equations.\", \"Hitoshi Kumano-Go\", \"1935-1982\", 2768], [681, 98, \"Joel E Hendricks  was an American mathematician important as the founder of  The Analyst  journal.\", \"Joel E Hendricks\", \"1818-1893\", 654], [223, 98, \"Jonas Moore  was an English man of science important for his support of mathematics and astronomy.\", \"Jonas Moore\", \"1627-1679\", 219], [147, 98, \"\\u00c9tienne Pascal  was a French lawyer and amateur mathematician. He was the father of Blaise Pascal.\", \"\\u00c9tienne Pascal\", \"1588-1651\", 153], [2021, 98, \"Hubert Stanley Wall  was an American mathematician who worked in the field of continued fractions.\", \"Hubert Wall\", \"1902-1971\", 1841], [2353, 98, \"Bill Tutte  was an English mathematician best known for his work on code-breaking in World War II.\", \"William Tutte\", \"1917-2002\", 2331], [2230, 98, \"Giuseppe Pompilj  was an Italian mathematician who worked in geometry and mathematical statistics.\", \"Giuseppe Pompilj\", \"1913-1968\", 2207], [2246, 98, \"Jan Mikusi\\u0144ski  was a Polish mathematician known for his pioneering work in mathematical analysis.\", \"Jan Mikusi\\u0144ski\", \"1913-1987\", 2212], [2629, 98, \"Louis Auslander  was an American mathematician who worked in both in pure and applied mathematics.\", \"Louis Auslander\", \"1928-1997\", 2631], [1351, 98, \"Jerzy S\\u0142upecki  was a Chinese-born Polish mathematician who made important contributions to logic.\", \"Jerzy S\\u0142upecki\", \"1904-1987\", 1920], [2703, 98, \"Czes\\u0142aw Olech  was a Polish mathematician who worked in differential equations and control theory.\", \"Czes\\u0142aw Olech\", \"1931-2015\", 2693], [2030, 98, \"Paul Dirac  is famous as the creator of the complete theoretical formulation of quantum mechanics.\", \"Paul Dirac\", \"1902-1984\", 1850], [2066, 98, \"Stephen Bosanquet  was an English mathematician who worked in analysis, especially Fourier series.\", \"Stephen Bosanquet\", \"1903-1984\", 1891], [2868, 99, \"Derek Waller  was an English mathematician who worked in category theory, algebra and graph theory.\", \"Derek Waller\", \"1941-1978\", 2860], [2929, 99, \"Jack Carr  was a Scottish mathematician who worked in differential equations and dynamical systems.\", \"John Carr\", \"1948-2016\", 2923], [1536, 99, \"Peter Ramsay  graduated from Glasgow University and taught at George Watson's School in Edinburgh. \", \"Peter Ramsay\", \"1879-1926\", 1373], [2259, 99, \"\\u00c5ke Pleijel  was a Swedish mathematician who worked on differential equations and potential theory.\", \"\\u00c5ke Pleijel\", \"1913-1989\", 2225], [2474, 99, \"Adegoke Olubummo  was a Nigerian mathematician who was the first Nigerian professor of mathematics.\", \"Adegoke Olubummo\", \"1923-1992\", 2458], [940, 99, \"Heinrich Suter  was a Swiss historian of science specializing in Islamic mathematics and astronomy.\", \"Heinrich Suter\", \"1848-1922\", 884], [2383, 99, \"Julia B Robinson  worked on computability, decision problems and non-standard models of arithmetic.\", \"Julia Bowman Robinson\", \"1919-1985\", 2372], [1626, 99, \"Erich Hecke  was a Polish-born German mathematician whose  best work was in analytic number theory.\", \"Erich Hecke\", \"1887-1947\", 1507], [1958, 99, \"Friedrich  Schmidt  was a German mathematician who made contributions to algebra and number theory.\", \"Friedrich Karl Schmidt\", \"1901-1977\", 1805], [1377, 99, \"Herta Freitag   was an Austrian-American mathematician known for her work on the Fibonacci numbers.\", \"Herta Freitag\", \"1908-2000\", 2065], [610, 99, \"Giusto Bellavitis  was an Italian mathematician who worked on a large range of mathematical topics.\", \"Giusto Bellavitis\", \"1803-1880\", 585], [1822, 99, \"Bertram Wilson  graduated from Cambridge and had posts at Liverpool and Dundee. He died very young.\", \"Bertram Wilson\", \"1896-1935\", 1694], [2194, 99, \"Donald Spencer  was an American mathematician, known for work on deformations of complex manifolds.\", \"Donald C Spencer\", \"1912-2001\", 2178], [1570, 99, \"David Enskog   was a Swedish mathematical physicist who helped develop the kinetic theory of gases.\", \"David Enskog\", \"1884-1947\", 1448], [1777, 99, \"Kurt Reidemeister  was a pioneer of knot theory and his work had a great influence on group theory.\", \"Kurt Reidemeister\", \"1893-1971\", 1641], [2484, 99, \"Christine Hamill  was an English mathematician who specialised in group theory and finite geometry.\", \"Christine Hamill\", \"1923-1956\", 2464], [1887, 99, \"Vladimir Fock  was a Russian physicist who worked in quantum mechanics and quantum electrodynamics.\", \"Vladimir Aleksandrovich Fock\", \"1898-1974\", 1756], [189, 99, \"Jean Leray  was a French mathematician who worked on algebraic topology and differential equations.\", \"Jean Leray\", \"1906-1998\", 1999], [1058, 99, \"Thomas Stieltjes  worked on almost all branches of analysis, continued fractions and number theory.\", \"Thomas Stieltjes\", \"1856-1894\", 989], [798, 99, \"Richard Rado  was a German-born British mathematician who worked on combinatorics and graph theory.\", \"Richard Rado\", \"1906-1989\", 2009], [2279, 99, \"Roger Ap\\u00e9ry  was a French mathematician best known for proving that \\u03b6 (3)  is an irrational number.\", \"Roger Ap\\u00e9ry\", \"1916-1994\", 2302], [2924, 99, \"Uri Rothblum  was an Israeli mathematician who made important contributions to operations research.\", \"Uriel Rothblum\", \"1947-2012\", 2918], [2035, 99, \"Alonzo Church  made important contributions to mathematical logic and theoretical computer science.\", \"Alonzo Church\", \"1903-1995\", 1862], [476, 99, \"William Wallace  worked on geometry and discovered the  ( so-called )   Simson line  of a triangle.\", \"William Wallace\", \"1768-1843\", 456], [163, 99, \"Adriaan Vlacq  was a Dutch bookseller and publisher who devised and published tables of logarithms.\", \"Adriaan Vlacq\", \"1600-1667\", 169], [2699, 99, \"Wang Yuan  ass a Chinese mathematician best known for his contributions to the Goldbach conjecture.\", \"Wang Yuan\", \"1930-2021\", 2689], [2283, 99, \"Chuan-Chih Hsiung  was a Chinese-born American mathematician specialising in differential geometry.\", \"Chuan-Chih Hsiung\", \"1915-2009\", 2262], [208, 99, \"Johann Rahn  was a Swiss mathematician who was the first to use the symbol  \\u00f7 \\\\div \\u00f7  for division.\", \"Johann Rahn\", \"1622-1676\", 206], [1088, 99, \"Florian Cajori  was a Swiss mathematician best known for his influential   History of Mathematics .\", \"Florian Cajori\", \"1859-1930\", 1018], [1856, 100, \"Myron Mathisson  was a Polish theoretical physicist who is known for his work in general relativity.\", \"Myron Mathisson\", \"1897-1940\", 1728], [1456, 100, \"Gilbert Bliss  was an American mathematician, best known for his work on the calculus of variations.\", \"Gilbert Bliss\", \"1876-1951\", 1313], [2729, 100, \"Jacques Neveu  was a Belgian mathematician who worked in France, specialising in probability theory.\", \"Jacques Neveu\", \"1932-2016\", 2717], [2228, 100, \"Emma Castelnuovo  was an Italian mathematician known for her contributions to mathematics education.\", \"Emma Castelnuovo\", \"1913-2014\", 2205], [303, 100, \"Nicholas Saunderson  was a blind English mathematician who developed a high reputation as a teacher.\", \"Nicholas Saunderson\", \"1682-1739\", 294], [150, 100, \"Jean Beaugrand  was a French mathematician who published works on Geostatics as well as mathematics.\", \"Jean Beaugrand\", \"1590-1640\", 156], [637, 100, \"James MacCullagh  was an Irish mathematician who published on crystalline refraction and reflection.\", \"James MacCullagh\", \"1809-1847\", 612], [981, 100, \"Friedrich Schottky  was a German mathematician who worked on elliptic, abelian, and theta functions.\", \"Friedrich Schottky\", \"1851-1935\", 919], [523, 100, \"John Walsh  was an eccentric Irish mathematician who wrote on a wide variety of mathematical topics.\", \"John Walsh\", \"1786-1847\", 503], [1542, 100, \"Riesz  was a founder of functional analysis and his work has many important applications in physics.\", \"Frigyes Riesz\", \"1880-1956\", 1379], [2522, 100, \"Linards Reizi\\u0146\\u0161  was a Latvian mathematician who specialised in the field of differential equations.\", \"Linards Reizi\\u0146\\u0161\", \"1924-1991\", 2511], [402, 100, \"Alexandre-Theophile Vandermonde  was a French mathematician best known for his work on determinants.\", \"Alexandre-Theophile Vandermonde\", \"1735-1796\", 381], [1861, 100, \"Lois Wilfred Griffiths   was an American mathematician best known for her work in polygonal numbers.\", \"Lois Griffiths\", \"1899-1981\", 1765], [2076, 100, \"Adolf Lindenbaum  was a Polish mathematician, logician and topologist. He was executed by the Nazis.\", \"Adolf Lindenbaum\", \"1904-1942\", 1900], [1815, 100, \"Stefan Bergman  was a Polish-born American mathematician whose primary work was in complex analysis.\", \"Stefan Bergman\", \"1895-1977\", 1688], [326, 100, \"Nathaniel Bliss  was an English mathematician and astronomer who went on to become Astronomer Royal.\", \"Nathaniel Bliss\", \"1700-1764\", 317], [2705, 100, \"Elias Stein  was a Belgian-born American mathematician who worked in the field of harmonic analysis.\", \"Elias Stein\", \"1931-2018\", 2695], [2409, 100, \"Herbert Federer  was an Austrian-born American mathematician who worked in geometric measure theory.\", \"Herbert Federer\", \"1920-2010\", 2396], [1470, 100, \"Carl Schoy  was a German historian of mathematics specialising in Arabian mathematics and astronomy.\", \"Carl Schoy\", \"1877-1925\", 1323], [2501, 100, \"Mikhail Kadets  was a Ukranian mathematician who worked in analysis and the theory of Banach spaces.\", \"Mikhail Iosiphovich Kadets\", \"1923-2011\", 2481], [1519, 100, \"Pierre Fatou   was a French mathematician and astronomer who worked in several branches of analysis.\", \"Pierre Fatou\", \"1878-1929\", 1360], [1339, 100, \"Ernst Zermelo  was a German mathematician who did pioneering work on the foundations of mathematics.\", \"Ernst Zermelo\", \"1871-1953\", 1233], [193, 100, \"Sarvadaman Chowla   was a British-born Indian American mathematician, specializing in number theory.\", \"Sarvadaman Chowla\", \"1907-1995\", 2043], [911, 100, \"Vaclav Jerabek  was a Czech mathematician whose main research interest was in constructive geometry.\", \"Vaclav Jerabek\", \"1845-1931\", 855], [1752, 100, \"Torsten Carleman  was a Swedish mathematician who worked in classical analysis and its applications.\", \"Torsten Carleman\", \"1892-1949\", 1624], [1464, 100, \"Ludwig Berwald  was a Czech mathematician who made important contributions to differential geometry.\", \"Ludwig Berwald\", \"1883-1942\", 1440], [96, 100, \"Giordano Bruno  was an Italian philosopher of science who was eventually burnt in Rome as a heretic.\", \"Giordano Bruno\", \"1548-1600\", 112], [1452, 100, \"Ernest Esclangon  was a French astronomer and mathematician who worked on almost-periodic functions.\", \"Ernest Esclangon\", \"1876-1954\", 1309], [1834, 100, \"Pavel Aleksandrov  was a Russian mathematician who made important contributions to general topology.\", \"Pavel Aleksandrov\", \"1896-1982\", 1705], [828, 100, \"Charles Peirce  was an eccentric American mathematician whose most important work was on philosophy.\", \"Charles S Peirce\", \"1839-1914\", 787], [21, 100, \"Levi ben Gerson  was a French scholar who wrote on trigonometry as well as astronomy and philosophy.\", \"Levi ben Gerson\", \"1288-1344\", 40], [143, 100, \"Peter Turner  was an English scholar who held two mathematical chairs, but published no mathematics.\", \"Peter Turner\", \"1586-1652\", 150], [1775, 101, \"Jason J Nassau  was an American mathematician who published papers in both mathematics and astronomy.\", \"Jason J Nassau\", \"1893-1965\", 1639], [569, 101, \"Olinde Rodrigues  was a French mathematician best known for his formula for the Legendre polynomials.\", \"Olinde Rodrigues\", \"1795-1851\", 548], [1708, 101, \"Johannes van der Corput  was a Dutch mathematician who worked in the field of analytic number theory.\", \"Johannes van der Corput\", \"1890-1975\", 1584], [276, 101, \"Louis Carr\\u00e9  was a French mathematician who published the first French book on the integral calculus.\", \"Louis Carr\\u00e9\", \"1663-1711\", 266], [582, 101, \"Mauritz Dahlin  was a Swedish mathematicianwho best known for his work on the history of mathematics.\", \"Mauritz Dahlin\", \"1843-1929\", 835], [1605, 101, \"Mauro Picone  was an Italian mathematician who worked on ordinary and partial differential equations.\", \"Mauro Picone\", \"1885-1977\", 1480], [2858, 101, \"Dan Quillen  was an American mathematician who won a Fields medal for his work in algebraic topology.\", \"Daniel Quillen\", \"1940-2011\", 2850], [1436, 101, \"Francesco Cantelli  was an Italian mathematician who made contributions to the theory of probability.\", \"Francesco Cantelli\", \"1875-1966\", 1292], [592, 101, \"Humphrey Lloyd  was an Irish applied mathematician who worked on conical refraction and geomagnetism.\", \"Humphrey Lloyd\", \"1800-1881\", 567], [2693, 101, \"Rudolf Kalman  was a Hungarian-born American mathematician best known for his work in control theory.\", \"Rudolf Kalman\", \"1930-2016\", 2683], [818, 101, \"Wilhelm Lexis  studied data presented as a series over time thus initiating the study of time series.\", \"Wilhelm Lexis\", \"1837-1914\", 778], [82, 101, \"Giovanni Benedetti  was an Italian mathematician who anticipated some of Galileo's work on free fall.\", \"Giovanni Benedetti\", \"1530-1590\", 98], [1376, 101, \"Hermann Ludwig Schmid   was a German mathematician who worked in algebra and algebraic number theory.\", \"Hermann Ludwig Schmid\", \"1908-1956\", 2064], [2225, 101, \"Andrzej Mostowski  was a Polish mathematician who worked on logic and the foundations of mathematics.\", \"Andrzej Mostowski\", \"1913-1975\", 2202], [961, 101, \"Nikolay Sonin  was a Russian mathematician who worked on special functions and numerical integration.\", \"Nikolay Sonin\", \"1849-1915\", 900], [1776, 101, \"Joseph Ritt  was an American mathematician who worked on ordinary and partial differential equations.\", \"Joseph Ritt\", \"1893-1951\", 1640], [2019, 101, \"Hans Petersson  was a German mathematician who worked in the theory of modular and automorphic forms.\", \"Hans Petersson\", \"1902-1984\", 1839], [2494, 101, \"Henri Cabannes  was a French mathematician who worked on the mechanics of fluids and vibrating ropes.\", \"Henri Cabannes\", \"1923-2016\", 2474], [1325, 101, \"Frank Jackson   was an English clergyman and mathematician who worked on basic hypergeometric series.\", \"Frank Jackson\", \"1870-1960\", 1219], [289, 101, \"Samuel Clarke  was an English clergyman who wrote on mechanics as well as philosophy and metaphysics.\", \"Samuel Clarke\", \"1675-1729\", 279], [1978, 101, \"Stephen C Kleene  was an American mathematician and logician best known his work on recursion theory.\", \"Stephen C Kleene\", \"1909-1994\", 2108], [726, 101, \"FrancescoBrioschi  was an Italian mathematician who contributed to the study of mathematical physics.\", \"Francesco Brioschi\", \"1824-1897\", 697], [1916, 101, \"\\u00d8ystein Ore  was a Norwegian mathematician who worked in ring theory, Galois theory and graph theory.\", \"\\u00d8ystein Ore\", \"1899-1968\", 1770], [2003, 101, \"Oene Bottema  was a Dutch mathematician who studied geometry and mechanics, specifically kinematics .\", \"Oene Bottema\", \"1901-1992\", 1818], [392, 101, \"James Glenie  was a Scottish mathematician who was involved in an early dispute in the Royal Society.\", \"James Glenie\", \"1750-1817\", 416], [1979, 101, \"Theodor Schneider  was a German mathematician, best known for his solution of Hilberts  7 th problem.\", \"Theodor Schneider\", \"1911-1988\", 2164], [284, 101, \"Leonty Magnitsky  was a Russian teacher who wrote the first guide to mathematics published in Russia.\", \"Leonty Filippovich Magnitsky\", \"1669-1739\", 274], [2421, 101, \"Sree Pillai  was an Indian mathematician who worked in America. His principle work was in statistics.\", \"Sree Pillai\", \"1920-1985\", 2407], [1382, 101, \"Nikolaos Hatzidakis  was a Greek mathematician, poet and patriot. He worked in differential geometry.\", \"Nikolaos Hatzidakis\", \"1872-1942\", 1256], [463, 101, \"Sylvestre Lacroix  was a French mathematician who wrote important textbooks on geometry and analysis.\", \"Sylvestre Lacroix\", \"1765-1843\", 443], [1963, 101, \"Conel Hugh O'Donel Alexander  was an Irish-born British cryptanalyst, chess player  and chess writer.\", \"Hugh Alexander\", \"1909-1974\", 2096], [1988, 101, \"Stanis\\u0142aw Go\\u0142\\u0105b  was a Polish mathematician who worked in particular on the field of affine geometry.\", \"Stanis\\u0142aw Go\\u0142\\u0105b\", \"1902-1980\", 1853], [2016, 101, \"Frank Yates  was an English  statistician whose work was important in the development of the subject.\", \"Frank Yates\", \"1902-1994\", 1836], [525, 102, \"William Horner  was an English mathematician best known for his method of solving algebraic equations.\", \"William Horner\", \"1786-1837\", 505], [1791, 102, \"Mikhail Suslin  was a Russian mathematician who worked in general topology and descriptive set theory.\", \"Mikhail Yakovlevich Suslin\", \"1894-1919\", 1661], [802, 102, \"Charles Ehresmann  was a French mathematician who worked in differential topology and category theory.\", \"Charles Ehresmann\", \"1905-1979\", 1941], [1960, 102, \"Ivan Petrovsky  was a Russian mathematician who worked in the field of partial differential equations.\", \"Ivan Georgievich Petrovsky\", \"1901-1973\", 1807], [2385, 102, \"Leopold Schmetterer  was an Austrian mathematician who worked on analysis, probability and statistics.\", \"Leopold Schmetterer\", \"1919-2004\", 2374], [1630, 102, \"Guido Ascoli  was an Italian mathematician who worked in the theory of partial differential equations.\", \"Guido Ascoli\", \"1887-1957\", 1511], [1527, 102, \"Lyudmila Keldysh  was a Russian mathematician known for her work in set theory and geometric topology.\", \"Lyudmila Vsevolodovna Keldysh\", \"1904-1976\", 1926], [1401, 156, \"Carath\\u00e9odory  made significant contributions to the calculus of variations, the theory of point set measure, and the theory of functions of a real variable.\", \"Constantin Carath\\u00e9odory\", \"1873-1950\", 1264], [149, 156, \"Thomas Hobbes  was an English scholar and amateur mathematician who wrote on optics and on geometry. He attacked the 'new' methods of mathematical analysis.\", \"Thomas Hobbes\", \"1588-1679\", 155], [1346, 156, \"Francisco Jos\\u00e9 Duarte  was a Venezuelan mathematician whose most important work in mathematics was done in algebra, number theory and mathematical analysis.\", \"Francisco Jos\\u00e9 Duarte\", \"1883-1972\", 1436], [393, 156, \"Lorenzo Mascheroni  was a geometer who proved in  1797  that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed.\", \"Lorenzo Mascheroni\", \"1750-1800\", 417], [3000, 156, \"Grigori Perelman  is a Russian mathematician who proved the Poincar\\u00e9 Conjecture and who refused to accept a Fields Medal or the $ 1   000   000  Clay Prize.\", \"Grigori Yakovlevich Perelman\", \"1966-\", 2995], [1858, 156, \"Stanis\\u0142aw Saks  was a Polish mathematician who worked in topology, set theory and functional analysis. He was one of the frequenters of the  Scottish Caf\\u00e9 .\", \"Stanis\\u0142aw Saks\", \"1897-1942\", 1729], [1480, 156, \"Landau  gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.\", \"Edmund Landau\", \"1877-1938\", 1327], [2841, 156, \"Sergei Novikov  is a  Russian mathematician who worked in algebraic topology and soliton theory. He won a Fields medal in  1970  and a Wolf prize in  2005 .\", \"Sergei Novikov\", \"1938-\", 2834], [242, 156, \"Georg Mohr  was a Danish mathematician who anticipated Mascheroni's proof that all ruler and compass constructions can be accomplished with compasses alone.\", \"Georg Mohr\", \"1640-1697\", 236], [1252, 156, \"James Craig  was a Scottish mathematician who made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.\", \"James Craig\", \"1868-1952\", 1195], [1884, 157, \"Mary Taylor Slow  was a British mathematician and physicist who worked on the theory of radio waves and the application of differential equations to physics.\", \"Mary Taylor\", \"1898-1984\", 1750], [2346, 157, \"Nathan Mendelsohn  was an American-born Canadian mathematician who worked in several areas of discrete mathematics, including group theory and combinatorics.\", \"Nathan Mendelsohn\", \"1917-2006\", 2324], [2310, 157, \"Abraham Seidenberg  was an American mathematician who worked in commutative algebra, algebraic geometry, differential algebra and the history of mathematics.\", \"Abraham Seidenberg\", \"1916-1988\", 2283], [2399, 157, \" C R Rao   is an Indian-born mathematician and statistician who has worked most of his life in America. His statistical work has been applied in many fields.\", \"Calyampudi Radhakrishna Rao\", \"1920-\", 2388], [2491, 157, \"Georg Kreisel  was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America and chiefly studied proof and computation.\", \"Georg Kreisel\", \"1923-2015\", 2471], [2807, 157, \"Charlie Sims  was an American mathematician best known for his work in group theory and in particular for the discovery of one of the sporadic simple groups.\", \"Charles Sims\", \"1937-2017\", 2801], [3009, 157, \"Q\\u00ebndrim Gashi  was a Yugoslavian mathematician, born in what is now Kosovo, who worked in group theory and was a founder of the Kosovan Mathematical Society.\", \"Q\\u00ebndrim Gashi\", \"1984-\", 3010], [2651, 157, \"Mikio Sato  was a Japanese mathematician whose vision of \\\"algebraic analysis\\\" and mathematical physics initiated several fundamental branches of mathematics.\", \"Mikio Sato\", \"1928-2023\", 2635], [160, 157, \"Bonaventura Cavalieri  was an Italian mathematician who developed a method of indivisibles which became a factor in the development of the integral calculus.\", \"Bonaventura Cavalieri\", \"1598-1647\", 166], [327, 157, \"William Braikenridge  was an Scottish mathematician and theologian who worked on geometry and independently discovered many of the same results as Maclaurin.\", \"William Braikenridge\", \"1700-1762\", 318], [620, 157, \"Lejeune Dirichlet  is best known for his proof that in any arithmetic progression with first term coprime to the difference there are infinitely many primes.\", \"Lejeune Dirichlet\", \"1805-1859\", 595], [1515, 157, \"Maurice Fr\\u00e9chet  was a French mathematician who made major contributions to the topology of point sets and defined and founded the theory of abstract spaces.\", \"Maurice Fr\\u00e9chet\", \"1878-1973\", 1356], [865, 158, \"Gaston Darboux  was a French mathematician who made important contributions to differential geometry and analysis and the Darboux integral is named after him.\", \"Gaston Darboux\", \"1842-1917\", 815], [746, 158, \"Charles Merrifield   was an English mathematician who worked on elliptic functions and played an important role in the development of mathematical ssocieties.\", \"Charles Merrifield\", \"1827-1884\", 715], [164, 158, \"Pierre de Carcavi  is a French amateur mathematician who is better known for his correspondence with other mathematicians rather than for his own mathematics.\", \"Pierre de Carcavi\", \"1600-1684\", 170], [2640, 158, \"Donald Higman  was an Canadian mathematician best known for his work in group theory and in particular for the discovery of one of the sporadic simple groups.\", \"Donald Higman\", \"1928-2006\", 2614], [2742, 158, \"Stanis\\u0142aw \\u015awierczkowski  was a Polish mathematician who worked in many areas including Diophantine approximation, geometry and the foundations of mathematics.\", \"Stanis\\u0142aw \\u015awierczkowski\", \"1932-2015\", 2730], [1710, 158, \"Martha Shapley  became a high school mathematics teacher. After marrying the astronomer Harlow Shapley she did outstanding research on eclipsing binary stars.\", \"Martha Betz Shapley\", \"1890-1981\", 1586], [795, 158, \"Omar Catunda  was a Brazilian mathematician. He worked hard to improve the level of mathematics education at both school and university level across Brazil.\\\\n \", \"Omar Catunda\", \"1906-1986\", 2006], [1591, 158, \"William Watson  graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh. \", \"William Watson\", \"1884-1952\", 1467], [935, 158, \"Diederik Korteweg  was a Dutch mathematician with wide interests, now best-known as the joint discoverer of the Korteweg-de Vries equation for solitary waves.\", \"Diederik Korteweg\", \"1848-1941\", 879], [2197, 158, \"Lyman Spitzer  was an American theoretical physicist and astronomer best known for pioneering the idea of a space telescope. He also worked on nuclear fusion.\", \"Lyman Spitzer\", \"1914-1997\", 2242], [39, 158, \"Al-Qalasadi  was a Spanish Islamic mathematician who took the first steps toward the introduction of algebraic symbolism by using letters in place of numbers.\", \"Al-Qalasadi\", \"1412-1486\", 58], [1366, 158, \"Forest Ray Moulton  was an American astronomer. He was one of the proponents of the  planetesimal hypothesis  of the origin and evolution of the solar system.\", \"Forest Ray Moulton\", \"1872-1952\", 1249], [2496, 158, \"Hidehiko Yamabe  was a Japanese mathematician who published important results in differential geometry and on group theory, including Hilbert's fifth problem.\", \"Hidehiko Yamabe\", \"1923-1960\", 2476], [2155, 158, \"William Cochran  was a Scottish born mathematician who did much to promote statistics in the USA. He wrote a number of books which became statistics classics.\", \"William Cochran\", \"1909-1980\", 2112], [1170, 158, \"Augustus Love  was an English mathematician known for his work on the theory of elasticity. He also worked on wave propagation and the structure of the Earth.\", \"Augustus Love\", \"1863-1940\", 1090], [1716, 158, \"Abram Besicovitch  was a Russian mathematician who worked mainly in England on functions of a real variable, analytic functions and almost periodic functions.\", \"Abram Samoilovitch Besicovitch\", \"1891-1970\", 1592], [892, 158, \"Moritz Pasch  was a German mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before.\", \"Moritz Pasch\", \"1843-1930\", 836], [971, 158, \"Sophie Willock Bryant  was an Irish mathematician who also published on many other topics: Irish history, religion, education, women's rights, and philosophy.\", \"Sophie Willock Bryant\", \"1850-1922\", 909], [1190, 159, \"J Watt Butters  graduated from Edinburgh and taught at George Heriot's School and James Gillespie's School in Edinburgh. He became Rector of Ardrossan Academy.\", \"J Watt Butters\", \"1863-1946\", 1102], [1167, 159, \"Aleksei Krylov  was a Russian applied mathematician who worked in many areas including shipbuilding, magnetism, artillery, mathematics, astronomy, and geodesy.\", \"Aleksei Krylov\", \"1863-1945\", 1087], [29, 159, \"Madhava  was a mathematician from South India. He made some important advances in infinite series including finding the expansions for trigonometric functions.\", \"Madhava\", \"1350-1425\", 48], [1302, 159, \"Donald McIntosh  graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education.\", \"Donald McIntosh\", \"1868-1957\", 1187], [770, 159, \"Richard Dedekind 's major contribution was a redefinition of irrational numbers in terms of Dedekind cuts. He introduced the notion of an ideal in Ring Theory.\", \"Richard Dedekind\", \"1831-1916\", 739], [1156, 159, \"Jules Richard  worked on Geometry but is best known for  Richard's paradox  involving the set of real numbers which can be defined in a finite number of words.\", \"Jules Richard\", \"1862-1956\", 1077], [1053, 159, \"Edward Marczewski  was a Polish mathematician who worked in measure theory, descriptive set theory, general topology, probability theory and universal algebra.\", \"Edward Marczewski\", \"1907-1976\", 2025], [901, 159, \"Thomas Muir  was a Scot who went on to be Superintendent General of Education in South Africa and  is best known for his five volume  History of Determinants .\", \"Thomas Muir\", \"1844-1934\", 845], [98, 159, \"Simon Stevin  was a Flemish mathematician who presented the first elementary and thorough account of decimal fractions and introduced their use in mathematics.\", \"Simon Stevin\", \"1548-1620\", 114], [1795, 159, \"Paul Finsler  was a German mathematician who worked on set theory, differential geometry, number theory, probability theory and the foundations of mathematics.\", \"Paul Finsler\", \"1894-1970\", 1665], [938, 159, \"Gottlob Frege  was a German mathematician who was one of the founders of modern symbolic logic putting forward the view that mathematics is reducible to logic.\", \"Gottlob Frege\", \"1848-1925\", 882], [2796, 159, \"Terence Tao  won a Fields Medal in  2006  for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.\", \"Terence Tao\", \"1975-\", 3006], [545, 159, \"Charles Babbage  originated the modern analytic computer. He invented the principle of the analytical engine, the forerunner of the modern electronic computer.\", \"Charles Babbage\", \"1791-1871\", 524], [1520, 159, \"Roland Richardson  was a Canadian mathematician who worked in the USA. He is known for his work at Brown University and with the American Mathematical Society.\", \"Roland Richardson\", \"1878-1949\", 1361], [2113, 159, \"Laurence Chisholm Young  was a German-born mathematician who worked in measure theory, the calculus of variations, optimal control theory and potential theory.\", \"Laurence Chisholm Young\", \"1905-2000\", 1957], [1790, 160, \"Jerzy Neyman  was a Russian born American mathematician who did important work in probability and statistics including applications to meteorology and medicine.\", \"Jerzy Neyman\", \"1894-1981\", 1660], [1324, 160, \"Ernst Lindel\\u00f6f  was a Finnish mathematician who worked on topology and partial differential equations. He also wrote on the history of Scandinavian mathematics.\", \"Ernst Lindel\\u00f6f\", \"1870-1946\", 1218], [970, 160, \"Sofia Kovalevskaya  was a Russian born mathematician who made valuable contributions to the theory of differential equations. She finished her career in Sweden.\", \"Sofia Kovalevskaya\", \"1850-1891\", 908], [825, 160, \"Konrad Knopp  was a German mathematician who worked on generalised limits and complex functions. He was the co-founder of  Mathematische Zeitschrift  in  1918 .\", \"Konrad Knopp\", \"1882-1957\", 1418], [1007, 160, \"Salvatore Pincherle  was an Italian mathematician who can claim to be one of the founders of functional analysis. He established the Italian Mathematical Union.\", \"Salvatore Pincherle\", \"1853-1936\", 950], [128, 160, \"Claude Bachet  was a French mathematician who wrote books on mathematical puzzles which formed the basis for almost all later books on mathematical recreations.\", \"Claude Gaspar Bachet\", \"1581-1638\", 144], [1892, 160, \"Bhama Srinivasan  is an Indian-born mathematician who has worked in England and America and is known for her work in the representation theory of finite groups.\", \"Bhama Srinivasan\", \"1935-\", 2763], [2865, 160, \"Aderemi Kuku  is a Nigerian mathematician who specialised in K-theory. He taught a wide range of mathematical courses at both undergraduate and graduate levels.\", \"Aderemi Kuku\", \"1941-\", 2857], [414, 160, \"Joseph-Louis Lagrange  was an Italian-born French mathematician who excelled in all fields of analysis and number theory and analytical and celestial mechanics.\", \"Joseph-Louis Lagrange\", \"1736-1813\", 388], [2855, 160, \"Mary Gray  is an American mathematician, statistician, and lawyer. She has written on mathematics, education, computer science, statistics and academic freedom.\", \"Mary Lee Wheat Gray\", \"1939-\", 2847], [771, 160, \"Carl Neumann  was a German mathematician who worked on the Dirichlet principle and on integral equations. He was one of the founders of  Mathematische Annalen .\", \"Carl Neumann\", \"1832-1925\", 740], [2625, 160, \"Slamet Dajono  was an Indonesian mathematician who founded the \\\"Mathematics Interest Association\\\" which was a forerunner of the Indonesian Mathematical Society.\", \"Slamet Dajono\", \"1927-1990\", 2605], [1907, 160, \"Gerhard Gentzen  invented a 'natural deduction' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert.\", \"Gerhard Gentzen\", \"1909-1945\", 2094], [2770, 160, \"Robert Grosseteste  was an English bishop who worked on geometry, optics and astronomy and made Latin translations of many Greek and Arabic scientific writings.\", \"Robert Grosseteste\", \"1168-1253\", 19], [1833, 160, \"Nora Calderwood  graduated from Edinburgh University and went on to a lectureship at Birmingham University. A prize in algebra at Birmingham is named after her.\", \"Nora Calderwood\", \"1896-1985\", 1704], [2571, 160, \"Albert Nijenhuis  was a Dutch-born American mathematician who worked in differential geometry and the theory of deformations.  He later worked in combinatorics.\", \"Albert Nijenhuis\", \"1926-2015\", 2545], [2497, 160, \"Igor Shafarevich  was a Russian mathematician who worked in algebraic number theory and algebraic geometry. He was an important dissident during the Soviet era.\", \"Igor Rostislavovich Shafarevich\", \"1923-2017\", 2477], [282, 160, \"William Whiston  was an English mathematician who succeeded Newton as Lucasian professor at Cambridge, but was later deprived of his chair on religious grounds.\", \"William Whiston\", \"1667-1752\", 272], [2564, 160, \"Martin Kruskal  was an American mathematician and physicist who worked in plasma physics as well as soliton equations, asymptotic analysis, and surreal numbers.\", \"Martin Kruskal\", \"1925-2006\", 2538], [337, 160, \"Jan Segner  was a Hungarian mathematician who was the first professor of mathematics at G\\u00f6ttingen. He made substantial contributions to the theoery of Dynamics.\", \"Johann Segner\", \"1704-1777\", 329], [2739, 160, \"Maurice Audin  was a French mathematician and an activist in the anticolonialist cause, who died under torture by the French state during the Battle of Algiers.\", \"Maurice Audin\", \"1932-1957\", 2727], [2520, 160, \"John Backus  was an American mathematician best known for the invention of FORTRAN and for the BNF notation for describing the syntax of a programming language.\", \"John Backus\", \"1924-2007\", 2509], [366, 160, \"Maria Agnesi  was an Italian mathematician who is noted for her work in differential calculus. She discussed the cubic curve now known as the 'witch of Agnesi'.\", \"Maria Agnesi\", \"1718-1799\", 353], [2455, 160, \"Walter Rudin  was an Austrian-born American mathematician who worked in complex and harmonic analysis and is also known for his mathematical analysis textbooks.\", \"Walter Rudin\", \"1921-2010\", 2438], [897, 161, \"Jacob L\\u00fcroth  was a German mathematician who worked on rational curves and the invariance of dimension. He discovered the  Student t -distribution before Gosset.\", \"Jacob L\\u00fcroth\", \"1844-1910\", 841], [1413, 161, \"Lev Landau  was an Azerbaijan-born mathematician who made fundamental discoveries in theoretical physics. He won the Nobel prize for his theory of superfluidity.\", \"Lev Landau\", \"1908-1968\", 2071], [2364, 161, \"Katherine Johnson  was an African-American mathematician who made contributions to NASA's space programmme. She was featured in the  2017  film  Hidden figures .\", \"Katherine Johnson\", \"1918-2020\", 2347], [105, 161, \"Jo\\u00e3o Delgado  was a Portuguese mathematician, priest and architect. He made important contributions to the debate about the place of mathematics in a curriculum.\", \"Jo\\u00e3o Delgado\", \"1553-1612\", 121], [2165, 161, \"George Gunter Lorentz  was a Russian-born American mathematician who worked in  approximation theory, interpolation theory of operators, and functional analysis.\", \"George G Lorentz\", \"1910-2006\", 2122], [311, 161, \"Roger Paman  was an English mathematician who took part in a voyage hoping to circumnavigate the world. He made contributions to the development of the calculus.\", \"Roger Paman\", \"1688-1748\", 302], [1844, 161, \"Annie Hutton Numbers  graduated from Edinburgh University and worked in the Chemistry department in Edinburgh. She taught in schools in Ipswich and High Wycombe.\", \"Annie Hutton Numbers\", \"1897-1988\", 1716], [1196, 161, \"John Morrison  was appointed Professor of Physics at Victoria College Stellenbosch in South Africa. He did important work on the magnetic survey of South Africa.\", \"John Morrison\", \"1863-1944\", 1108], [345, 161, \"Giordano Riccati  made contributions to music, architecture, mechanics and mathematics. He studied and experimented with Young's modulus  25  years before Young.\", \"Giordano Riccati\", \"1709-1790\", 336], [2968, 161, \"Don\\u010do Dimovski  is a Macedonian mathematician whose areas of interest include algebra and topology with applications to physics, statistics and computer science.\", \"Don\\u010do Dimovski\", \"1954-\", 2955], [2605, 161, \"John Nash  was an American mathematician who won the Nobel Prize for Economics for his work in game theory. He achieved fame through the film  A Beautiful Mind .\", \"John F Nash\", \"1928-2015\", 2626], [1080, 162, \"Giuseppe Peano  was the founder of symbolic logic and his interests centred on the foundations of mathematics and on the development of a formal logical language.\", \"Giuseppe Peano\", \"1858-1932\", 1010], [2989, 162, \"James Vanstone  was a Canadian mathematician who dealt with differential geometry and multilinear algebra, especially in connection with the theory of relativity.\", \"Ray Vanstone\", \"1933-2001\", 2747], [2256, 162, \"Shaun Wylie  was a British mathematician who made important contributions to code-breaking in World War II. He wrote an important text-book on algebraic topology.\", \"Shaun Wylie\", \"1913-2009\", 2222], [2794, 162, \"Iossif Ostrovskii  was a Ukrainian mathematician who worked in the theory of integer and meromorphic functions and their application in the theory of probability.\", \"Iossif Vladimirovich Ostrovskii\", \"1934-2020\", 2752], [443, 162, \"Lazare Carnot  is best known as a geometer. In  1803  he published  G\\u00e9om\\u00e9trie de position   in which sensed magnitudes were first systematically used in geometry.\", \"Lazare Carnot\", \"1753-1823\", 424], [2187, 162, \"Aleksandr Danilovic Aleksandrov  was a Russian mathematician and physicist who worked in geometry and a wide variety of areas of physics. He wrote many textbooks.\", \"Aleksandr Aleksandrov\", \"1912-1999\", 2170], [779, 162, \"Rudolf Lipschitz  is remembered for the \\\"Lipschitz condition\\\", an inequality that guarantees a unique solution to the differential equation  y ' =  f   ( x, y ) .\", \"Rudolf Lipschitz\", \"1832-1903\", 748], [721, 162, \"Leopold Kronecker 's primary contributions were in the theory of equations. He made major contributions in elliptic functions and the theory of algebraic numbers.\", \"Leopold Kronecker\", \"1823-1891\", 693], [2657, 162, \"Andor Kert\\u00e9sz  was a Hungarian mathematician who worked in the theory of Abelian groups, modules and  rings. He was also interested in the history of mathematics.\", \"Andor Kert\\u00e9sz\", \"1929-1974\", 2641], [2009, 162, \"Richard Gwilt  was an actuary who worked for various Edinburgh insurance companies. He was a Fellow of the Faculty of Actuaries and of the Institute of Actuaries.\", \"Richard Gwilt\", \"1901-1972\", 1823], [814, 162, \"Leo K\\u00f6nigsberger  was a German mathematician who worked on elliptic functions and differential equations. He is known for his biographies of Helmholtz and Jacobi.\", \"Leo K\\u00f6nigsberger\", \"1837-1921\", 774], [1478, 162, \"David Drysdale  graduated from Edinburgh University and then taught at George Heriot's School Edinburgh, at the Royal Academy Irvine and at Arbroath High School. \", \"David Drysdale\", \"1877-1946\", 1325], [103, 162, \"Luca Valerio  was an Italian mathematician who applied methods of Archimedes to find volumes and centres of gravity of solid bodies. He corresponded with Galileo.\", \"Luca Valerio\", \"1552-1618\", 119], [1747, 162, \"Dorothy Maud Wrinch  was an Argentinian-English-American mathematician and biochemist famous for her use of mathematical techniques to deduce protein structure.\\\\n \", \"Dorothy Wrinch\", \"1894-1976\", 1653], [891, 162, \"Karl Geiser  was a Swiss mathematician who worked in algebraic geometry and minimal sufaces. He organised the first International Mathematical Congress in Zurich.\", \"Karl Geiser\", \"1843-1934\", 834], [1410, 162, \"Jacob Bronowski  was a Polish-born mathematician and historian. He is best known for developing a humanistic approach to science. He made frequent TV appearances.\", \"Jacob Bronowski\", \"1908-1974\", 2068], [387, 162, \"Jean-Baptiste-Joseph  Delambre  was an astronomer who produced tables of the location of planets and their satellites. He also worked at the bureau of longitudes.\", \"Jean-Baptiste-Joseph Delambre\", \"1749-1822\", 411], [1407, 162, \"Karl Schwarzschild  was a German physicist and astronomer who investigated the mathematics which eventually led to the prediction of the existence of black holes.\", \"Karl Schwarzschild\", \"1873-1916\", 1270], [740, 162, \"Christian Wiener  was a German mathematician, physicist and philosopher. He was the first person to identify qualitatively the molecular cause of Brownian motion.\", \"Christian Wiener\", \"1826-1896\", 710], [1985, 162, \"Kurt Friedrichs  was a German American mathematician who worked on many aspects of partial differential equations. He was the co-founder of the Courant Institute.\", \"Kurt Friedrichs\", \"1901-1982\", 1810], [2910, 163, \"Persi Diaconis  is an American mathematician and magician who works in combinatorics and statistics, but may be best known for his card tricks and other conjuring.\", \"Persi Diaconis\", \"1945-\", 2897], [2890, 163, \"Luis Caffarelli  is an Argentine mathematician who has won several major prizes for his work in the field of partial differential equations and their applications.\", \"Luis Caffarelli\", \"1948-\", 2925], [2101, 163, \"Harold Ruse  graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces.\", \"Harold Ruse\", \"1905-1974\", 1949], [1679, 163, \"Vyacheslaw Stepanov  was a Russian mathematician who worked in analysis, especially in the theory of ordinary differential equations and almost periodic functions.\", \"Vyacheslaw Vassilievich Stepanov\", \"1889-1950\", 1574], [2255, 163, \"Samuel Eilenberg  was a Polish-born American mathematician who worked on algebraic topology and homological algebra. He was one of the founders of category theory.\", \"Samuel Eilenberg\", \"1913-1998\", 2221], [2461, 163, \"Gaetano Fichera  was an Italian mathematician who worked in mathematical analysis, linear elasticity, partial differential equations and several complex variables.\", \"Gaetano Fichera\", \"1922-1996\", 2445], [1151, 163, \"Gino Loria  was an Italian mathematician and historian of mathematics who worked on projective geometry, special curves, algebraic geometry and elliptic functions.\", \"Gino Loria\", \"1862-1954\", 1072], [1953, 163, \"Alfred Tarski  made important contributions in many areas of mathematics, including metamathematics, set theory, measure theory, model theory, and general algebra.\", \"Alfred Tarski\", \"1901-1983\", 1800], [2245, 163, \"Israil Gelfand  was a Ukranian mathematician who made important contributions to many areas including  group theory, representation theory and functional analysis.\", \"Israil Gelfand\", \"1913-2009\", 2211], [359, 163, \"Nicolas-Louis de Lacaille  was a French astronomer and geodesist who catalogued the stars of the Southern Hemisphere and named  14  out of the  88  constellations.\", \"Nicolas-Louis de Lacaille\", \"1713-1762\", 346], [2558, 163, \"John Pople  was an English theoretical chemist who shared the Nobel Prize in Chemistry in  1998  for his development of computational methods in quantum chemistry.\", \"John Pople\", \"1925-2004\", 2532], [662, 163, \" Ludwig Schl\\u00e4fli 's work was in geometry, arithmetic and function theory. He is best known for the so-called Schl\\u00e4fli symbols which are used to classify polyhedra.\", \"Ludwig Schl\\u00e4fli\", \"1814-1895\", 636], [1356, 163, \"John Miller  studied at Glasgow and G\\u00f6ttingen. He returned to Glasgow to the Royal College of Science and Technology  ( the precursor to Strathclyde University ) .\", \"John Miller\", \"1871-1956\", 1238], [664, 163, \"Pierre  Wantzel  was a French mathematician who proved that several ancient geometric problems were impossible to solve using only ruler and compass constructions.\", \"Pierre Wantzel\", \"1814-1848\", 638], [2590, 164, \"Benjamin Moiseiwitsch  was an English mathematician who worked on differential and integral equations and was interested in connections between art and mathematics.\", \"Benjamin Moiseiwitsch\", \"1927-2016\", 2583], [291, 164, \"Jacopo Riccati  was an Italian mathematician who wrote on philosophy, physics and differential equations. He is chiefly known for the Riccati differential equation.\", \"Jacopo Riccati\", \"1676-1754\", 281], [902, 164, \"Charles Niven  was a Scot who became Professor of Mathematics at Cork. He returned to Aberdeen as Professor of Natural Philosophy and held this post for  42  years.\", \"Charles Niven\", \"1845-1923\", 846], [1800, 164, \"Archil Kharadze  was a Georgian mathematician who worked in special functions and was influential in the re-founding of the Georgian Mathematical Society in  1962 .\", \"Archil Kirillovich Kharadze\", \"1895-1976\", 1672], [1017, 164, \"Ivan \\u015aleszy\\u0144ski  was a Ukranian born mathematician whose main work was on continued fractions, least squares and axiomatic proof theory based on mathematical logic.\", \"Ivan \\u015aleszy\\u0144ski\", \"1854-1931\", 959], [314, 164, \"Christian Goldbach  was a Prussian mathematician best known for the conjecture he made in a letter to Euler that every even integer &gt;  2  is a sum of two primes.\", \"Christian Goldbach\", \"1690-1764\", 305], [1612, 164, \"Wilhelm Blaschke  was an Austrian mathematician whose research was on various aspects of geometry. He also initiated the study of topological differential geometry.\", \"Wilhelm Blaschke\", \"1885-1962\", 1488], [863, 164, \"Alexander von Brill  was a German mathematician who worked in algebraic geometry. He also made mathematical models and was interested in the history of mathematics.\", \"Alexander von Brill\", \"1842-1935\", 813], [1300, 164, \"Gianfranco Cimmino   was an Italian mathematician who worked in mathematical analysis, numerical analysis and the theory of elliptic partial differential equations.\", \"Gianfranco Cimmino\", \"1908-1989\", 2055], [1122, 164, \"Heinrich Burkhardt  was a German mathematician who worked on the theory of the elliptical functions, series expansions, group theory and the history of mathematics.\", \"Heinrich Burkhardt\", \"1861-1914\", 1051], [2147, 164, \"Grace Hopper  was one of the pioneers in the development of the electronic computer. She is  ( probably )  the only mathematician to have a warship named after her.\", \"Grace Hopper\", \"1906-1992\", 1994], [1129, 164, \"Hassler Whitney  was an American mathematician who did important work in manifolds, embeddings, immersions, characteristic classes and geometric integration theory.\", \"Hassler Whitney\", \"1907-1989\", 2029], [112, 164, \"Henry Briggs  was was an English mathematician who published tables of Napier's logarithm and was the man most responsible for scientists' acceptance of logarithms.\", \"Henry Briggs\", \"1561-1630\", 128], [2292, 164, \"Kiyosi Ito  was a Japanese mathematician who pioneered the theory of stochastic integration and stochastic differential equations. He won the Gauss prize in  2006 .\", \"Kiyosi Ito\", \"1915-2008\", 2271], [1939, 164, \"Shen Kua  was a Chinese scholar who wrote on a wide variety of topics including mathematics, music, astronomy, calendars, cartography, geology, optics and medicine.\", \"Shen Kua\", \"1031-1095\", 6], [1911, 164, \"Hermann of Reichenau  was a German mathematician who important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe.\", \"Hermann of Reichenau\", \"1013-1054\", 3], [1389, 164, \"Guillaume Bigourdan  was a French astronomer who spent twenty years reviewing and describing the positions of  6380  nebulae. He discovered about  500  new objects.\", \"Guillaume Bigourdan\", \"1851-1932\", 923], [1, 164, \"John of Holywood  or  Johannes de Sacrobosco  was an English scholar who wrote an important text on astronomy and promoted Arabic methods of arithmetic and algebra.\", \"John Sacrobosco\", \"1195-1256\", 23], [653, 165, \"Duncan Gregory  was a Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra. He was a great-great-grandson of James Gregory\", \"Duncan Gregory\", \"1813-1844\", 627], [1201, 165, \"Hausdorff  worked in topology creating a theory of topological and metric spaces. He also worked in set theory and introduced the concept of a partially ordered set.\", \"Felix Hausdorff\", \"1868-1942\", 1189], [839, 165, \"Gustav Roch  was a German mathematician known for the  Riemann-Roch theorem  which relates the genus of a topological surface to algebraic properties of the surface.\", \"Gustav Roch\", \"1839-1866\", 790], [2799, 165, \"Peter Ladislaw Hammer  was a Romanian-born mathematician who worked in Israel, Canada and the USA. He worked in operations research and applied discrete mathematics.\", \"Peter Ladislaw Hammer\", \"1936-2006\", 2792], [356, 165, \"Ruggero Boscovich 's main work was in mathematical physics. He was the first to give a procedure to compute a planet's orbit from three observations of its position.\", \"Ruggero Giuseppe Boscovich\", \"1711-1787\", 342], [625, 165, \"John Graves  was an Irish lawyer and mathematician who is credited with inspiring Hamilton to discover the quaternions and with personally discovering the octonions.\", \"John T Graves\", \"1806-1870\", 600], [1592, 165, \"Alfr\\u00e9d Haar  was a Hungarian mathematician who is best remembered for his work on analysis on groups, introducing a measure on groups, now called the  Haar measure .\", \"Alfr\\u00e9d Haar\", \"1885-1933\", 1468], [1152, 166, \"Henri Andoyer  was a French astronomer and mathematician who worked on the motion of the moon. He published mathematical tables and works on the history of astronomy.\", \"Henri Andoyer\", \"1862-1929\", 1073], [1432, 166, \"Beppo Levi  was an Italian mathematician who wrote articles on logic, differential equations, complex variable, as well as on the border between analysis and physics.\", \"Beppo Levi\", \"1875-1961\", 1289], [1908, 166, \"Hidegor\\u00f4 Nakano  was a Japanese mathematician who is remembered today for Nakano spaces, and for his results on vector lattices and operator theory in Hilbert spaces.\", \"Hidegor\\u00f4 Nakano\", \"1909-1974\", 2095], [1005, 166, \"Hendrik Lorentz  is best known for his work on electromagnetic radiation and the FitzGerald-Lorentz contraction. He developed the mathematical theory of the electron.\", \"Hendrik Lorentz\", \"1853-1928\", 948], [2981, 166, \"Curtis McMullen  is an American mathematician who was awarded the Fields Medal in  1998  for his work in complex dynamics, hyperbolic geometry and Teichm\\u00fcller theory.\", \"Curtis McMullen\", \"1958-\", 2973], [1950, 166, \"William John Youden   was an Australian born American statistician who formulated new statistical techniques in statistical analysis and in the design of experiments.\", \"William Youden\", \"1900-1971\", 1798], [2162, 167, \"Ernst Max Mohr  was a German mathematician who worked in the field of hydrodynamics, applied mathematics and differential equations, but also published on polynomials.\", \"Ernst Mohr\", \"1910-1989\", 2119], [2538, 167, \"James Serrin  was an American mathematician who worked in nonlinear analysis, partial differential equations, fluid mechanics, continuum mechanics, and thermodynamics.\", \"James Serrin\", \"1926-2012\", 2560], [2000, 167, \"Naum Il'ich Akhiezer  was a Soviet mathematician whose main work was on function theory and approximation theory. He also produced works on the history of mathematics.\", \"Naum Il'ich Akhiezer\", \"1901-1980\", 1815], [1526, 167, \"Leo F\\u00e9lix Pollaczek  was an Austrian-French engineer and mathematician who worked in number theory, mathematical analysis, mathematical physics and probability theory.\", \"F\\u00e9lix Pollaczek\", \"1892-1981\", 1614], [1113, 167, \"Vito Volterra  published papers on partial differential equations, particularly the equation of cylindrical waves. His most famous work was done on integral equations.\", \"Vito Volterra\", \"1860-1940\", 1043], [571, 167, \"Adolphe Quetelet  was a Flemish scientist who was influenced by Pierre Laplace and Joseph Fourier. He was the first to use the normal curve other than as an error law.\", \"Adolphe Quetelet\", \"1796-1874\", 550], [762, 167, \"Thomas Hirst  was an English mathematician who worked in geometry. He is best known for his journal in which he recorded impressions of the many mathematicians he met.\", \"Thomas Hirst\", \"1830-1892\", 731], [1921, 167, \"Szolem Mandelbrojt  was a Polish-born French mathematician who specialized in mathematical analysis. He was an early Bourbakist and was the uncle of Benoit Mandelbrot.\", \"Szolem Mandelbrojt\", \"1899-1983\", 1774], [145, 167, \"Joachim Jungius  was a German mathematician who was one of the first to use exponents to represent powers and who used mathematics as a model for the natural sciences.\", \"Joachim Jungius\", \"1587-1657\", 151], [1286, 167, \"Eugenio Levi  was an Italian mathematician who worked in complex analysis, differential geometry, Lie groups, partial differential equations and the minimum principle.\", \"Eugenio Levi\", \"1883-1917\", 1434], [225, 167, \"Johann Hudde  was a Dutch mathematician who worked on maxima and minima and the theory of equations. He gave an ingenious method to find multiple roots of an equation.\", \"Johann Hudde\", \"1628-1704\", 221], [1582, 167, \"John Raymond Wilton  studied at Adelaide and Cambridge. He lectured at Sheffield before returning to Adelaide as a Professor. He worked in Analysis and Number Theory. \", \"John Raymond Wilton\", \"1884-1944\", 1458], [1499, 167, \"Felix Bernstein  established his famous theorem on the equivalence of sets while in Cantor's seminar at Halle in  1897 . He also worked on transfinite ordinal numbers.\", \"Felix Bernstein\", \"1878-1956\", 1346], [1875, 167, \"Artin  made a major contribution to the theory of noncommutative rings and later worked on rings with the minimum condition on right ideals, now called Artinian rings.\", \"Emil Artin\", \"1898-1962\", 1740], [1876, 168, \"Fritz Zwicky  was a Bulgarian-born  Swiss astronomer who worked most of his life in the USA. He made important contributions in theoretical and observational astronomy.\", \"Fritz Zwicky\", \"1898-1974\", 1742], [2691, 168, \"Norman Alling  is an American mathematician who worked in a wide range of mathematics, from the theory of ordered groups to Riemann surfaces, including surreal numbers.\", \"Norman Alling\", \"1930-\", 2681], [2607, 168, \"Ho\\u00e0ng T\\u1ee5y  was a Vietnamese mathematician who was one of the founders of higher education in Vietnam. He was the first secretary of the Vietnamese Mathematical Society.\", \"Ho\\u00e0ng T\\u1ee5y\", \"1927-2019\", 2595], [517, 168, \"Wilhelm Bessel  determined the positions and proper motions of stars. He also used a method of mathematical analysis involving what is now known as the Bessel function.\", \"Wilhelm Bessel\", \"1784-1846\", 497], [2951, 168, \"Qamil Haxhibeqiri  was a Yugoslavian mathematician, born in what is now Kosovo, who worked in topology and was the second president of the Kosovan Mathematical Society.\", \"Qamil Haxhibeqiri\", \"1949-\", 2935], [540, 168, \"Jean-Baptiste B\\u00e9langer  was a French engineer and mathematician. His ideas influenced strongly the teaching of statics and dynamics, and mechanics in France and Europe.\", \"Jean-Baptiste B\\u00e9langer\", \"1790-1874\", 519], [1026, 169, \"Robert Philip  graduated from St Andrews and became a teacher at Madras College St Andrews. He moved to Hutcheon's School Glasgow and eventually became headmaster there.\", \"Robert Philip\", \"1854-1913\", 964], [2493, 169, \"Harish-Chandra   was an Indian-born mathematician and physicist who worked mainly in America and did fundamental work in representation theory, especially on Lie groups.\", \"Harish-Chandra\", \"1923-1983\", 2473], [1227, 169, \"Alfred Dixon  graduated from London and Cambridge and then had professorial appointments in Galway and Belfast. He worked on ordinary and partial differential equations.\", \"Alfred Dixon\", \"1865-1936\", 1129], [1855, 169, \"Max Newman  was an English mathematician who worked on combinatorial topology and theoretcal computer science. His codebreaking work in World War II has made him famous.\", \"Max Newman\", \"1897-1984\", 1727], [1539, 169, \"Alexander Merriles  graduated from Edinburgh University and afterwards taught at Edinburgh Provincial Training College and George Watson's Ladies' College in Edinburgh. \", \"Alexander Merriles\", \"1880-1950\", 1376], [941, 169, \"Hermann Schubert  was a German mathematiciaan who worked on parts of algebraic geometry that involve a finite number of solutions. This is called  Enumerative Geometry .\", \"Hermann Schubert\", \"1848-1911\", 885], [152, 169, \"Pierre Gassendi  was a French astronomer who was the first to observe a transit of Venus. He wrote on astronomy, his own astronomical observations and on falling bodies.\", \"Pierre Gassendi\", \"1592-1655\", 158], [999, 169, \"Sch\\u00f6nflies  worked first on geometry and kinematics but became best known for his work on set theory and crystallography. He classified the  230  space groups in  1891 .\", \"Arthur Sch\\u00f6nflies\", \"1853-1928\", 943], [1976, 169, \"Saunders Mac Lane  was an American mathematician who worked in cohomology and category theory, but who is best known for the algebra book he wrote with Garrett Birkhoff.\", \"Saunders Mac Lane\", \"1909-2005\", 2106], [1689, 169, \"Hans Ludwig Hamburger  was a German mathematician. He spent the Second World War in England and afterwards was a professor at universities in Berlin, Cologne and Ankara.\", \"Hans Hamburger\", \"1889-1956\", 1561], [503, 169, \"Louis Poinsot  was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple.\", \"Louis Poinsot\", \"1777-1859\", 483], [1931, 169, \"Frederick Bath  graduated from Bristol and Cambridge and held posts at King's College London, University College Dundee, St Andrews and Edinburgh. He worked in Geometry.\", \"Frederick Bath\", \"1900-1982\", 1784], [1969, 169, \"Max Black  was an Azerbaijan-born philosopher who made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art.\", \"Max Black\", \"1909-1988\", 2102], [1082, 170, \"Max Planck  initiated the study of quantum mechanics when he announced in  1900  his theoretical research into the radiation and absorption of heat/light by a black body.\", \"Max Planck\", \"1858-1947\", 1012], [2018, 170, \"Gheorghe  Calug\\u0103re\\u0103nu  was a Romanian mathematician who studied the theory of functions of a complex variable  as well as of differential geometry and algebraic topology.\", \"Gheorghe  Calug\\u0103re\\u0103nu\", \"1902-1976\", 1838], [1143, 170, \"William J Greenstreet  graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the  Mathematical Gazette .\", \"William J Greenstreet\", \"1861-1930\", 1064], [2372, 170, \"Alexander Andreevich Samarskii   was a Ukranian-born mathematician who worked in mathematical physics, applied mathematics, numerical analysis and mathematical modelling.\", \"Alexander Andreevich Samarskii\", \"1919-2008\", 2361], [1497, 170, \"Edwin Adams  studied at Harvard, G\\u00f6ttingen and Cambridge and became Physics Professor at Princeton. He is best known for his translations of some of Einstein's lectures. \", \"Edwin P Adams\", \"1878-1956\", 1344], [2833, 170, \"Donald Knuth  is an American mathematician and computer scientist most famous for his contributions to the study of algorithms and inventing the TeX typesetting language.\", \"Donald Knuth\", \"1938-\", 2826], [1981, 170, \"Caleb Gattegno  was an Egyption mathematical educator who is best known for his innovative approaches to teaching and learning mathematics, foreign languages and reading.\", \"Caleb Gattegno\", \"1911-1988\", 2144], [1283, 170, \"John Dougall  graduated from Glasgow. He taught at Glasgow University before joining a publishing firm. He wrote a number of papers on both pure and applied mathematics. \", \"John Dougall\", \"1867-1960\", 1175], [439, 170, \"John Bonnycastle  was an English teacher of mathematics and prolific writer. He wrote for the early volumes of Rees's  Cyclop\\u00e6dia , about algebra, analysis and astronomy.\", \"John Bonnycastle\", \"1751-1821\", 420], [2024, 171, \"Karl Menger  was an Austrian-American mathematician who worked on algebras, geometries, curve and dimension theory. He also contributed to game theory and social sciences.\", \"Karl Menger\", \"1902-1985\", 1844], [896, 171, \"George-Henri Halphen  was a French mathematician who worked on the singularity theory of algebraic curves as well as invariant theory and projective differential geometry.\", \"George-Henri Halphen\", \"1844-1889\", 840], [1831, 171, \"Kazimierz Kuratowski  worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.\", \"Kazimierz Kuratowski\", \"1896-1980\", 1702], [2122, 171, \"Marian Adam Rejewski  was a Polish mathematician and cryptologist. He was one of the team that reconstructed the German military Enigma cypher machine before World War II.\", \"Marian Rejewski\", \"1905-1980\", 1961], [1050, 171, \"Rudio  was a German mathematician who helped organise the first International Congress of Mathematicians at Zurich and edited the first volumes of Euler's collected works.\", \"Ferdinand Rudio\", \"1856-1929\", 984], [3006, 171, \"Maryam Mirzakhani  was an Iranian mathematician who worked in America and was the first woman to be awarded a Fields Medal. She worked in the geometry of Riemann surfaces.\", \"Maryam Mirzakhani\", \"1977-2017\", 3007], [1705, 171, \"Glenny Smeal  studied at Melbourne University and Imperial College London. After some time in Edinburgh he moved to a post in Statistical Methods and Computation at Leeds.\", \"Glenny Smeal\", \"1890-1974\", 1580], [2402, 171, \"Ernst Specker  was a Swiss mathematician who made decisive contributions towards shaping directions in topology, algebra, mathematical logic, combinatorics and algorithms.\", \"Ernst Specker\", \"1920-2011\", 2391], [1712, 172, \"Philip Stein  was a Lithuanian-born mathematician who became a professor of mathematics in South Africa. He worked on the theory of functions of real and complex variables.\", \"Philip Stein\", \"1890-1974\", 1588], [648, 172, \"Otto Hesse  worked on the development of the theory algebraic functions and the theory of invariants. He is remembered particularly for introducing the Hessian determinant.\", \"Otto Hesse\", \"1811-1874\", 622], [1737, 172, \"Hans Rademacher  was a German-born mathematician who worked in analytic number theory, mathematical genetics, the theory of functions of a real variable and quantum theory.\", \"Hans Rademacher\", \"1892-1969\", 1616], [968, 172, \"Oliver Heaviside  proved important results in electromagnetism and vector calculus. He reduced Maxwell's  20  equations in  20  variables to  4  equations in  2  variables.\", \"Oliver Heaviside\", \"1850-1925\", 906], [660, 172, \"J J Sylvester  did important work on matrix theory. He discovered the discriminant of a cubic equation and first used the name 'discriminant' for equations of higher order.\", \"James Joseph Sylvester\", \"1814-1897\", 634], [1767, 172, \"Eduard \\u010cech  was a Czech mathematician known for his work in projective differential geometry and topology. He introduced the idea of the higher homotopy groups of a space.\", \"Eduard \\u010cech\", \"1893-1960\", 1633], [2142, 172, \"Ernst Peschl  was a German mathematician who worked on geometric complex analysis, partial differential equations  and the theory of functions of several complex variables.\", \"Ernst Peschl\", \"1906-1986\", 1988], [2215, 172, \"Norman Levinson  was an American mathematician who worked with Fourier transforms, complex analysis, non-linear differential equations, number theory and signal processing.\", \"Norman Levinson\", \"1912-1975\", 2192], [1303, 172, \"John Airey  graduated from Cambridge and became Principal of the West Ham Technical Institute. He is best known for his work in producing tables of mathematical functions. \", \"John Airey\", \"1868-1937\", 1198], [1272, 172, \"Kazimierz \\u017borawski  was a Polish mathematician who worked on invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics.\", \"Kazimierz \\u017borawski\", \"1866-1953\", 1164], [2795, 172, \"James Glimm  is an American mathematician who researched in both pure and applied mathematics and whose work has revolutionised shock-wave theory and other fields of study.\", \"James Glimm\", \"1934-\", 2753], [2945, 172, \"Vladimir Voevodsky  was a Russian-born American mathematician who was awarded a Fields Medal in  2002  for his work in developing a homotopy theory for algebraic varieties.\", \"Vladimir Voevodsky\", \"1966-2017\", 2998], [308, 172, \"Nicolaus Bernoulli  was one of the famous Swiss family of mathematicians. He is most important for his correspondence with other mathematicians including Euler and Leibniz.\", \"Nicolaus (I) Bernoulli\", \"1687-1759\", 299], [947, 173, \"Andrew Barclay  was a Scottish School teacher who with Fraser and Knott he was one of the writers who originally proposed the founding of the Edinburgh Mathematical Society.\", \"Andrew Jeffrey Gunion Barclay\", \"1849-1943\", 891], [2740, 173, \"Pierre Cartier  is a French mathematician who has worked in algebraic geometry, representation theory, mathematical physics and category theory. He was a member of Bourbaki.\", \"Pierre Cartier\", \"1932-\", 2728], [2514, 173, \"Aldo Andreotti  was an Italian mathematician who worked on algebraic geometry, on the theory of functions of several complex variables and on partial differential operators.\", \"Aldo Andreotti\", \"1924-1980\", 2493], [2507, 173, \"Ren\\u00e9 Thom  was a French mathematician who is known for his development of catastrophe theory, a mathematical treatment of continuous action producing a discontinuous result.\", \"Ren\\u00e9 Thom\", \"1923-2002\", 2486], [1588, 173, \"Thomas MacRobert  studied at Glasgow and Cambridge universities. He returned to Glasgow to a series of posts culminating in the professorship. He worked on Complex Analysis.\", \"Thomas MacRobert\", \"1884-1962\", 1464], [1066, 173, \"Alexander Yule Fraser  was an Edinburgh teacher. With Barclay and Knott he was one of the writers who originally proposed the founding of the Edinburgh Mathematical Society.\", \"Alexander Yule Fraser\", \"1857-1890\", 996], [2028, 173, \"Mina Spiegel Rees  was an American mathematician and a pioneer in the history of computing. She had a major impact on the academic and research culture of the United States.\", \"Mina Rees\", \"1902-1997\", 1848], [617, 173, \"Viktor Bunyakovsky  worked on Number Theory as well as geometry, mechanics and hydrostatics. He discovered the Cauchy-Schwarz inequality  25  years before Cauchy or Schwarz.\", \"Viktor Yakovlevich Bunyakovskii\", \"1804-1889\", 592], [715, 173, \"Enrico Betti  is noted for his contributions to algebra and topology. Betti also did important work in theoretical physics, in particular in potential theory and elasticity.\", \"Enrico Betti\", \"1823-1892\", 688], [2316, 173, \"Edmund Hlawka  was an Austrian mathematician who made important contributions to the geometry of numbers, to the theory of uniform distribution and to numerical integration.\", \"Edmund Hlawka\", \"1916-2009\", 2289], [384, 173, \"Gianfrancesco Malfatti  was an Italian mathematician who worked on geometry, probability and mechanics and made contributions to the problem of solving polynomial equations.\", \"Gianfrancesco Malfatti\", \"1731-1807\", 371], [130, 173, \"Stanislaw Mazur  was a Polish mathematician  ( born in what is now Ukraine )  who worked in functional analysis, summability theory, infinite games and computable functions.\", \"Stanis\\u0142aw Mazur\", \"1905-1981\", 1968], [1383, 174, \"Onorato Nicoletti   was an Italian mathematician who worked in various fields of mathematics, including numerical analysis, infinitesimal analysis and differential equations.\", \"Onorato Nicoletti\", \"1872-1929\", 1257], [2830, 174, \"Daniel Akyeampong  was a Ghanaian mathematician known for applying algebraic methods to theoretical physics. He was important in the development of higher education in Ghana.\", \"Daniel Akyeampong\", \"1938-2015\", 2823], [2040, 174, \"Bertha Swirles Jeffreys  was an English physicist who carried out research on quantum theory. She co-authored an important text-book on mathematical physics with her husband.\", \"Bertha Swirles Jeffreys\", \"1903-1999\", 1867], [1073, 174, \"Hans Freudenthal  was a German-born Dutch mathematician who made important contributions to algebraic topology. He also published works on history and mathematical education.\", \"Hans Freudenthal\", \"1905-1990\", 1948], [2044, 174, \"Ernest Walton  was an Irish physicist who won a Nobel Prize for his work on particle accelerators. He was a founder member of the Trinity College Dublin Mathematical Society.\", \"Ernest Walton\", \"1903-1995\", 1871], [17, 174, \"Ibn al-Banna  was an Islamic mathematician who wrote a large number of works including an introduction to Euclid's  Elements , an algebra text and various works on astronomy.\", \"Ibn al-Banna\", \"1256-1321\", 36], [1203, 174, \"Georgy Voronoy  was a Ukranian mathematician best known for the  Voronoi diagram  which is a partitioning of a plane into regions based on distance to a finite set of points.\", \"Georgy Voronoy\", \"1868-1908\", 1191], [1363, 174, \"In a long and varied career  Russell  published a vast number of books on logic, theory of knowledge, and many other topics. His best known work was  Principia Mathematica  .\", \"Bertrand Russell\", \"1872-1970\", 1246], [2892, 174, \"Edmund Robertson  is a Scottish mathematician who worked in computational group theory and is best known as one of the creators of the MacTutor History of Mathematics archive\", \"Edmund Robertson\", \"1943-\", 2880], [1648, 174, \"David Kennedy Fraser  studied at Glasgow, Leipzig and Cornell Universities. He returned to Edinburgh as a Lecturer in Education before moving to Jordanhill Training College. \", \"David Kennedy Fraser\", \"1888-1962\", 1528], [1668, 174, \"Robert  Remak  was a German mathematician. He worked in group theory as well as algebraic number theory, mathematical economics and geometry of numbers. He died in Auschwitz.\", \"Robert Remak\", \"1888-1942\", 1543], [1827, 174, \"Eleanor Pairman  graduated from Edinburgh. She went to London where she worked with Karl Pearson and then went to the USA where she gained a doctorate from Radcliffe College.\", \"Eleanor Pairman\", \"1896-1973\", 1698], [2036, 175, \"Andrey Kolmogorov  was one of the developers of probability theory. He later used this work to study the motion of the planets and the turbulent flow of air from a jet engine.\", \"Andrey Kolmogorov\", \"1903-1987\", 1863], [2388, 175, \"Raimundo Chela  was a Venezuelan mathematician who made a substantial contribution to improving the teaching of mathematics in Venezuela at all school and university levels.\\\\n \", \"Raimundo Chela\", \"1919-1984\", 2377], [2938, 175, \"Gerd Faltings  is a German mathematician whose work in algebraic geometry led to important results in number theory, including helping with the proof of Fermat's Last Theorem.\", \"Gerd Faltings\", \"1954-\", 2956], [1278, 175, \"Arthur Lee Dixon  was an English mathematician who worked on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions.\", \"Arthur Lee Dixon\", \"1867-1955\", 1169], [477, 175, \"Annibale Giordano  was an Italian-French mathematician and revolutionary who produced some works on geometry. He was involved in Republican plots against the Bourbon monarchy.\", \"Annibale Giordano\", \"1769-1835\", 457], [240, 175, \"Nicolas Malebranche  was a major French philosopher and follower of Descartes whose ideas he developed to bring them more in line with standard Roman Catholic orthodox belief.\", \"Nicolas Malebranche\", \"1638-1715\", 234], [1232, 175, \"David Tweedie  graduated from Edinburgh University and taught at George Watson's College in Edinburgh. He spent more than  30  years teaching in various institutions in Egypt.\", \"David Tweedie\", \"1865-1934\", 1134], [1438, 176, \"Lebesgue  formulated the theory of measure in  1901  and the following year he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral.\", \"Henri Lebesgue\", \"1875-1941\", 1294], [2005, 176, \"Petr Sergeevich Novikov  is a Russian mathematician known for his work on combinatorial problems in group theory including the word problem for groups and the Burnside problem.\", \"Petr Sergeevich Novikov\", \"1901-1975\", 1820], [532, 176, \"Jean-Victor Poncelet  was one of the founders of modern projective geometry. His development of the pole and polar lines associated with conics led to the principle of duality.\", \"Jean-Victor Poncelet\", \"1788-1867\", 512], [881, 176, \"Hermann Schwarz  worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area.\", \"Hermann Schwarz\", \"1843-1921\", 831], [63, 176, \"Francisco Maurolico  was an Italian Benedictine who wrote important books on Greek mathematics. He also worked on geometry, the theory of numbers, optics, conics and mechanics.\", \"Francesco Maurolico\", \"1494-1575\", 80], [1920, 176, \"Salomon Bochner  was a pure mathematician who was born in what is now Poland and moved to America to escape the Nazis. He worked on integral transforms and distribution theory.\", \"Salomon Bochner\", \"1899-1982\", 1773], [2864, 177, \"Srinivasa Varadhan  is an Indian mathematician who works in America. He is who is known for his fundamental contributions to probability theory. He won the Abel prize in  2007 .\", \"Srinivasa Varadhan\", \"1940-\", 2856], [2138, 177, \"Edward Wright  was a number theorist and collaborator of G H Hardy. He was Professor of Mathematics at Aberdeen for many years and went on to become Principal of the university.\", \"Edward Maitland Wright\", \"1906-2005\", 1984], [931, 177, \"John Wilson  was a Scottish mathematician who took over the Rectorship of his father's Academy in Bannockburn and later moved to Edinburgh as a tutor in mathematics and physics.\", \"John Wilson\", \"1847-1896\", 875], [138, 177, \"Shizuo Kakutani  was a Japanese-born American mathematician who worked in probability theory, ergodic theory and complex analysis, and is best known for his fixed-point theorem.\", \"Shizuo Kakutani\", \"1911-2004\", 2163], [1059, 177, \"Von Dyck  made important contributions to function theory, group theory  ( where a fundamental result on group presentations is named after him )  topology and potential theory.\", \"Walther von Dyck\", \"1856-1934\", 990], [2735, 177, \"Lee Segel  was an American mathematical biologist who moved to Israel. He is known for his work in the spontaneous appearance of order in convection, slime molds and chemotaxis.\", \"Lee Segel\", \"1932-2005\", 2723], [1191, 177, \"James Watt  was an Edinburgh lawyer and actuary. He was interested in science, being a member of the Scottish Meteorological Society and the Royal Scottish Geographical Society.\", \"James Watt\", \"1863-1945\", 1103], [2212, 177, \"Louis Goodstein  was an English mathematician who worked on mathematical logic, in particular ordinal numbers, recursive arithmetic, analysis, and the philosophy of mathematics.\", \"Louis Goodstein\", \"1912-1985\", 2189], [307, 177, \"George Berkeley  was an Irish bishop and philosopher whose best known contribution to mathematics is his attack on the logical foundation of the calculus as developed by Newton.\", \"George Berkeley\", \"1685-1753\", 298], [709, 178, \"Francis Galton  was an English polymath, explorer, anthropologist and statistician. He invented the concept of \\\"regression to the mean\\\" and is famous as \\\"the father of eugenics\\\".\", \"Francis Galton\", \"1822-1911\", 682], [2182, 178, \"Walter Ledermann  was a refugee from Germany who did his doctorate at St Andrews and taught here until  1946 . He did important work in algebra and in particular in group theory.\", \"Walter Ledermann\", \"1911-2009\", 2165], [2526, 178, \"Norrie Everitt  was an English mathematician who spent most of his career at Dundee and Birmingham. He was an expert in the field of spectral analysis and differential equations.\", \"Norrie Everitt\", \"1924-2011\", 2515], [2008, 178, \"Richard Brauer  became interested in work on group characters. He formulated a method to classify all finite simple groups and spent the rest of his life working on this problem.\", \"Richard Brauer\", \"1901-1977\", 1822], [651, 178, \"Charles Graves  was an Irish mathematician who published on geometry and on Gaelic history. He and his brother John are credited with inspiring Hamiton to invent the quaternions.\", \"Charles Graves\", \"1812-1899\", 625], [699, 178, \"William Chauvenet  was an American professor of mathematics, astronomy, navigation and surveying who was instrumental in the establishment of the U.S. Naval Academy at Annapolis.\", \"William Chauvenet\", \"1820-1870\", 672], [2285, 178, \"Fred Hoyle  was an English astronomer best known for his espousal of the \\\"steady-state\\\" theory of the universe and rejecting the \\\"big bang\\\" theory. He also wrote science fiction.\", \"Fred Hoyle\", \"1915-2001\", 2264], [22, 178, \"William of Ockham  was an English mathematician and philosopher best known for  Ockham's razor , one version of which is:  It is vain to do with more what can be done with less .\", \"William of Ockham\", \"1288-1348\", 41], [347, 179, \"John Smith  graduated from Glasgow University and then stayed on as a lecturer. He taught at Campbeltown Grammar School and Dollar Academy and then became an HM Schools Inspector.\", \"John Smith\", \"1906-1962\", 2000], [2550, 179, \"Kristen Nygaard  was a Norwegian computer scientist, programming language pioneer, and politician. He was the co-inventor of object-oriented programming and the language  Simula .\", \"Kristen Nygaard\", \"1926-2002\", 2568], [231, 179, \"Henry Coley  was an English  17 th century astrologer and mathematician who published a famous astrology text  Clavis astrologiae  and taught mathematics at his house in London.\\\\n \", \"Henry Coley\", \"1633-1704\", 227], [26, 179, \"Nicole Oresme  was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series.\", \"Nicholas Oresme\", \"1323-1382\", 45], [611, 179, \"Guglielmo Libri  was an Italian mathematician who worked on mathematical physics, number theory and the theory of equations. He also published works on the history of mathematics.\", \"Guglielmo Libri\", \"1803-1869\", 586], [2181, 179, \"Tjalling Charles Koopmans  was a Dutch American mathematician and economist. He won the Nobel prize in Economics for his work on the theory of the optimum allocation of resources.\", \"Tjalling Charles Koopmans\", \"1910-1985\", 2142], [2781, 179, \"John Howie  was a Scottish mathematician who was Regius Professor of Mathematics at the University of St Andrews for more than  40  years. He was a specialist in semigroup theory.\", \"John Howie\", \"1936-2011\", 2784], [1651, 179, \"Giovanni Sansone  was an Italian mathematician, known for his works on mathematical analysis, the theory of orthogonal functions and the theory of ordinary differential equations.\", \"Giovanni Sansone\", \"1888-1979\", 1531], [1460, 179, \"Otto Blumenthal  was a German mathematician who worked in complex function theory and aerodynamics. He was executive editor of the journal  Mathematischen Annalen  for many years.\", \"Otto Blumenthal\", \"1876-1944\", 1317], [917, 180, \"G\\u00f6sta Mittag-Leffler  was a Swedish mathematician who worked on the general theory of functions. His best known work concerned the analytic representation of a one-valued function.\", \"G\\u00f6sta Mittag-Leffler\", \"1846-1927\", 861], [1403, 180, \"Edmund Whittaker 's best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. \", \"Edmund Whittaker\", \"1873-1956\", 1266], [1467, 180, \"Tatiana Alexeyevna Afanassjewa  was a Ukrainian-born Dutch mathematician and physicist who made contributions to the fields of statistical mechanics and statistical thermodynamics.\", \"Tatiana Alexeyevna Afanassjewa\", \"1876-1964\", 1320], [363, 180, \"Jean d'Alembert  was a a French mathematician who was a pioneer in the study of differential equations and their use of in physics. He studied the equilibrium and motion of fluids.\", \"Jean d'Alembert\", \"1717-1783\", 350], [2589, 180, \"Allen Shields  was an American mathematician who worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory.\", \"Allen Shields\", \"1927-1989\", 2582], [1144, 180, \"William Peddie  graduated from Edinburgh University and then lectured in Physics. He was appointed Professor of Physics at Queen's College Dundee and held this post for  37  years.\", \"William Peddie\", \"1861-1946\", 1065], [2489, 180, \"Freeman Dyson  was an English theoretical physicist and mathematician who worked in quantum electrodynamics, solid-state physics and astronomy. He worked in America for many years.\", \"Freeman Dyson\", \"1923-2020\", 2469], [578, 180, \"William Hunter McCrea  was an English astronomer and mathematician whose research on the composition of the Sun and on star formation led to the development of the big bang theory.\", \"William McCrea\", \"1904-1999\", 1934], [619, 180, \"Edward Sang  was a Scottish mathematician who wrote extensively on mathematical, mechanical, optical and actuarial topics as well as publishing astronomical and logarithmic tables.\", \"Edward Sang\", \"1805-1890\", 594], [1362, 180, \"Alexander Durie Russell  graduated from Edinburgh University at taught at Morelands School Edinburgh, at Stranraer High School and at Falkirk High School where he spent  38  years.\", \"Alexander Durie Russell\", \"1872-1955\", 1245], [1900, 180, \"Rajeev Motwani  was an Indian-born American computer scientist whose research focused on theoretical computer science and is known for his contribution to the Google search engine.\", \"Rajeev Motwani\", \"1962-2009\", 2986], [1706, 180, \"Herbert Dingle  was an English physicist and philosopher of science who wrote a number of influential books. He was involved in several long-running disputes with other physicists.\", \"Herbert Dingle\", \"1890-1978\", 1582], [1511, 180, \"Leon Lichtenstein  was a Polish-born mathematician, who made contributions to the areas of differential equations, conformal mapping, potential theory, hydrodynamics and astronomy.\", \"Leon Lichtenstein\", \"1878-1933\", 1351], [1178, 180, \"Albert Ch\\u00e2telet   was a French politician and mathematician who researched in number theory and in algebra. He stood for the post of French president but was defeated by de Gaulle.\", \"Albert Ch\\u00e2telet\", \"1883-1960\", 1426], [2621, 180, \"Victor Olunloyo  is a Nigerian mathematician who published results on number theory. He became governor of Oyo State in Nigeria in October  1983  until unseated by a military coup.\", \"Victor Olunloyo\", \"1935-\", 2776], [194, 181, \"Wilhelm Magnus  was a German American mathematician who worked in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.\", \"Wilhelm Magnus\", \"1907-1990\", 2044], [1180, 181, \"Anna Johnson Wheeler  was an American mathematician. She is best known for early work on linear algebra in infinite dimensions, which has later become a part of functional analysis.\", \"Anna Johnson Wheeler\", \"1883-1966\", 1428], [1458, 181, \"James Gray  was the son of Andrew Gray. He graduated from University College Bangor and occupied a series of posts in Glasgow University, finishing as Professor of Applied Physics. \", \"James Gray\", \"1876-1934\", 1315], [2431, 181, \"Chike Obi  was a Nigerian mathematician and politician. He was the first Nigerian to hold a doctorate in mathematics. His research was on non-linear ordinary differential equations.\", \"Chike Obi\", \"1921-2008\", 2416], [2483, 181, \"Cathleen Morawetz  was a Canadian mathematician who worked on the  partial differential equations governing fluid flow, particularly those of mixed type occurring in transonic flow.\", \"Cathleen Morawetz\", \"1923-2017\", 2463], [1208, 181, \"William Sheppard  read Mathematics at Cambridge and then went on to study Law. He was appointed to the Department of Education. His mathematical interests were mainly in Statistics.\", \"William Sheppard\", \"1863-1936\", 1116], [1598, 182, \"From  1923 - 38   Weyl  evolved the concept of continuous groups using matrix representations. With his application of group theory to quantum mechanics he set up the modern subject.\", \"Hermann Weyl\", \"1885-1955\", 1474], [2124, 182, \"Lucien Alexandre Charles Ren\\u00e9 de Possel  was a French mathematician and computer scientist who worked on optical character recognition. He was one of the founders of the Bourbakists.\", \"Ren\\u00e9 de Possel\", \"1905-1974\", 1963], [2498, 182, \"J Ernest Wilkins  was an African-American mathematician and nuclear scientist. He worked on various pure mathematical topics as well as researching in nuclear engineering and optics.\", \"J Ernest Wilkins\", \"1923-2011\", 2478], [316, 182, \"James Stirling  was a Scottish mathematician whose most important work  Methodus Differentialis   in  1730  is a treatise on infinite series, summation, interpolation and quadrature.\", \"James Stirling\", \"1692-1770\", 307], [707, 182, \"Samuel Haughton  was an Irish mathematician, geologist and priest who published on a wide variety of topics. He is remembered for his work on hanging as a humane method of execution.\", \"Samuel Haughton\", \"1821-1897\", 680], [2541, 182, \"Jean-Pierre Serre  is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was a member of Bourbaki.\", \"Jean-Pierre Serre\", \"1926-\", 2563], [704, 182, \"Pafnuty Chebyshev  is largely remembered for his investigations in number theory. Chebyshev was also interested in mechanics and is famous for the orthogonal polynomials he invented.\", \"Pafnuty Chebyshev\", \"1821-1894\", 677], [187, 182, \"Kamalakara  was an Indian astronomer and mathematician who combined traditional Indian astronomy with Aristotelian physics and Ptolemaic astronomy as presented by Islamic scientists.\", \"Kamalakara\", \"1616-1700\", 194], [1079, 182, \"George Gibson  graduated from Glasgow University and went on to become Professor there. He published several important textbooks and was an enthusiast for the History of Mathematics.\", \"George Gibson\", \"1858-1930\", 1009], [2996, 182, \"Maxim Kontsevich  is a Russian and French mathematician best known for his work on geometric aspects of mathematical physics including knot theory, quantisation, and mirror symmetry.\", \"Maxim Kontsevich\", \"1964-\", 2991], [148, 182, \"Marin Mersenne  was a French monk who is best known for his role as a clearing house for correspondence between eminent philosophers and scientists and for his work in number theory.\", \"Marin Mersenne\", \"1588-1648\", 154], [1553, 182, \"Sergei Bernstein  was a Ukranian mathematician who made important contributions to partial differential equations, differential geometry, probability theory and approximation theory.\", \"Sergei Bernstein\", \"1880-1968\", 1390], [894, 182, \"\\u00c1goston Scholtz  was a Hungarian mathematician, one of the founders of the Hungarian Mathematics and Physics Association. He worked on projective geometry and theory of determinants.\", \"\\u00c1goston Scholtz\", \"1844-1916\", 838], [2633, 182, \"Madan Lal Puri  is an Indian-born statistician whose work in nonparametric statistics and probability theory has had profound effects on the way statistics is understood and applied.\", \"Madan Lal Puri\", \"1929-\", 2654], [2504, 183, \"Peter Hilton  was an English mathematician who made important contributions to homotopy theory. He is best known for his text-books and for his work as a code-breaker in World War II.\", \"Peter Hilton\", \"1923-2010\", 2484], [1717, 183, \"Andrew Young  graduated from Edinburgh and taught at St Andrews and London Universities. He then trained as a lawyer and worked as a solicitor in Edinburgh for the rest of his career.\", \"Andrew Young\", \"1891-1968\", 1593], [1061, 183, \"William Thomson  was appointed Professor of Mathematics at Victoria College Stellenbosch in South Africa and went on to become Principal of the University of South Africa in Pretoria.\", \"William Thomson\", \"1856-1947\", 992], [1768, 183, \"Ernst \\u00d6pik  was an Estonian astronomer who specialised in the study of minor bodies, such as asteroids, comets and meteors  He spent the second half of his career in Northern Ireland.\", \"Ernst \\u00d6pik\", \"1893-1985\", 1634], [1009, 183, \"M J M Hill  was professor at University College, London. He did important work on hydrodynamics and also on the teaching of mathematics, particularly on teaching Euclid's  Elements . \", \"Micaiah Hill\", \"1856-1929\", 988], [1142, 183, \"Theodor Anghelu\\u021b\\u0103  was a Romanian mathematician who made important contributions to Function Theory, to Differential and Integral Equations, and to Functional and Algebraic Equations.\", \"Theodor Anghelu\\u021b\\u0103\", \"1882-1964\", 1424], [12, 184, \"Yang Hui  was a Chinese mathematician who wrote several outstanding mathematical texts. These contained solutions of quadratic equations as well as Pascal's triangle and magic squares.\", \"Yang Hui\", \"1238-1298\", 34], [613, 184, \"Juan Manuel Cajigal  was the founder of mathematical and engineering studies in Venezuela and trained many mathematicians. He founded the first astronomical observatory in Venezuela.\\\\n \", \"Juan Manuel Cajigal\", \"1803-1856\", 588], [1624, 184, \"Walter Brown  graduated from Glasgow University and worked at Hong Kong University. He was interned by the Japanese in World War II and on his release he returned to posts in Scotland.\", \"Walter Brown\", \"1886-1957\", 1505], [1218, 184, \"Archibald Macintyre  was an English mathematician who worked on complex analysis. He taught in Aberdeen and at the Univeversity of Cincinatti. He was married to Sheila Scott Macintyre.\", \"Archibald Macintyre\", \"1908-1967\", 2050], [2682, 185, \"Ismail Mohamed  was a South African mathematician who specialised in group theory. He was imprisoned by the South African government but later became a member of parliament for the ANC.\", \"Ismail Mohamed\", \"1930-2013\", 2672], [765, 185, \"Edward Routh  was a Canadian-born English mathematician, best-known as an outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge.\", \"Edward Routh\", \"1831-1907\", 734], [437, 185, \"John Playfair  worked on geology, physics and geometry and studied at the University of St Andrews. His best-known contribution to mathematics is his form of Euclid's parallelism axiom.\", \"John Playfair\", \"1748-1819\", 410], [687, 185, \"James Cockle  was an English lawyer and mathematician who wrote papers on both pure and applied mathematics, as well as on the history of science. He became Chief Justice of Queensland.\", \"James Cockle\", \"1819-1895\", 660], [1603, 185, \"Karlis Zalts  was a Latvian mathematician with wide-ranging interests in topics such as mechanical calculators, statistics and nomography as well as folklore, education, and philosophy.\", \"Karlis Zalts\", \"1885-1953\", 1478], [1564, 185, \"Toeplitz  worked on infinite linear and quadratic forms. In the  1930 's he developed a general theory of infinite dimensional spaces and criticised Banach's work as being too abstract.\", \"Otto Toeplitz\", \"1881-1940\", 1402], [2046, 185, \"Frank Ramsey  was an English mathematician most important for his work on the foundations of mathematics and philosophy, but best known for his so-called Ramsey theory in combinatorics.\", \"Frank Ramsey\", \"1903-1930\", 1873], [2823, 185, \"Yuri Ivanovich Manin  was a Soviet  mathematician, known for work in algebraic geometry and diophantine geometry. He also wrote on mathematical logic, computing and theoretical physics.\", \"Yuri Ivanovich Manin\", \"1937-2023\", 2817], [2755, 186, \"Paul Cohen  was an American mathematian who used a technique called  forcing   to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis.\", \"Paul Cohen\", \"1934-2007\", 2757], [864, 186, \"Edouard Lucas  was a French mathematician who is best known for his results in number theory. He studied the Fibonacci sequence and devised the test for Mersenne primes still used today.\", \"\\u00c9douard Lucas\", \"1842-1891\", 814], [2123, 186, \"Marie-Louise Dubreil-Jacotin  was a French mathematician who worked in fluid mechanics and abstract algebra. She was the second woman in France to obtain a doctorate in pure mathematics.\", \"Marie-Louise Dubreil-Jacotin\", \"1905-1972\", 1962], [2886, 186, \"Welington de Melo  was an outstanding Brazilian mathematician working on dynamical systems. He is perhaps best known as the Ph.D. supervisor of the  2014  Fields Medallist Artur Avila.\\\\n \", \"Welington de Melo\", \"1946-2016\", 2910], [249, 186, \"Choi Seok-jeong  was a Korean politician and mathematician who was the first to find orthogonal Latin squares. He constructed magic squares and invented the Hexagonal Tortoise Problem.\\\\n \", \"Choi Seok-jeong\", \"1646-1715\", 243], [1024, 186, \"Donald Coxeter 's work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics.\", \"Donald Coxeter\", \"1907-2003\", 2022], [1693, 186, \"Mildred Sanderson  was L E Dickson's first female Ph.D. student and was described by him as \\\"my most gifted pupil.\\\" Tragically, she died in the year following the award of her doctorate.\", \"Mildred Sanderson\", \"1889-1914\", 1565], [1431, 186, \"Arthur Conway  was an Irish mathematician and mathematical physicist who wrote one of the first books on relativity and co-edited two volumes of William Rowan Hamilton's collected works.\", \"Arthur Conway\", \"1875-1950\", 1288], [1481, 187, \"Hardy 's interests covered many topics of pure mathematics:- Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function and the distribution of primes.\", \"G H Hardy\", \"1877-1947\", 1328], [1219, 187, \"Arthur Erd\\u00e9lyi  was a Hungarian mathematician who became a lecturer at Edinburgh and after a period in the USA returned to Edinburgh as a Professor. He was an expert on Special Functions.\", \"Arthur Erd\\u00e9lyi\", \"1908-1977\", 2051], [2188, 187, \"Andy Guinand  was an Australian mathematician who worked in number theory  ( particularly prime numbers and the Riemann hypothesis ) , as well as generalizations of the Fourier transform.\", \"Andy Guinand\", \"1912-1987\", 2171], [2209, 187, \"Kathleen Ollerenshaw  was an English mathematician and educationalist who overcame deafness and went on to become an important political advisor. She was elected Lord Mayor of Manchester.\", \"Kathleen Ollerenshaw\", \"1912-2014\", 2186], [1479, 188, \"David Johnstone  graduated from Edinburgh University and taught at Spier's School Beith and George Heriot's School Edinburgh before moving to the Provincial Training College in Edinburgh. \", \"David Johnstone\", \"1877-1935\", 1326], [2532, 188, \"Chris Zeeman  was a British mathematician known for his work in geometric topology and singularity theory. He was responsible for founding the mathematics department at Warwick University.\", \"Chris Zeeman\", \"1925-2016\", 2522], [2, 188, \"Albert   ( or  Albertus Magnus )  was a German Dominican who wrote a commentary on Euclid's  Elements . He was made a Saint in  1931  and, in  1941 , was made patron of natural scientists.\", \"Albertus\", \"1200-1280\", 24], [111, 188, \"Duncan Liddel  was a Scottish mathematician, physician and astronomer who lectured on mathematics and astronomy on the continent. He made several endowments to Marischal College, Aberdeen.\", \"Duncan Liddel\", \"1561-1613\", 127], [567, 188, \"Gabriel Lam\\u00e9  worked on a wide variety of different topics. His work on differential geometry and contributions to Fermat's Last Theorem are important. He proved the theorem for  n  =  7 .\", \"Gabriel Lam\\u00e9\", \"1795-1870\", 546], [708, 188, \"Charles Hermite 's work in the theory of functions includes the application of elliptic functions to the quintic equation. He published the first proof that  e  is a transcendental number.\", \"Charles Hermite\", \"1822-1901\", 681], [2007, 188, \"Raj Chandra Bose  was an Indian mathematician and statistician who worked in America. He best known for his work in design theory, finite geometry and the theory of error-correcting codes.\", \"Raj Chandra Bose\", \"1901-1987\", 1821], [2597, 188, \"Geoffrey Shephard  was an outstanding geometer who wrote many interesting and important papers. His books, especially one co-authored with Branko Gr\\u00fcnbaum on tilings, have become classics.\", \"Geoffrey Shephard\", \"1927-2016\", 2591], [1555, 188, \"Marcel Riesz  was a Hungarian-born mathematician who worked on summation methods, potential theory and other parts of analysis, as well as number theory and partial differential equations.\", \"Marcel Riesz\", \"1886-1969\", 1498], [628, 189, \"Thomas Kirkman  wrote on the theory of groups and his writings are the first systematic account of the elements of group theory in English. He also made many contributions to combinatorics.\", \"Thomas Kirkman\", \"1806-1895\", 603], [1072, 189, \"Balfour Lockhart  graduated from Edinburgh University, his studies being interrupted by war service. He taught for most of his career at Edinburgh Academy, finishing as Head of Mathematics.\", \"Balfour Lockhart\", \"1886-1969\", 1493], [2708, 189, \"Igor Kluv\\u00e1nek  was Slovakian mathematician who worked in applied mathematics, functional analysis and operator theory. He spent part of his career in Australia before returning to Slovakia.\", \"Igor Kluv\\u00e1nek\", \"1931-1993\", 2698], [2994, 189, \"Richard Borcherds  is a South African born mathematician known for his work in lattices, group theory and infinite-dimensional algebras, for which he was awarded the Fields Medal in  1998 .\", \"Richard Borcherds\", \"1959-\", 2979], [1516, 189, \"Dehn  wrote one of the first systematic expositions of topology  (1907)  and later formulated important problems on group presentations, namely the word problem and the isomorphism problem.\", \"Max Dehn\", \"1878-1952\", 1357], [1665, 189, \"Feodor Theilheimer  was a German mathematician who was forced to move to America. He worked for the US Department of Defense on the research and development of ship design and construction.\", \"Feodor Theilheimer\", \"1909-2000\", 2090], [2378, 189, \"Hermann Bondi  was an Austrian-born scientist who made contributions to a wide variety of areas in mathematics and physics and was associated with the \\\"Steady-state\\\" theory of the universe.\", \"Hermann Bondi\", \"1919-2005\", 2367], [1926, 189, \"Zygmund 's work in harmonic analysis has application in the theory of waves and vibrations. He also did major work in Fourier analysis and its application to partial differential equations.\", \"Antoni Zygmund\", \"1900-1992\", 1779], [1894, 189, \"Gloria Hewitt  is an American mathematician who undertook research in algebra. She became the first African American woman to chair a university mathematics department in the United States.\", \"Gloria Hewitt\", \"1935-\", 2765], [2269, 190, \"Hanna Neumann  worked in group theory. Her thesis examined free products with amalgamation. Later she worked on varieties of groups and her book  Varieties of Groups    (1967)  is a classic.\", \"Hanna Neumann\", \"1914-1971\", 2235], [2047, 190, \"Geoffrey Timms  studied at Leeds and Cambridge and then took up a post at St Andrews. During World War II he served at Bletchley Park and Cheltenham and joined the Foreign Office afterwards.\", \"Geoffrey Timms\", \"1903-1982\", 1874], [716, 190, \"Gotthold Eisenstein  worked on a variety of topics including quadratic and cubic forms, the reciprocity theorem for cubic residues, quadratic partition of prime numbers and reciprocity laws.\", \"Gotthold Eisenstein\", \"1823-1852\", 689], [772, 190, \"Charles Dodgson  was a mathematics lecturer and author of mathematics books who is better known by the pseudonym Lewis Carroll. He is known especially for  Alice's Adventures in Wonderland .\", \"Charles Lutwidge Dodgson\", \"1832-1898\", 741], [1881, 190, \"K K Weatherhead  graduated from Edinburgh University although his studies were interrupted by service in World War I. He became an actuary, working for various Edinburgh insurance companies.\", \"K K Weatherhead\", \"1898-1979\", 1747], [1445, 190, \"Raymond C Archibald  studied in Canada, at Harvard and at Strasbourg. He spent most of his career at Brown University in Rhode Island. His main interests were in the History of Mathematics. \", \"Raymond Archibald\", \"1875-1955\", 1301], [1643, 190, \"Alexander Friedmann  was a Russian physicist and mathematician best-known for his work on the theory of relativity and in particular for introducing the possibility of an expanding universe.\", \"Alexander Friedmann\", \"1888-1925\", 1524], [856, 190, \"Ernst Schr\\u00f6der  was a German mathematician who did important work is in the area of algebra, set theory and logic. His work on ordered sets and ordinal numbers is fundamental to the subject.\", \"Ernst Schr\\u00f6der\", \"1841-1902\", 807], [992, 190, \"Francis Upton  was an American physicist and mathematician who worked with Thomas Edison in the development of incandescent light bulbs, electric generators, and electric power distribution.\", \"Francis Upton\", \"1852-1921\", 936], [1162, 191, \"Robert Alladice  studied at Edinburgh University and was then appointed assistant to Professor Chrystal there. He became Professor at Stanford University in California. He worked in geometry.\", \"Robert Allardice\", \"1862-1928\", 1082], [1726, 191, \"Leopold Vietoris  was a long-lived Austrian mathematician best known for his contributions to topology, especially the Mayer-Vietoris sequence. He was also interested in mathematical history.\", \"Leopold Vietoris\", \"1891-2002\", 1602], [1977, 191, \"Stan Ulam  solved the problem of how to initiate fusion in the hydrogen bomb. He also devised the 'Monte-Carlo method' widely used in solving mathematical problems using statistical sampling.\", \"Stan Ulam\", \"1909-1984\", 2107], [1597, 191, \"Herbert Turnbull  was Regius Professor of Mathematics at University of St Andrews from  1921  to  1950 . He was an expert in Invariant Theory and an enthusiast for the History of Mathematics.\", \"Herbert Turnbull\", \"1885-1961\", 1473], [2015, 191, \"Eugene Paul Wigner  was a Hungarian-American theoretical physicist and mathematician who won a Nobel prize for his contributions to the theory of the atomic nucleus and  elementary particles.\", \"Eugene Paul Wigner\", \"1902-1995\", 1835], [432, 191, \"Giuseppe Piazzi  was a mathematician and astronomer, most famed for his discovery of Ceres between the orbits of Mars and Jupiter. He also did important work on the proper motions of stars.\\\\n \", \"Giuseppe Piazzi\", \"1746-1826\", 405], [2517, 191, \"Benoit Mandelbrot  was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.\", \"Benoit Mandelbrot\", \"1924-2010\", 2496], [2751, 191, \"Gilbert Baumslag  had a long career as one of the leading researchers on infinite group theory. In the last part of his career he used his skill in group theory applying it to cryptography.\\\\n \", \"Gilbert Baumslag\", \"1933-2014\", 2739], [2563, 192, \"Louis Nirenberg  was a Canadian mathematician whohas made important contributions to linear and nonlinear partial differential equations and their application to complex analysis and geometry.\", \"Louis Nirenberg\", \"1925-2020\", 2537], [1756, 193, \"Bill Ferrar  was an English mathematician who worked on the convergence of series.  He is best known for his undergraduate text-books. He eventually became Principal of Hertford College Oxford.\", \"Bill Ferrar\", \"1893-1990\", 1628], [230, 193, \"Christopher Wren  was an English architect and mathematician who became Savilian Professor of Astronomy at Oxford. He is best known for the buildings he designed after the Great Fire of London.\", \"Christopher Wren\", \"1632-1723\", 226], [768, 193, \"P G Tait  collaborated with Maxwell, Thomson  ( Lord Kelvin )  and Hamilton to make important contributions in both mathematics and physics. He wrote extensively on quaternions and knot theory.\", \"P G Tait\", \"1831-1901\", 737], [3, 193, \"Nasir al-Tusi  was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.\", \"Nasir al-Din al-Tusi\", \"1201-1274\", 25], [219, 193, \"Giovanni Cassini   ( Cassini I )  was an Italian mathematician and astronomer who studied the curve which is the locus of a point the product of whose distances from two fixed foci is constant.\", \"Giovanni Cassini\", \"1625-1712\", 215], [1534, 193, \"Hans Hahn  was an Austrian mathematician who is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass.\", \"Hans Hahn\", \"1879-1934\", 1371], [234, 193, \"Robert Hooke  was an English scientist who made contributions to many different fields including mathematics, optics, mechanics, architecture and astronomy. He had a famous quarrel with Newton.\", \"Robert Hooke\", \"1635-1703\", 230], [2955, 193, \"Gamal Ismail  is an Egyptian mathematician who became Professor of Pure Mathematics at the University College of Women for Art, Science and Education at Ain Shams University in Cairo in  1995 .\", \"Gamal Ismail\", \"1950-\", 2939], [1759, 193, \"Alec Aitken  was a New Zealand mathematician who served at Gallipoli and in France.  He had a prodigious memory and calculating ability and worked in Statistics, Numerical Analysis and Algebra.\", \"Alec Aitken\", \"1895-1967\", 1671], [280, 193, \"Johann Bernoulli  was a Swiss mathematician who studied reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachistochrone.\", \"Johann Bernoulli\", \"1667-1748\", 270], [348, 193, \"G\\u00f6del  proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system.\", \"Kurt G\\u00f6del\", \"1906-1978\", 2001], [2120, 193, \"Mstislav Keldysh  was a Latvian-born Soviet mathematician and engineer who did important work on aerohydrodynamics. He also worked on functions of a complex variable and differential equations.\", \"Mstislav Vsevolodovich Keldysh\", \"1911-1978\", 2157], [1659, 194, \"Paul Bernays  was a Swiss mathematician, who made important contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He is the  B  in the  NBG  axiom system.\", \"Paul Bernays\", \"1888-1977\", 1540], [723, 194, \"Stephen Parkinson  became famous when he was Senior Wrangler, pushing William Thomson into second place. He had a highly successful career at a lecturer and tutor at St John's College Cambridge.\", \"Stephen Parkinson\", \"1823-1889\", 695], [1023, 194, \"Dmitrii Faddeev  was a Russian mathematician who worked mainly in algebra, and who made significant contributions to other areas such as number theory, function theory, geometry and probability.\", \"Dmitrii Konstantinovich Faddeev\", \"1907-1989\", 2021], [2307, 194, \"Warren Hill Brothers Jr  was the thirteenth African American to be awarded a Ph.D. in mathematics. He taught at Talladega College, being Professor of Mathematics and Physics there from  1950 .\\\\n \", \"Warren Brothers\", \"1915-1984\", 2280], [1576, 194, \"George Birkhoff  was an American mathematician who was educated at Chicago and Harvard. He became a Professor at Harvard. His most important work was the Ergodic Theorem he discovered in  1931 .\", \"George Birkhoff\", \"1884-1944\", 1454], [966, 194, \"Arthur Downing  was trained as a mathematician at Trinity College, Dublin before spending half his career at the Royal Observatory Greenwich and half as Superintendent of the Nautical Almanac.\\\\n \", \"Arthur Downing\", \"1850-1917\", 904], [127, 194, \"Willebrord Snell  was a Dutch mathematician who is best known for the law of refraction, a basis of modern geometric optics; but this only become known after his death when Huygens published it.\", \"Willebrord Snell\", \"1580-1626\", 143], [1869, 195, \"William Greaves  graduated from Cambridge and then worked at the Royal Observatory Greenwich. He became Professor of Astronomy in Edinburgh. He worked on both theoretical and practical astronomy.\", \"William Greaves\", \"1897-1955\", 1734], [53, 195, \"Philip Hall  was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the  20 th Century was largely due to him.\", \"Philip Hall\", \"1904-1982\", 1929], [1572, 195, \"Helly  worked on functional analysis and proved the Hahn-Banach theorem in  1912  fifteen years before Hahn published essentially the same proof and  20  years before Banach gave his new setting.\", \"Eduard Helly\", \"1884-1943\", 1450], [176, 195, \"Giovanni Alfonso Borelli   was an Italian Italian physiologist and physicist who was the first to explain muscular movement and other body functions according to the laws of statics and dynamics.\", \"Giovanni Alfonso Borelli\", \"1608-1679\", 182], [2702, 195, \"Andr\\u00e1s Hajnal  was a Hungarian mathematician who worked on set theory, particularly combinatorial set theory, set theoretic topology and combinatorics. He wrote over  60  joint papers with Erd\\u0151s.\", \"Andr\\u00e1s Hajnal\", \"1931-2016\", 2692], [643, 196, \"Oliver Byrne  was an Irish civil engineer and prolific author of works on subjects including mathematics, geometry and engineering. He is best known for his 'coloured' book of Euclid's  Elements .\", \"Oliver Byrne\", \"1810-1880\", 617], [1298, 196, \"Charles Tweedie  studied at Edinburgh, G\\u00f6ttingen and Berlin. He returned to Edinburgh as assistant to Chrystal. He served as a Schools Inspector and published works on the History of Mathematics. \", \"Charles Tweedie\", \"1868-1925\", 1186], [843, 196, \"James Bolam  was an English mathematician who became head of the Government Navigation School  ( later the Leith Nautical College ) . He was a founder member of the Edinburgh Mathematical Society.\", \"James Bolam\", \"1839-1930\", 794], [2057, 196, \"John Von Neumann  built a solid framework for quantum mechanics. He also worked in game theory, studied what are now called  von Neumann Algebras , and was one of the pioneers of computer science.\", \"John von Neumann\", \"1903-1957\", 1884], [875, 196, \"Sophus Lie  was a Norwegian mathematician who made major advances in the theory of continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him.\", \"Sophus Lie\", \"1842-1899\", 825], [1173, 196, \"lya Vekua  was a  Georgian mathematician, specializing in partial differential equations, singular integral equations, generalized analytic functions and the mathematical theory of elastic shells.\", \"Ilya Vekua\", \"1907-1977\", 2033], [2726, 196, \"Grace Alele-Williams  was the first Nigerian to be awarded a doctorate. She became a professor of mathematical education, then the first female Nigerian Vice-Chancellor of the University of Benin.\", \"Grace Alele-Williams\", \"1932-2022\", 2714], [343, 196, \"Leonhard Euler  was a Swiss mathematician who made enormous contibutions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory.\", \"Leonhard Euler\", \"1707-1783\", 334], [2271, 196, \"Alberto Dou  was a Spanish Jesuit and mathematician who worked in differential geometry, elasticity, and partial differential equations. He fought on the Nationalist side in the Spanish Civil War.\", \"Alberto Dou\", \"1915-2009\", 2257], [38, 196, \"Leone Alberti  was an Italian mathematician who wrote the first general treatise on the laws of perspective and also wrote a book on cryptography containing the first example of a frequency table.\", \"Leone Battista Alberti\", \"1404-1472\", 57], [1378, 196, \"Ida Busbridge  worked on integral equations and radiative transfer. She was the first woman appointed to an Oxford fellowship in mathematics. She taught at the University of Oxford for  35  years.\", \"Ida Busbridge\", \"1908-1988\", 2066], [72, 197, \"Regnier Gemma Frisius  was a Dutch mathematician who applied his mathematical expertise to geography, astronomy and map making. He became the leading theoretical mathematician in the Low Countries.\", \"Gemma Frisius\", \"1508-1555\", 89], [1102, 197, \"D'Arcy Thompson  was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. His book  On Growth and Form  had a great influence on both biologists and mathematicians.\", \"D'Arcy Thompson\", \"1860-1948\", 1032], [8, 197, \"Jordanus Nemorarius  was a German scholar who wrote several books on arithmetic, algebra, geometry and astronomy. He was among the first to use letters to replace numbers in algebraic calculations.\", \"Jordanus Nemorarius\", \"1225-1260\", 30], [2972, 197, \"Bernadette Perrin-Riou  is a French mathematician who has made important contributions to number theory. She was awarded the  1999  Ruth Lyttle Satter Prize from the American Mathematical Society. \", \"Bernadette Perrin-Riou\", \"1955-\", 2964], [1471, 198, \"Charles Barkla  was an influential English physicist who became professor of Natural Philosophy in Edinburgh. He was awarded the Nobel Prize for Physics in  1917  for his work on X-ray spectroscopy.\", \"Charles Glover Barkla\", \"1877-1944\", 1324], [1845, 198, \"Charles Fox  was an English mathematician who worked on hypergeometric functions, integral transforms, integral equations, the theory of statistical distributions, and the mathematics of navigation.\", \"Charles Fox\", \"1897-1977\", 1717], [1789, 198, \"Hopf 's work was in algebraic topology. He studied vector fields and extended Lefschetz's fixed point formula. He also studied homotopy classes and defined what is now known as the 'Hopf invariant'.\", \"Heinz Hopf\", \"1894-1971\", 1657], [205, 198, \"William Brouncker  was an Irish mathematician who was a founder and the first president of the Royal Society of London. He worked on continued fractions and calculated logarithms by infinite series.\", \"William Brouncker\", \"1620-1684\", 203], [1743, 198, \"Banach  founded modern functional analysis and made major contributions to the theory of topological vector spaces. In addition, he contributed to measure theory, integration, and orthogonal series.\", \"Stefan Banach\", \"1892-1945\", 1622], [1301, 199, \"Guacolda Antoine Lazzerini  was a mathematics teacher at both school and university level in Chile. She made many contributions to the development of education in Chile during her long active life.\\\\n \", \"Guacolda Lazzerini\", \"1908-2015\", 2056], [942, 199, \"Lee Glaisher  was an English mathematician and astronomer who wrote over  400  articles on astronomy, special functions, calculation of numerical tables, number theory and the history of mathematics.\", \"James Whitbread Lee Glaisher\", \"1848-1928\", 886], [764, 199, \"Dorothea Beale  studied at Queen's College, London where she became the first female mathematics tutor. She became Principal of Cheltenham Ladies' College and a founder of St Hilda's College, Oxford.\", \"Dorothea Beale\", \"1831-1906\", 733], [57, 199, \"Copernicus  was a Polish astronomer and mathematician whose theory that the Earth moved around the Sun profoundly altered later workers' view of the universe, but was rejected by the Catholic church.\", \"Nicolaus Copernicus\", \"1473-1543\", 74], [508, 199, \"Mary Somerville  wrote many works which influenced Maxwell. Her discussion of a hypothetical planet perturbing Uranus led Adams to his investigation. Somerville College in Oxford was named after her.\", \"Mary Somerville\", \"1780-1872\", 488], [1076, 199, \"Charlotte Angas Scott  studied at Cambridge but was not allowed to take her degree. After graduate work at Cambridge she became the first Head of Mathematics at Bryn Mawr College in Pennsylvania USA.\", \"Charlotte Angas Scott\", \"1858-1931\", 1005], [714, 200, \"August Yulevich Davidov  was a Russian mathematician and engineer who worked on differential equations, partial derivatives, definite integrals and the application of probability theory to statistics.\", \"August Yulevich Davidov\", \"1823-1885\", 687], [530, 200, \"Fearon Fallows  was a mathematician and astronomer who was appointed as the first Astronomer at the Cape of Good Hope. He arranged for the building of the Royal Observatory at the Cape of Good Hope.\\\\n \", \"Fearon Fallows\", \"1788-1831\", 510], [1064, 200, \"Aleksandr Lyapunov  was a Russian mathematician best known for his development of the stability theory of a dynamical system. He also made contributions to mathematical physics and probability theory.\", \"Aleksandr Mikhailovich Lyapunov\", \"1857-1918\", 994], [1740, 200, \"Morse  developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis.\", \"Marston Morse\", \"1892-1977\", 1619], [2578, 200, \"Franz Kahn  was a mathematician and astrophysicist who was a professor at the University of Manchester. He was a world leading expert in theoretical studies of the dynamics of the interstellar medium.\", \"Franz Kahn\", \"1926-1998\", 2552], [1154, 200, \"James Wattie  studied at Aberdeen and Oxford. He taught for a while at George Watson's College in Edinburgh and the Church of Scotland Training College in Aberdeen before becoming a Schools Inspector.\", \"James Wattie\", \"1862-1943\", 1075], [81, 201, \"John Dee  was an English scholar who wrote on trigonometry, on calendar reform, on navigation, on geography and on astrology. He became astrologer to Queen Mary but was imprisoned for being a magician.\", \"John Dee\", \"1527-1609\", 97], [121, 201, \"William Oughtred  was an English mathematician who is best known for his invention of an early form of the slide rule. He invented many new symbols including X for multiplication and :: for proportion.\", \"William Oughtred\", \"1574-1660\", 138], [1322, 201, \"David J Tweedie  graduated with an Ordinary degree from Edinburgh University and then taught at George Heriot's Hospital School in Edinburgh. He became headmaster of the school at Kilconquhar in Fife. \", \"David J Tweedie\", \"1870-1926\", 1216], [703, 201, \"Hermann von Helmholtz  was a German mathematician who trained as a medical doctor and made important contributions to mathematical physics, optics and acoustics as well as to physiology and psychology.\", \"Hermann von Helmholtz\", \"1821-1894\", 676], [1593, 201, \"Andreas Speiser  was a Swiss mathematician and philosopher of science who worked in number theory, group theory and the theory of Riemann surfaces. He was also interested in the history of mathematics.\", \"Andreas Speiser\", \"1885-1970\", 1469], [2772, 201, \"Jean-Paul Pier  was a Luxembourg mathematician who published on harmonic analysis, functional analysis and also on the History of Mathematics. He was the founder of the Luxembourg Mathematical Society.\", \"Jean-Paul Pier\", \"1933-2016\", 2741], [1560, 201, \"Jur Hronec  was a Slovak mathematician who made extraordinary contributions to the development of higher mathematics in Slovakia. He was a major figure in establishing several universities in Slovakia.\", \"Jur Hronec\", \"1881-1959\", 1398], [1629, 202, \"Griffith Evans  was an American mathematician whose work dealt with potential theory, functional analysis, integral equations and minimal surfaces. He was head of mathematics at Berkeley for many years.\", \"Griffith Evans\", \"1887-1973\", 1510], [1246, 202, \"Henrietta Leavitt  was an American astronomer who discovered the relation between the luminosity and the period of Cepheid variables. This was a vital step in measuring the distance to remote galaxies. \", \"Henrietta Swan Leavitt\", \"1868-1921\", 1194], [1699, 202, \"Robert Dunbar  graduated from Edinburgh University. After service in World War I he lectured in Physics at Edinburgh. He later moved to University College Cardiff and became Professor of Physics there. \", \"Robert Dunbar\", \"1889-1965\", 1571], [1919, 202, \"Robert Schlapp  studied at Edinburgh and Cambridge universities. He spent his whole career at Edinburgh University teaching mathematics and Physics. He was also interested in the History of Mathematics.\", \"Robert Schlapp\", \"1899-1991\", 1772], [2946, 202, \"Marie Fran\\u00e7oise Ouedraogo  became the first female doctorate from Burkina Faso. She is President of the African Women Mathematicians Association, and a member of IMU Women in Mathematics Advisory Group.\", \"Marie Fran\\u00e7oise Ouedraogo\", \"1967-\", 2999], [2467, 202, \"Kathleen Booth  was a pioneer in computer development being the first to create assembly language and, with her husband, produced the \\\"Booth multiplier algorithm\\\" and the first rotating storage device. \", \"Kathleen Booth\", \"1922-2022\", 2451], [915, 202, \"Eugen Netto  was a German mathematician who made major steps towards abstract group theory when he combined permutation group results and groups in number theory. He also worked on space-filling curves.\", \"Eugen Netto\", \"1846-1919\", 859], [1575, 202, \"Fritz Noether  was a German mathematician who emigrated from Nazi Germany to the Soviet Union and was later executed by the Stalinist NKVD. He was the son of Max Noether and the brother of Emmy Noether.\", \"Fritz Noether\", \"1884-1941\", 1453], [1415, 202, \"Dan Rutherford  was appointed to be the first  Gregory Professor of Applied Mathematics at St Andrews in  1964 . In spite of his title, he was primarily a pure mathematician with an interest in algebra.\", \"Daniel Rutherford\", \"1906-1966\", 1983], [1161, 203, \"Sierpi\\u0144ski 's most important work is in the area of set theory, point set topology and number theory. In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.\", \"Wac\\u0142aw Sierpi\\u0144ski\", \"1882-1969\", 1425], [1043, 203, \"Ernst Carl Gerlach Stueckelberg  was a Swiss mathematician and physicist. Although he made important advances never received the recognition for his achievements which many felt that he clearly deserved.\", \"Ernst Stueckelberg\", \"1905-1984\", 1946], [1700, 203, \"Bevan Braithwaite Baker  graduated from University College London. After service in World War I he became a lecturer at Edinburgh University. He left to become Professor at Royal Holloway College London.\", \"Bevan Braithwaite Baker\", \"1890-1963\", 1575], [1123, 203, \"Henry White  worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves. He is one of the few mathematicians in our archive to die on his birthday  ( in  1943) .\", \"Henry White\", \"1861-1943\", 1052], [1502, 204, \"Viktor Ambartsumian  was an Armenian astrophysicist who was born in what is now Georgia. He was one of the founders of theoretical astrophysics and worked in the field of the physics of stars and nebulae.\", \"Victor Amazaspovich Ambartsumian\", \"1908-1996\", 2079], [531, 204, \"Griffith Davies  was Welsh, born of poor parents, and began life as a slate quarry worker. He set up as a teacher of mathematics in London and became the first Actuary of the Guardian Assurance Company.\\\\n \", \"Griffith Davies\", \"1788-1855\", 511], [1045, 204, \"Cargill Knott  became a Reader in Applied Mathematics at Edinburgh University. With Barclay and Fraser he was one of the writers who originally proposed the founding of the Edinburgh Mathematical Society.\", \"Cargill Knott\", \"1856-1922\", 979], [1567, 204, \"Richard Von Mises  was an applied mathematician who worked on fluid mechanics, aerodynamics, aeronautics statistics and probability theory. He gave the first university course on powered flight in  1913 .\", \"Richard von Mises\", \"1883-1953\", 1444], [2725, 204, \"Gilberto Francisco Loibel  was a Brazilian mathematician who played a major role in the development of mathematical sciences in Brazil. He supervised  19  Master's dissertations and  8  Doctoral theses.\\\\n \", \"Gilberto Loibel\", \"1932-2013\", 2713], [2860, 205, \"Enrico Bombieri  is an Italian Fields medal winner, known for his work in analytic number theory, algebraic geometry, theory of several complex variables,  minimal surfaces and the theory of finite groups.\", \"Enrico Bombieri\", \"1940-\", 2852], [1449, 205, \"Anderson McKendrick  trained as a medical doctor in Glasgow and came to Edinburgh as Superintendent of the College of Physicians Laboratory. He made some significant mathematical contributions to biology. \", \"Anderson McKendrick\", \"1876-1943\", 1305], [1594, 205, \"F F P Bisacre  was an engineer who was educated at Cambridge and worked for the Edinburgh publishers Blackie with whom he published a Calculus textbook. He wrote some research papers on X-ray diffraction. \", \"F F P Bisacre\", \"1885-1954\", 1470], [2513, 205, \"Yvonne Choquet-Bruhat  is a French mathematician and physicist who made important contributions to the general theory of relativity. She was the first woman to be elected to the French Academy of Sciences.\", \"Yvonne Bruhat\", \"1923-\", 2492], [1086, 205, \"Boris Yakovlevic  was a Russian mathematician who worked on the theory of functions of a complex variable, on mathematical analysis, on algebra, on the calculus of variations, and on differential geometry.\", \"Boris Yakovlevic Bukreev\", \"1859-1962\", 1016], [869, 205, \"Henry Martyn Taylor  was an outstanding English mathematician who lost the sight of both eyes. He devised a Braille system to allow mathematical and other scientific works to become available to the blind.\", \"Henry Taylor\", \"1842-1927\", 819], [548, 205, \"Johann Franz Encke  was a German astronomer. He worked on the calculation of the periods of comets and asteroids, measured the distance from the earth to the sun, and made observations of the planet Saturn\", \"Johann Franz Encke\", \"1791-1865\", 527], [2407, 205, \"George Hench Butcher Jr  was one of the first twenty African American to be awarded a Ph.D. in mathematics. Awarded his Ph.D. by University of Pennsylvania, he taught at Howard University for  39  years.\\\\n \", \"George Butcher\", \"1920-2016\", 2394], [1849, 206, \"Francesco Tricomi  studied differential equations which became very important in the theory of supersonic flight. He wrote a number of excellent books which were translated into several different languages.\", \"Francesco Tricomi\", \"1897-1978\", 1721], [320, 206, \"Colin Maclaurin  was a Scottish mathematician who published the first systematic exposition of Newton's methods, written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.\", \"Colin Maclaurin\", \"1698-1746\", 311], [1719, 206, \"George Jeffery  worked on hydrodynamics, viscous liquids, elasticity and general relativity and he produced exact solutions to Einstein's field equations. He also made contributions to teaching mathematics.\", \"George Jeffery\", \"1891-1957\", 1595], [851, 206, \"Franz Mertens  was a Polish-born mathematician who made contributions to a wide variety of areas. He formulated the Mertens conjecture which  ( had it been true )  would have implied the Riemann Hypothesis.\", \"Franz Mertens\", \"1840-1927\", 802], [2450, 206, \"Maur\\u00edcio Peixoto  was a Brazilian mathematician who did outstanding work on the structural stability of dynamical systems. In a series of four papers he developed what today is known as Peixoto's Theorem.\\\\n \", \"Maur\\u00edcio Peixoto\", \"1921-2019\", 2433], [2619, 206, \"Rolando Chuaqui  was a Chilean mathematician who trained first as a medic before turning to mathematics. He was an active researcher and important figure in the development of mathematical logic in Chile.\\\\n \", \"Rolando Chuaqui\", \"1935-1994\", 2774], [1863, 206, \"Zariski 's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.\", \"Oscar Zariski\", \"1899-1986\", 1767], [1239, 206, \"Hector Macdonald  graduated from Aberdeen and Cambridge Universities. He stayed on at Cambridge and won the Adams prize. He returned to Aberdeen as Professor. He did important work on electromagnetic waves.\", \"Hector Macdonald\", \"1865-1935\", 1141], [167, 206, \"Pierre de Fermat  was a French lawyer and government official most remembered for his work in number theory; in particular for Fermat's Last Theorem. He is also important in the foundations of the calculus.\", \"Pierre Fermat\", \"1601-1665\", 173], [88, 207, \"Fran\\u00e7ois Vi\\u00e8te  was a French amateur mathematician and astronomer who introduced the first systematic algebraic notation in his book  In artem analyticam isagoge  . He was also involved in deciphering codes.\", \"Fran\\u00e7ois Vi\\u00e8te\", \"1540-1603\", 104], [1293, 207, \"Anne Bosworth Focke  was an American mathematician who became the first female doctoral student of David Hilbert. She was a professor of mathematics and physics at what is now the University of Rhode Island.\", \"Anne Bosworth\", \"1868-1907\", 1181], [224, 207, \"Robert Boyle  was an Irish-born scientist who was a founding fellow of the Royal Society. His work in chemistry was aimed at establishing it as a mathematical science based on a mechanistic theory of matter.\", \"Robert Boyle\", \"1627-1691\", 220], [1288, 207, \"Laurence Crawford  graduated from Glasgow University. After a period at Birmingham University he became Professor of Pure Mathematics at South African College which later became the University of Cape Town. \", \"Lawrence Crawford\", \"1867-1951\", 1176], [375, 208, \"Patrick d'Arcy  was an Irish mathematician and soldier who studied in France and made original contributions to dynamics. He is best known for his part in the discovery of the  principle of angular momentum .\", \"Patrick d'Arcy\", \"1725-1779\", 362], [1236, 208, \"Georg Landsberg  was a German mathematician, known for his work in the theory of algebraic functions and as a co-author with Kurt Hensel of a classic text on the theory of algebraic functions of one variable.\", \"Georg Landsberg\", \"1865-1912\", 1138], [186, 208, \"John Wallis  was an English mathematician who built on Cavalieri's method of indivisibles to devise a method of interpolation. Using Kepler's concept of continuity he discovered methods to evaluate integrals.\", \"John Wallis\", \"1616-1703\", 193], [840, 208, \"Hermann Hankel  was a German mathematician who worked on the theory of complex numbers, the theory of functions and the history of mathematics. He is remembered for the Hankel transform and the Hankel matrix.\", \"Hermann Hankel\", \"1839-1873\", 791], [1970, 208, \"Nikolai Bogolyubov  was a Russian mathematician and theoretical physicist who made contributions to quantum field theory, to classical and quantum statistical mechanics and to the theory of dynamical systems.\", \"Nikolai Nikolaevich Bogolyubov\", \"1909-1992\", 2103], [431, 208, \"Gaspard Monge  is considered the father of differential geometry because of his work  Application de l'analyse \\u00e0 la g\\u00e9om\\u00e9trie   where he introduced the concept of lines of curvature of a surface in  3 -space.\", \"Gaspard Monge\", \"1746-1818\", 404], [473, 208, \"Joseph Fourier  studied the mathematical theory of heat conduction. He established the partial differential equation governing heat diffusion and solved it by using infinite series of trigonometric functions.\", \"Joseph Fourier\", \"1768-1830\", 453], [1566, 208, \"Nikolai Nikolaevich Luzin  was a Russian mathematician who made important contributions to the foundations of mathematics, measure theory and topology. He was head of the \\\"Luzitania\\\" research group at Moscow.\", \"Nikolai Luzin\", \"1883-1950\", 1443], [2426, 208, \"Alexander Kronrod  was a Russian mathematician and computer scientist who worked on applications of mathematical methods to physical problems. He is also known for his contributions to economics and medicine.\", \"Alexander Kronrod\", \"1921-1986\", 2411], [54, 208, \"D\\u00fcrer  was a German artist who is known for his work as an engraver. The foundations of descriptive geometry are laid in D\\u00fcrer's treatise on human proportions published in Nuremberg after his death in  1528 .\", \"Albrecht D\\u00fcrer\", \"1471-1528\", 72], [354, 209, \"Fran\\u00e7ois Jacquier  was a French  18 th century mathematician who spent most of his life in the Minim Monastery in Rome. Along with Thomas Le Seur he edited a highly annotated edition of Newton's  Principia .\\\\n \", \"Fran\\u00e7ois Jacquier\", \"1711-1788\", 340], [509, 209, \"Bernard Bolzano  successfully freed calculus from the concept of the infinitesimal. He also gave examples of  1 - 1  correspondences between the elements of an infinite set and the elements of a proper subset.\", \"Bernard Bolzano\", \"1781-1848\", 489], [1125, 209, \"Bendixson  taught at Stockholm, then from  1913  to  1927  he was rector of Stockholm University. He worked on set theory and differential equations. He is best remembered for the Poincar\\u00e9 - Bendixson theorem.\", \"Ivar Bendixson\", \"1861-1935\", 1054], [395, 210, \"Jos\\u00e9 Celestino Mutis  was a Spanish scientist who organised and directed the Royal Botanical Expedition of the New Kingdom of Granada, one of the most important scientific expeditions of the eighteenth century.\", \"Jos\\u00e9 Mutis\", \"1732-1808\", 374], [84, 210, \"Giambattista della Porta  was an Italian scholar who worked on cryptography and also on optics. He claimed to be the inventor of the telescope although he does not appear to have constructed one before Galileo.\", \"Giambattista della Porta\", \"1535-1615\", 100], [1677, 210, \"Adolphe Rome  was a classical philologist who worked on the history of ancient Greek mathematics and astronomy, particularly the work of Archimedes, Ptolemy, Heron and especially Pappus and Theon of Alexandria.\", \"Adolphe Rome\", \"1889-1971\", 1552], [657, 210, \"Eug\\u00e8ne Catalan  was a Belgian mathematician who defined the numbers called after him, while considering the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals.\", \"Eug\\u00e8ne Catalan\", \"1814-1894\", 631], [2545, 210, \"John Aitchison  was a Scottish statistician who made contributions to distribution theory, practical Bayesian statistics, statistical diagnosis in medicine and other areas of applied and theoretical statistics.\", \"John Aitchison\", \"1926-2016\", 2564], [440, 211, \"Adrien-Marie Legendre 's major work on elliptic integrals provided basic analytical tools for mathematical physics. He gave a simple proof that \\u03c0 is irrational as well as the first proof that \\u03c0 2  is irrational.\", \"Adrien-Marie Legendre\", \"1752-1833\", 421], [281, 211, \"John Arbuthnot  was a Scottish scholar who translated Huygens' tract on probability in  1692  and extended it by adding a few further games of chance. This was the first work on probability published in English.\", \"John Arbuthnot\", \"1667-1735\", 271], [1899, 211, \"Nkechi Agwu  was born in Nigeria where she eared her first degree, then went to the United States for her doctorate. She is an expert on mathematical education and is particularly interested in ethnomathematics.\", \"Nkechi Agwu\", \"1962-\", 2985], [928, 211, \"George Greenhill   became Professor of Mathematics at the Royal Military Academy at Woolwich. His main work was on Elliptic Functions but he published widely on applications of mathematics to practical problems.\", \"George Greenhill\", \"1847-1927\", 872], [2267, 211, \"George  Dantzig  was an American mathematical scientist who worked in operations research, computer science, economics and statistics. He is best known for inventing the simplex algorithm for linear programming.\", \"George Dantzig\", \"1914-2005\", 2233], [2130, 211, \"William Guthrie  graduated from Cambridge and gained an appointment at the University of St Andrews. He moved to become a professor at Magee College in Londonderry and eventually became Principal of the College.\", \"William Guthrie\", \"1905-1978\", 1972], [1210, 211, \"Charles Joly  was an Irish mathematician who did outstanding work on the quaternions. He became Andrews Professor of Astronomy in the University of Dublin and Royal Astronomer of Ireland at Dunsink Observatory. \", \"Charles Joly\", \"1864-1906\", 1118], [760, 212, \"Luigi Cremona  was the originator of graphical statics, the study of forces in equilibrium, using graphical methods. He wrote papers on geometrical transformations, projective geometry and on graphical solutions.\", \"Luigi Cremona\", \"1830-1903\", 729], [665, 212, \"William Donkin  was a mathematician who became Savilian Professor of Astronomy at the University of Oxford. He had broad interests writing on least squares, Laplace's functions, attraction of solids, and music.\\\\n \", \"William Donkin\", \"1814-1869\", 639], [2171, 212, \"Lamberto Cesari  was an Italian mathematician who worked in the United States. He was known for his work on surface area, functions of bounded variation, optimal control and on the stability of dynamical systems.\", \"Lamberto Cesari\", \"1910-1990\", 2131], [2077, 213, \"Archibald Richardson  graduated from Imperial College London and then taught at the college. He was badly wounded in World War I. He became Professor of Mathematics at Swansea. His main interests were in algebra. \", \"Archibald Richardson\", \"1881-1954\", 1391], [581, 213, \"Anna Stafford Henriques  was an American mathematician who became one of the first two women to undertake research at the Institute for Advanced Study. She worked at several universities concentrating on teaching.\", \"Anna Adelaide Stafford Henriques\", \"1905-2004\", 1939], [1417, 213, \"Tullio Levi-Civita  was an Italian mathematician who is best known for his work on the absolute differential calculus and the theory of tensors. He had problems later in his life with the rise of Fascism in Italy.\", \"Tullio Levi-Civita\", \"1873-1941\", 1274], [1490, 213, \"William Gentle  graduated from the University of Edinburgh and taught at George Heriot's School Edinburgh. After being wounded in World War I he returned to George Heriot's and eventually became headmaster there. \", \"William Gentle\", \"1877-1964\", 1337], [739, 213, \"Bernhard Riemann 's ideas concerning geometry of space had a profound effect on the development of modern theoretical physics. He clarified the notion of integral by defining what we now call the Riemann integral.\", \"Bernhard Riemann\", \"1826-1866\", 709], [1104, 213, \"Frank Carey  was Professor of Mathematics in Liverpool for over  37  years. He was important in University College, Liverpool becoming the University of Liverpool. He wrote several excellent undergraduate texts.\\\\n \", \"Frank Carey\", \"1860-1928\", 1034], [2632, 213, \"Laurence Raymond Harper Jr  was an African American whose Ph.D. at the University of Chicago was supervised by Abraham Adrian Albert. He was a mathematics professor at the University of Minnesota for  47  years.\\\\n \", \"Laurence Raymond Harper\", \"1929-2002\", 2653], [2611, 213, \"Marguerite Straus Frank  is famed both for her remarkable new discoveries of simple Lie algebras, and her solution to the problem of maximising a concave quadratic function, now known as the Frank-Wolfe algorithm.\", \"Marguerite Straus Frank\", \"1927-\", 2600], [2037, 214, \"Aurel Wintner  studied at Budapest and Leipzig. He spent most of his career in Johns Hopkins University in Baltimore, USA. He published on Number Theory, Differential Equations, Probability and Celestial Mechanics.\", \"Aurel Wintner\", \"1903-1958\", 1864], [2406, 214, \"Donald Davies  was a British physicist and mathematician who worked on the early development of computers and networks. His idea of 'packet switching' made the Internet, and ultimately the world wide web, possible.\", \"Donald Davies\", \"1924-2000\", 2498], [1957, 214, \"Enrico Fermi  was an Italian physicist who created the world's first nuclear reactor. He made important contributions to the development of quantum theory, nuclear and particle physics and to statistical mechanics.\", \"Enrico Fermi\", \"1901-1954\", 1804], [1175, 214, \"John Womersley  was an applied mathematician who became involved in the early development of computers. Perhaps his most significant work, however, was in essentially creating the mathematical theory of blood flow.\", \"John Womersley\", \"1907-1958\", 2035], [1133, 214, \"George McVittie  studied at Edinburgh and Cambridge. He then held posts at Leeds, Edinburgh and London and became Professor of Astronomy at the University of Illinois. His main work was in Relativity and Cosmology.\", \"George McVittie\", \"1904-1988\", 1910], [389, 214, \"Pierre-Simon Laplace  proved the stability of the solar system. In analysis Laplace introduced the potential function and Laplace coefficients. He also put the theory of mathematical probability on a sound footing.\", \"Pierre-Simon Laplace\", \"1749-1827\", 413], [324, 214, \"Daniel Bernoulli  was a Dutch-born member of the Swiss mathematical family. His most important work considered the basic properties of fluid flow, pressure, density and velocity, and gave the  Bernoulli principle .\", \"Daniel Bernoulli\", \"1700-1782\", 315], [1782, 214, \"Thomas Brown  studied at Edinburgh and Cambridge Universities. He lectured at University College London and became Professor at the University College of the South West which later became the University of Exeter. \", \"Thomas Arnold Brown\", \"1893-1965\", 1646], [1544, 214, \"Heinrich Tietze  was an Austrian mathematician, known for the Tietze extension theorem. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem.\", \"Heinrich Tietze\", \"1880-1964\", 1381], [755, 215, \"Joaquim Gomes de Souza  was the first Brazilian to be awarded a doctorate in mathematics. He had great difficulty in getting his memoirs published since leading mathematicians of the time failed to report on them.\\\\n \", \"Joaquim Gomes de Souza\", \"1829-1864\", 724], [1287, 215, \"Frances Wood  was an English chemist and statistician who became a fellow of the Royal Statistical Society in  1913 . She was awarded the Order of the British Empire in  1917 , and an officer in the order in  1918 .\", \"Frances Chick Wood\", \"1883-1919\", 1435], [1212, 215, \"George Bryan  made important contributions to kinematics, thermodynamics and the mathematical theory of flight. He wrote two important monographs and a whole series of undergraduate texts intended for private study.\", \"George Bryan\", \"1864-1928\", 1120], [741, 216, \"Ernst Meissel 's mathematical work covers number theory, work on M\\u00f6bius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem.\", \"Ernst Meissel\", \"1826-1895\", 711], [1779, 216, \"Mohammed  Madwar  graduated from Edinburgh University and after a period in Egypt returned to Edinburgh to gain his doctorate in Astronomy. He went back to Egypt and became Professor of Astronomy at Cairo University.\", \"Mohammed Reda Madwar\", \"1893-1973\", 1643], [2843, 216, \"Brian Hartley  was an English mathematician whose main topic was locally finite groups where he used his wide knowledge of finite groups in proving properties of infinite groups which were in a sense close to finite.\", \"Brian Hartley\", \"1939-1994\", 2836], [266, 216, \"Jacob Bernoulli  was a Swiss mathematician who was the first to use the term integral. He studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone.\", \"Jacob Bernoulli\", \"1655-1705\", 256], [2262, 217, \"Dorothy Bernstein  was awarded a Ph.D. in  1939  and had an excellent career overcoming prejudice against her as a woman and as a Jew. She became the first woman president of the Mathematical Association of America.\\\\n \", \"Dorothy Bernstein\", \"1914-1988\", 2228], [871, 217, \"Lord Raleigh   ( John Strutt )  was an English scientist who worked on the theory of waves. He became the Cavendish Professor of Physics at Cambridge and was awarded the Nobel prize for the discovery of the gas Argon.\", \"John William Strutt\", \"1842-1919\", 821], [1546, 217, \"Fej\\u00e9r 's main work was in harmonic analysis working on Fourier series and their singularities. Fej\\u00e9r collaborated to produce important papers with Carath\\u00e9odory on entire functions and with Riesz on conformal mappings.\", \"Lip\\u00f3t Fej\\u00e9r\", \"1880-1959\", 1383], [1731, 217, \"Pierre Humbert  graduated from the \\u00c9cole Polytechnique in Paris and then moved to Edinburgh to do research under Whittaker. He spent most of his career in the University of Montpellier. He worked on Special Functions.\", \"Pierre Humbert\", \"1891-1953\", 1607], [2442, 217, \"Eugene B Dynkin  was a Russian-born American mathematician who worked in the fields of probability and algebra, especially semisimple Lie groups and algebras, and Markov processes. Dynkin diagrams are named after him.\", \"Evgenii B Dynkin\", \"1924-2014\", 2501], [1548, 218, \"Oskar Perron  was a German mathematician best known for the Perron paradox: Suppose the largest natural number is  N . Then if  N  &gt;  1  we have  N 2   &gt;  N  contradicting the definition. Hence  ( ! )   N  =  1 .\", \"Oskar Perron\", \"1880-1975\", 1385], [1364, 218, \"Chrystal Macmillan  was the first female science graduate at Edinburgh University and the first female honours graduate in Mathematics. She became active in the Women's Suffrage Movement and went on to become a lawyer.\", \"Chrystal Macmillan\", \"1872-1937\", 1247], [1330, 218, \"Horatio Carslaw  studied at Glasgow and Cambridge. He lectured at the University of Glasgow before moving to a professorship in Sydney, Australia. He worked on a variety of topics in both pure and applied mathematics. \", \"Horatio Carslaw\", \"1870-1954\", 1224], [2168, 218, \"Johanna Weber  was a mathematician who began her career in Germany but continued after World War II in England. She worked on aerodynamics and played a large part in designing the wings of Concorde and of the Airbus.\\\\n \", \"Johanna Weber\", \"1910-2014\", 2127], [2290, 218, \"Jos\\u00e9 Luis Massera  was an outstanding Uruguayan mathematician who had problems with his career due to his left-wing political views. He was imprisoned for nine years by the right-wing Uruguayan military dictatorship.\\\\n \", \"Jos\\u00e9 Luis Massera\", \"1915-2002\", 2269], [304, 218, \"Roger Cotes  was an English mathematician who edited the second edition of Newton's  Principia . He made advances in the theory of logarithms, the integral calculus and in numerical methods, particularly interpolation.\", \"Roger Cotes\", \"1682-1716\", 295], [1635, 219, \"John Jackson  graduated from Glasgow and Cambridge. He went to the Royal Observatory at Greenwich but his career there was interrupted by World War I. He was then appointed HM Astronomer at the University of Cape Town. \", \"John Jackson\", \"1887-1958\", 1516], [1126, 219, \"John Alison  graduated from Edinburgh University and taught at George Watson's College in Edinburgh, He became head of the Glasgow United Free Church Training College and later returned to George Watson's as headmaster.\", \"John Alison\", \"1861-1952\", 1055], [1447, 219, \"Thomas Bromwich  grew up in South Africa and then graduated from Cambridge. He was Professor of Mathematics in Galway before returning to Cambridge. He made important contributions in both pure and applied mathematics. \", \"Thomas Bromwich\", \"1875-1929\", 1303], [1240, 219, \"Jacques Hadamard  was a French mathematician whose most important result is the prime number theorem which he proved in  1896 . This states that the number of primes &lt;  n  tends to infinity as fast as  n /log  e  n .\", \"Jacques Hadamard\", \"1865-1963\", 1143], [835, 219, \"Tom Cowling  graduated from Oxford and worked at Imperial College London. He lectured at Swansea, Dundee and Manchester and became a professor at Bangor and Leeds. He worked on theoretical astronomy and stellar physics.\", \"Tom Cowling\", \"1906-1990\", 2015], [108, 219, \"Thomas Harriot  was an English mathematician who did outstanding work on the solution of equations, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.\", \"Thomas Harriot\", \"1560-1621\", 124], [2991, 220, \"Lene Hau  is a Danish physicist and mathematician. She has led a team at Harvard University who have slowed light and in  2001  succeeded in stopping a beam of light. This has important applications to quantum computing.\", \"Lene Vestergaard Hau\", \"1959-\", 2976], [3007, 220, \"Artur \\u00c1vila  is a Brazilian mathematician who has made deep contributions to dynamical systems theory which has transformed the subject. His work has been honoured with numerous prizes including a Fields Medal in  2014 .\", \"Artur \\u00c1vila\", \"1979-\", 3008], [614, 221, \"Carl Jacobi  made basic contributions to the theory of elliptic functions. He carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics.\", \"Carl Jacobi\", \"1804-1851\", 589], [1645, 221, \"Archibald Goldie  studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of the British Army in World War I and continued to work in various branches of the Meteorological Office.\", \"Archibald Goldie\", \"1888-1964\", 1525], [175, 221, \"Evangelista Torricelli  was an Italian scientist who was the first man to create a sustained vacuum and to discover the principle of a barometer. He also achieved some important results in the development of the calculus.\", \"Evangelista Torricelli\", \"1608-1647\", 181], [950, 221, \"Georg Frobenius  combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups, the representation theory of groups and the character theory of groups.\", \"Georg Frobenius\", \"1849-1917\", 893], [710, 221, \"Joseph Bertrand  was a Paris professor who, in  1845 , conjectured:\\\\n \\\\n \\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0 I've told you once and I'll tell you again\\\\n \\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0\\u00a0There's always a prime between n and  2 n.  \\\\n This was proved by Chebyshev in  1850 .\", \"Joseph Bertrand\", \"1822-1900\", 683], [1313, 222, \"\\u00c9lie Cartan  worked on continuous groups, Lie algebras, differential equations and geometry. His work achieves a synthesis between these areas. He is one of the most important mathematicians of the first half of the  20 C.\", \"\\u00c9lie Cartan\", \"1869-1951\", 1208], [1632, 223, \"Harald Bohr  worked on Dirichlet series, and applied analysis to the theory of numbers. He is  ( as far as we know )  the only mathematician to win an Olympic medal  ( a silver for representing Denmark at soccer in  1908) .\", \"Harald Bohr\", \"1887-1951\", 1513], [1001, 223, \"George Halsted  was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States. He was interested in mathematical education and in the history of mathematics.\", \"George Halsted\", \"1853-1922\", 945], [1469, 223, \"Alexander Brown  studied at Edinburgh and later at Cambridge. He became Professor of Applied Mathematics at the South African College which later became the University of Cape Town. His main contributions were to Geometry. \", \"Alexander Brown\", \"1877-1947\", 1322], [420, 223, \"Pietro Giannini  was an  18 th century Italian mathematician who spent most of his career in Spain. He wrote several articles and books, the most important being the four volume work  Curso matem\\u00e1tico  written in Spanish.\\\\n \", \"Pietro Giannini\", \"1740-1810\", 394], [271, 223, \"David Gregory  was was a nephew of James Gregory who become a professor of mathematics in Edinburgh and Oxford. He did important work on series and in optics and was a strong supporter of Newton in his dispute with Leibniz.\", \"David Gregory\", \"1659-1708\", 261], [1033, 224, \"John Steggall   was appointed to be the first Professor of Mathematics at the newly-formed University College Dundee: soon to become Queen's College and part of the University of St Andrews. He held this post for  50  years.\", \"John Steggall\", \"1855-1935\", 971], [37, 224, \"Ali Qushji  was an Islamic astronomer and mathematician, born in what is now Uzbekistan, who worked at observatories in Samarkand and Constantinople and whose results influenced Copernicus to produce his heliocentric system.\", \"Ali Qushji\", \"1403-1474\", 56], [2686, 224, \"James Ezeilo  was a Nigerian mathematician who worked in the theory of ordinary differential equations. He was the first professor of mathematics in Nigeria and went on to become vice chancellor of two Nigerian universities.\", \"James Ezeilo\", \"1930-2013\", 2676], [457, 224, \"Fran\\u00e7ois Budan de Boislaurent  was a Haitian born amateur mathematician best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have  n  real roots between two given numbers.\", \"Fran\\u00e7ois Budan\", \"1761-1840\", 437], [226, 225, \"Christiaan Huygens  was a Dutch mathematician who patented the first pendulum clock, which greatly increased the accuracy of time measurement. He laid the foundations of mechanics and also worked on astronomy and probability.\", \"Christiaan Huygens\", \"1629-1695\", 222], [196, 225, \"Emil Hilb  was a German mathematician who did excellent work on special functions, differential equations and difference equations. His contributions to the  Enzyklop\\u00e4die der mathematischen Wissenschaften  are also important.\", \"Emil Hilb\", \"1882-1929\", 1409], [1810, 226, \"Lancelot Hogben  was a biologist who wrote  Mathematics for the Million , one of the most popular mathematics books of all time. As well as many important contributions to biology, he published on linguistics and statistics.\\\\n \", \"Lancelot Hogben\", \"1895-1975\", 1683], [2420, 226, \"Roman Sikorski  was a Polish mathematician whose research interests included  Boolean algebras, mathematical logic, functional analysis, the theory of distributions, measure theory, general topology and descriptive set theory.\", \"Roman Sikorski\", \"1920-1983\", 2406], [2328, 227, \"Clarence Francis Stephens  was the ninth African American to be awarded a Ph.D. in mathematics. He developed what became known as the 'Morgan-Potsdam Miracle' method of teaching, based on problem solving with very few lectures.\", \"Clarence Francis Stephens\", \"1917-2018\", 2308], [669, 227, \"George Boole  approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He also worked on differential equations, the calculus of finite differences and general methods in probability.\", \"George Boole\", \"1815-1864\", 641], [306, 227, \"Brook Taylor  was an English mathematician who added to mathematics a new branch now called the 'calculus of finite differences', invented integration by parts, and discovered the celebrated formula known as Taylor's expansion.\", \"Brook Taylor\", \"1685-1731\", 297], [1070, 227, \"Karl Pearson  was an English mathematician and biostatistician. He introduced the idea of correlation and applied statistics to biological problems of heredity and evolution. With Francis Galton, he was a supporter of eugenics.\", \"Karl Pearson\", \"1857-1936\", 1001], [2983, 228, \"Judita Cofman  was the first person to be awarded a Ph.D. in mathematics from the University of Novi Sad. She worked on finite geometry and mathematical education. The second half of her career was as a school teacher in London.\", \"Judita Cofman\", \"1936-2001\", 2786], [1854, 228, \"Letitia Chitty  began studying the mathematical tripos but, after war work during World War I, she studied the mechanical sciences tripos. She became a civil engineer, applying mathematical theory and carrying out experiments.\\\\n \", \"Letitia Chitty\", \"1897-1982\", 1726], [258, 228, \"Ehrenfried Tschirnhaus  was a German mathematician who worked on the solution of equations and the study of curves. He is best known for the transformation which removes the term of degree  n - 1  from an equation of degree  n .\", \"Ehrenfried Walter von Tschirnhaus\", \"1651-1708\", 251], [1254, 229, \"James McBride  studied at Queen's College Belfast and then taught at various Glasgow schools finishing as Rector of Queen's Park School. He published a number of papers in Geometry and was a founder member of the Euclidean Club. \", \"James McBride\", \"1868-1949\", 1197], [227, 229, \"Isaac Barrow  was an English mathematician who developed a method of determining tangents that closely approached the methods of calculus, and he was first to recognise that integration and differentiation are inverse operations.\", \"Isaac Barrow\", \"1630-1677\", 223], [1600, 229, \"'Mamphono Khaketla  is a Lesotho mathematician who became a lecturer in mathematics at the National Teacher Training College. She has served in the Lesotho government, holding positions such as Minister of Education and Training.\", \"'Mamphono Khaketla\", \"1960-\", 2980], [2192, 230, \"Cora Ratto de Sadosky  was a mathematician and political activist who taught at the University of Buenos Aires, Argentina for ten years before a coup in Argentina forced her to resign. She spent her last years in exile in Spain.\\\\n \", \"Cora Ratto de Sadosky\", \"1912-1981\", 2175], [412, 230, \"Henry Sheffer  was a mathematical logician who introduced what is now called the NAND operator which lies at the basis of the entire computer industry. He showed that all logical operators can be derived from a single one, NAND.\\\\n \", \"Henry Sheffer\", \"1882-1964\", 1414], [1914, 230, \"Hildegard Rothe-Ille  was a German mathematician advised by Issai Schur. She married the mathematician Erich Rothe in  1928  and after her marriage reviewed around  170  papers before having to flee from the Nazi regime in  1937 .\", \"Hildegard Ille\", \"1899-1942\", 1762], [246, 230, \"Isaac Newton  was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.\", \"Isaac Newton\", \"1643-1727\", 240], [565, 230, \"Charles Whish  was an English civil servant who worked for the East India Company. He was the first to bring to the notice of the western mathematical scholarship the achievements of the Kerala school of astronomy and mathematics.\", \"Charles Whish\", \"1795-1833\", 544], [645, 231, \"\\u00c9variste Galois  was a French mathematician who produced a method of determining when a general equation could be solved by radicals and is famous for his development of early group theory. He died very young after fighting a duel.\", \"\\u00c9variste Galois\", \"1811-1832\", 619], [2666, 231, \"Jock Hoe , a New Zealander with Cantonese parents, made a substantial contribution with his work on  The Jade Mirror of the Four Unknowns  translating and giving an important commentary on this Chinese mathematical work of  1303 . \", \"Jock Hoe\", \"1929-2016\", 2652], [157, 231, \"Ren\\u00e9 Descartes  was a French philosopher whose work,  La g\\u00e9om\\u00e9trie , includes his application of algebra to geometry from which we now have Cartesian geometry. His work had a great influence on both mathematicians and philosophers.\", \"Ren\\u00e9 Descartes\", \"1596-1650\", 163], [1714, 231, \"Raymond Brink  was an American mathematician who studied at Kansas State University, Harvard and Paris. He taught at the University of Minnesota though he spent a year in Edinburgh in  1919 . He worked on the convergence of series.\", \"Raymond Brink\", \"1890-1973\", 1590], [597, 232, \"Henry Moseley  was an English churchman, mathematician, and scientist. He served as Professor of Natural and Experimental Philosophy and Astronomy at King's College, London. He then became of of the first H.M. inspectors of schools.\", \"Henry Moseley\", \"1801-1872\", 572], [2773, 232, \"John Frankland Rigby  worked for his whole career at the University of Cardiff. As a geometer he was famed for the 'Rigby points'. A leading expert on mathematics and art, he was also an enthusiastic and highly successful teacher.\\\\n \", \"John Frankland Rigby\", \"1933-2014\", 2742], [2784, 232, \"Orymbek Zhautykov  was a Kazakh mathematician who published over  200  works consisting of research papers, popular science works, pedagogical works, works on the history of mathematics, undergraduate textbooks and other articles.\\\\n \", \"Orymbek Zhautykov\", \"1911-1989\", 2158], [1521, 232, \"Einstein  contributed more than any other scientist to the modern vision of physical reality. His special and general theories of relativity are still regarded as the most satisfactory model of the large-scale universe that we have.\", \"Albert Einstein\", \"1879-1955\", 1362], [2825, 232, \"Alexander D D Craik  was an expert on fluid mechanics writing many significant papers on the topic, but he was also interested in the history of mathematics, particularly Scottish mathematics, and wrote over  30  historical works.\\\\n \", \"Alex Craik\", \"1938-2019\", 2818], [2847, 232, \"Doris Schattschneider  is an American mathematician who became professor of mathematics at the Moravian College. She was the first female editor of  Mathematics Magazine  and won many awards for her excellence in expository writing.\", \"Doris Schattschneider\", \"1939-\", 2840], [1613, 232, \"William Coutts  graduated from Edinburgh University and after a period in the Army in World War I he became interested in the mathematical theory of artillery. He became a Professor at the Military College of Science at Shrivenham. \", \"William B Coutts\", \"1885-1946\", 1489], [2582, 233, \"Rebeca Guber  was one of the first Argentinian women mathematicians. She played a major role in the development of computing in Argentina. She also made important contributions to education particularly teaching science in schools.\\\\n \", \"Rebeca Cherep de Guber\", \"1926-2020\", 2574], [1235, 233, \"Flora Philip  was a Scottish mathematician who studied at Edinburgh University and was among the first women to receive a degree there when they changed the rules. She was the first woman member of the Edinburgh Mathematical Society.\", \"Flora Philip\", \"1865-1943\", 1137], [1077, 233, \"\\u00c9douard Goursat  was a French mathematician who is best known for his version of the Cauchy-Goursat theorem stating that the integral of a function round a simple closed contour is zero if the function is analytic inside the contour.\", \"\\u00c9douard Goursat\", \"1858-1936\", 1006], [598, 234, \"Henry Perigal  was a clerk, stockbroker, amateur mathematician and astronomer. He is known for his mechanical production of geometric curves, for his dissection proof of Pythagoras' theorem and for his unorthodox ideas on astronomy.\\\\n \", \"Henry Perigal\", \"1801-1898\", 573], [2940, 234, \"Jean Bourgain  was a Belgian mathematician who worked on mathematical analysis and its application to partial differential equations, mathematical physics, combinatorics, number theory, ergodic theory and theoretical computer science.\", \"Jean Bourgain\", \"1954-2018\", 2958], [612, 235, \"John Hymers  wrote many excellent textbooks. He organised the painting of a portrait of William Wordsworth for St John's College, Cambridge. He left a considerable sum of money for the founding and endowment of Hymers' College in Hull.\", \"John Hymers\", \"1803-1887\", 587], [2012, 235, \"Carolyn Eisele  was a mathematician who spent her whole career teaching at Hunter College. She is famed for her work on Charles Sanders Peirce, particularly in seeing the importance of mathematics in his work on philosophy and logic.\\\\n \", \"Carolyn Eisele\", \"1902-2000\", 1832], [1867, 235, \"Theodore Combridge  was an English  20 th century mathematician and administrator. He published papers on general relativity and on the beginnings of the Mathematical Association and the Inititute of Mathematics and its Applications.\\\\n \", \"Theodore Combridge\", \"1897-1986\", 1732], [2374, 235, \"David Blackwell  was an American statistician and mathematician who worked in game theory, probability theory, information theory and Bayesian statistics. He was the first African-American member of the US National Academy of Sciences.\", \"David Blackwell\", \"1919-2010\", 2363], [1986, 236, \"Reinhold Baer 's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups.\", \"Reinhold Baer\", \"1902-1979\", 1851], [1488, 236, \"Thomas Havelock  was an English applied mathematician, hydrodynamicist and mathematical physicist. He became a professor at the Armstrong College in Durham. He had close contacts with the Department of Naval Architecture for many years.\", \"Thomas Havelock\", \"1877-1968\", 1335], [907, 236, \"Georg Cantor  was a Russian-born mathematician who can be considered as the founder of set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series.\", \"Georg Cantor\", \"1845-1918\", 851], [1581, 237, \"Neville Watson  studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. \", \"Neville Watson\", \"1886-1965\", 1500], [1906, 237, \"Geoffrey Walker  studied at Oxford and Edinburgh. He taught at Imperial College London, Liverpool and Sheffield before returning to Liverpool as Professor of Pure Mathematics. He worked on Differential Geometry, Relativity and Cosmology.\", \"Geoffrey Walker\", \"1909-2001\", 2093], [100, 237, \"John Napier  was a Scottish scholar who is best known for his invention of logarithms, but other mathematical contributions include a mnemonic for formulas used in solving spherical triangles and two formulas known as Napier's analogies.\", \"John Napier\", \"1550-1617\", 116], [946, 237, \"Alfred Kempe  published a false \\\"proof\\\" of the four colour theorem in  1879  which stood until Heawood showed the mistake  11  years later. The 'proof' is however still the basis for the computer aided proof discovered  100  years later.\", \"Alfred Kempe\", \"1849-1922\", 890], [1556, 238, \"Edward Ross  studied at Edinburgh and Cambridge universities. After working with Karl Pearson in London he was appointed Professor of Mathematics at the Christian College in Madras India. Ill health forced him to retire back to Scotland. \", \"Edward Ross\", \"1881-1947\", 1394], [2746, 238, \"Chen Jingrun  was a Chinese mathematician who made outstanding advances in the study of Goldbach's Conjecture, proving that every sufficiently large integer can be represented as the sum of a prime and the product of at most two primes.\\\\n \", \"Chen Jingrun\", \"1933-1996\", 2734], [2282, 238, \"Boris Khvedelidze  was a Georgian mathematician who worked in the partial differential equations, integral equations, and mathematical physics. He was appointed as a Vice-President of the re-formed Georgian Mathematical Society in  1962 .\", \"Boris Khvedelidze\", \"1915-1993\", 2261], [47, 239, \"Leonardo da Vinci  was an Italian artist and scholar who had many talents in addition to his painting. He worked on mechanics, though geometry was his main love. He was involved in hydrodynamics, anatomy, mechanics, mathematics and optics.\", \"Leonardo da Vinci\", \"1452-1519\", 66], [34, 239, \"Ulugh Beg  was the grandson of the conqueror Tamerlane and was a mathematician and astronomer. He founded an important centre for study at Samarkand staffed with the best scientists of the time. He did important early work on trigonometry.\", \"Ulugh Beg\", \"1393-1449\", 53], [1883, 239, \"Marguerite Lehr  was an outstanding lecturer and, as one of the first to present a course of mathematics on television in  1952 - 53 , she was in great demand both as a lecturer and as a consultant for presenting mathematics on film or TV.\", \"Marguerite Lehr\", \"1898-1987\", 1749], [501, 240, \"Carl Friedrich Gauss  worked in a wide variety of fields in both mathematics and physics incuding number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas.\", \"Carl Friedrich Gauss\", \"1777-1855\", 481], [1524, 241, \"David Picken  studied at Glasgow and Cambridge universities. After a period as a lecturer at Glasgow he became Professor of Mathematics at Victoria College, Wellington New Zealand. He later moved to the University of Melbourne in Australia. \", \"David Picken\", \"1879-1956\", 1365], [982, 242, \"George Chrystal  is best remembered today for  Algebra : a two volume work which was completed by  1889 . He was also involved in educational reform throughout his career and was a major figure in setting up an educational system in Scotland.\", \"George Chrystal\", \"1851-1911\", 920], [2975, 242, \"Laila Soueif  is an Egyptian mathematician who became a professor of mathematics at Cairo University. She is an activist for human rights and has been involved in many demonstrations including calling for academic freedom at Cairo University.\", \"Laila Soueif\", \"1956-\", 2967], [2041, 243, \"Cadambathur Tiruvenkatacharlu Rajagopal  was an Indian mathematician who worked on three main areas:  ( i )  sequences, series and summability;  ( ii )  functions of a complex variable; and  ( iii )  the history of medieval Kerala mathematics.\", \"C T Rajagopal\", \"1903-1978\", 1868], [238, 244, \"James Gregory  was a Scottish scientist and first Regius Professor of Mathematics at St Andrews who described the first practical reflecting telescope. He worked on using infinite convergent series to find the areas of the circle and hyperbola.\", \"James Gregory\", \"1638-1675\", 233], [683, 244, \"Francis Bashforth  was an applied mathematician who invented the Bashforth Chronograph and conducted experiments to determine air resistance. He became the leading British authority on ballistics in the late  19 th and early  20 th centuries.\\\\n \", \"Francis Bashforth\", \"1819-1912\", 656], [2685, 244, \"Jaime Escalante  was a high school mathematics teacher in both his native Bolivia and in the United States. He became famous when his students became so successful they were accused of cheating, leading to the  1988  film 'Stand and Deliver'.\\\\n \", \"Jaime Escalante\", \"1930-2010\", 2675], [1450, 244, \"Earle Hedrick  was an American mathematician who worked on partial differential equations and on functions of complex variables. He was the first president of the MAA and he became the Vice-president and Provost of the University of California.\", \"Earle Raymond Hedrick\", \"1876-1943\", 1307], [1128, 244, \"Harold Davenport  worked on number theory, in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. He wrote a number of important textbooks and monographs including  The higher arithmetic    (1952) .\", \"Harold Davenport\", \"1907-1969\", 2028], [2970, 245, \"Verdiana Masanja  is the first Tanzanian woman to earn a doctorate in mathematics. She became a professor at the University of Dar es Salaam. She works to increase women's participation in science, mathematics and technology education in Africa.\", \"Verdiana Masanja\", \"1954-\", 2962], [2697, 245, \"Vera S\\u00f3s  is a Hungarian mathematician who specialises in number theory and combinatorics. She worked at the Alfr\\u00e9d R\\u00e9nyi Institute of Mathematics and has won many prizes including the Tibor Szele Medal  (1974)  and the Sz\\u00e9chenyi Prize  (1997) .\", \"Vera S\\u00f3s\", \"1930-\", 2687], [328, 246, \"Anders Celsius  was a Swedish astronomer, physicist and mathematician. He participated in Maupertuis' expedition to measure a degree of latitude in Lapland. He is best known for the temperature scale that he proposed and which is named after him.\", \"Anders Celsius\", \"1701-1744\", 319], [1355, 246, \"Johannes Kepler  was a German mathematician and astronomer who discovered that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. He also did important work in optics and geometry.\", \"Johannes Kepler\", \"1571-1630\", 135], [752, 247, \"Rudolf Skuhersky  was the first Professor of Descriptive Geometry at the Prague Polytechnic. He argued for reforms of the Polytechnic to have lectures in both Czech and German. He was elected to parliament as a member of the Czech National Party. \", \"Rudolf Skuhersk\\u00fd\", \"1828-1863\", 721], [2639, 247, \"Donald Greenspan  was expert in numerical analysis and computational modelling who wrote many books, many of which took a different approach to teaching applied mathematics using numerical methods instead of the differential and integral calculus.\", \"Donald Greenspan\", \"1928-2010\", 2613], [2941, 247, \"Jos\\u00e9 Escobar  was a Colombian mathematician who made outstanding contributions to the Yamabe problem. He worked most of his life in the United States but made decisive contributions to developing and improving the mathematical level in Colombia.\\\\n \", \"Jos\\u00e9 Escobar\", \"1954-2004\", 2959], [318, 248, \"Nicolaus  ( II )  Bernoulli  was the favourite of three sons of Johann Bernoulli. He made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute between Newton and Leibniz.\", \"Nicolaus (II) Bernoulli\", \"1695-1726\", 309], [2771, 249, \"Leonard of Pisa  or  Fibonacci  played an important role in reviving ancient mathematics and made significant contributions of his own.  Liber abaci  introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe.\", \"Fibonacci\", \"1170-1250\", 20], [1962, 249, \"John Williamson  graduated from Edinburgh University and then had an appointment at St Andrews. He spent some time in Chicago and eventually moved to the USA to a post at Johns Hopkins University in Baltimore. His most important work was in Algebra.\", \"John Williamson\", \"1901-1949\", 1808], [2997, 249, \"Sijue Wu  was born and brought up in China but went to the United States to study for her doctorate. She became Robert W and Lynne H Browne Professor of Mathematics at the University of Michigan. Her research involves the mathematics of water waves.\", \"Sijue Wu\", \"1964-\", 2992], [635, 249, \"Benjamin Peirce  was an early American mathematician who worked on celestial mechanics and geodesy on the applied side and linear associative algebra and number theory on the pure side. He has been called the \\\"Father of pure mathematics\\\" in America.\", \"Benjamin Peirce\", \"1809-1880\", 610], [2042, 249, \"Catherine Steele  graduated from the University of St Andrews. She went on to a doctorate in Chemistry and studied at the University of Illinois and at Harvard. She taught for some time at a Horticultural College in Kent before returning to the USA.\", \"Catherine Steele\", \"1903-1995\", 1869], [2667, 250, \"Michael Atiyah  worked in Topology and Geometry and was best known for his work on K-theory and the Atiyah-Singer Index Theorem. He was awarded a Fields Medal in  1966 . He retired from the mastership of Trinity College Cambridge to live in Scotland.\", \"Michael Atiyah\", \"1929-2019\", 2656], [949, 250, \"Felix Klein  was a German mathematician whose synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the  Erlanger Programm , profoundly influenced mathematical development.\", \"Felix Klein\", \"1849-1925\", 892], [1811, 251, \"Leslie Cunningham  graduated from Edinburgh University though the First World War interrupted his studies. He worked for the RAF as an education officer but returned to Edinburgh to complete his doctorate. He worked on various problems of air warfare.\", \"Leslie Cunningham\", \"1895-1946\", 1684], [975, 251, \"Alexander Macfarlane  began his research on experimental physics but moved to mathematics and logic. He is best known for his two famous posthumous publications on British mathematicians of the nineteenth century, many of whom he had personally known.\", \"Alexander Macfarlane\", \"1851-1913\", 913], [1940, 251, \"Omar Khayyam  was an Islamic scholar who was a poet as well as a mathematician. He compiled astronomical tables and contributed to calendar reform and discovered a geometrical method of solving cubic equations by intersecting a parabola with a circle.\", \"Omar Khayyam\", \"1048-1131\", 7], [1412, 251, \"John Todd  graduated from Cambridge and stayed on to do research under Baker. After a period at Manchester and Princeton he returned to Cambridge where he spent the rest of his career. He worked on invariant theory, group theory and canonical systems.\", \"John Todd\", \"1908-1994\", 2070], [2071, 252, \"Zygmunt Wilhelm Birnbaum  was a Polish-born American mathematician and statistician who contributed to functional analysis, nonparametric testing and estimation, probability inequalities, survival distributions, competing risks, and reliability theory.\", \"William Birnbaum\", \"1903-2000\", 1895], [933, 252, \"Wilhelm Killing  was a German mathematician who introduced Lie algebras independently of Lie in his study of non-euclidean geometry. His classification of the simple Lie algebras was one of the finest achievements in the whole of mathematical research.\", \"Wilhelm Killing\", \"1847-1923\", 877], [2933, 253, \"Sun-Yung Alice Chang  is a Chinese born American mathematician  whose research interests include the study of certain geometric types of nonlinear partial differential equations and the related extremal inequalities and problems in isospectral geometry.\", \"Sun-Yung Alice Chang\", \"1948-\", 2928], [1561, 253, \"L E J Brouwer  was a Dutch mathematician best known for his topological fixed point theorem. He founded the doctrine of mathematical intuitionism, which views mathematics as the formulation of mental constructions that are governed by self-evident laws.\", \"L E J Brouwer\", \"1881-1966\", 1399], [2405, 253, \"Clive Kilmister  was an applied mathematician who had broad interests including the history of mathematics, philosophy of mathematics and teaching of mathematics. He wrote several books on relativity, Arthur Eddington and Eddington's fundamental theory.\", \"Clive William Kilmister\", \"1924-2010\", 2497], [1056, 255, \"Ida Martha Metcalf  was the second woman to be awarded a Ph.D. in mathematics in America. She was never able to gain a position in keeping with her abilities and qualifications. She was open in her criticisms of the education system and of discrimination.\", \"Ida Metcalf\", \"1856-1952\", 986], [899, 255, \"Max Noether  was a German mathematician who was one of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father.\", \"Max Noether\", \"1844-1921\", 843], [2551, 255, \"Fred Boyer Wright  was an African American mathematician whose Ph.D. was supervised by Irving Kaplansky. After working at the Institute for Air Weapons Research for the Navy he was appointed as an Assistant Professor of Mathematics at Tulane University.\\\\n \", \"Fred Wright\", \"1925-2006\", 2525], [1530, 256, \"Duncan Sommerville  studied at St Andrews and then had a post as a lecturer there. He left to become Professor of Pure and Applied mathematics at Victoria College, Wellington New Zealand. He worked on non-Euclidean geometry and the History of Mathematics. \", \"Duncan Sommerville\", \"1879-1934\", 1367], [1938, 256, \"Ida Rhodes  was born in the Ukraine but emigrated to the United States as a teenager. She studied mathematics and had a variety of jobs before joining the Mathematical Tables Project in New York City. She did important work on the development of computers.\", \"Ida Rhodes\", \"1900-1986\", 1791], [1808, 256, \"J\\u00falio C\\u00e9sar de Mello e Souza  was a Brazilian mathematician who wrote very popular texts such as  The man who counted  under the pseudonym Malba Tahan. Brazil's National Day of Mathematics was instituted in  2013  to be on  6  May, Mello e Souza's birthday\", \"J\\u00falio Mello e Souza\", \"1895-1974\", 1681], [1987, 256, \"Reuben R McDaniel  was the fifth African American to be awarded a Ph.D. in mathematics. He served most of his career at Virginia State College  ( now Virginia State University ) , as head of mathematics, then as Director of the School of Arts and Sciences.\", \"Reuben R McDaniel\", \"1902-1975\", 1852], [1509, 256, \"Haroutune Dadourian  was professor of mathematics and physics at Trinity College, Hartford, Connecticut. He did important work on radioactivity and wrote five mathematics textbooks for science students taking a different approach from that of most authors.\", \"Haroutune Dadourian\", \"1878-1974\", 1349], [2902, 256, \"George Saitoti  was a Kenyan mathematician and economist who did research in topology. He became a member of the Kenyan parliament and Executive Chairman of the World Bank and the International Monetary Fund. He was killed in a suspicious helicopter crash.\", \"George Saitoti\", \"1945-2012\", 2890], [2206, 257, \"Gerald Whitrow  undertook research on relativity and wrote a number of books, especially on 'time'. He believed that the history of science was important in works describing technical mathematics. He put this into practice in both his papers and his books. \", \"Gerald Whitrow\", \"1912-2000\", 2183], [1285, 257, \"Esteban Terradas  was Spanish was a mathematician, physicist and engineer. He held prestigious positions in Barcelona and Madrid universities and also made considerable contributions to the development of Spanish railways, aerospace, and other industries.\\\\n \", \"Esteban Terradas\", \"1883-1950\", 1433], [1096, 257, \"Otto H\\u00f6lder  worked on the convergence of Fourier series and in  1884  he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series.\", \"Otto H\\u00f6lder\", \"1859-1937\", 1026], [2356, 257, \"George Carrier  was considered to be one of the best applied mathematicians the United States ever produced. He loved applied mathematical problems developing complex mathematical models, which he solved with ingenious approximations and asymptotic results.\", \"George Carrier\", \"1918-2002\", 2338], [2634, 257, \"Margaret Rayner  was a British mathematician who did important work on isoperimetric inequalities, mathematical education, and the history of mathematics. She became vice principal of St Hilda's College, Oxford and president of the Mathematical Association.\", \"Margaret Rayner\", \"1929-2019\", 2655], [2939, 258, \"Ingrid Daubechies  is a Belgium mathematician and physicist who has done important work on wavelets in image compression. She is on the Board of Enhancing Diversity in Graduate Education, an organisation which helps women get advanced degrees in mathematics.\", \"Ingrid Daubechies\", \"1954-\", 2957], [1666, 259, \"Raymond Butchart  was a Scottish mathematician who was badly wounded in World War I and afterwards returned to Dundee as a lecturer. He was appointed Professor of Mathematics at Raffles College Singapore but died of malaria on his way home on his first leave.\", \"Raymond Butchart\", \"1888-1930\", 1541], [250, 260, \"Gottfried Leibniz  was a German mathematician who developed the present day notation for the differential and integral calculus though he never thought of the derivative as a limit. His philosophy is also important and he invented an early calculating machine.\", \"Gottfried Leibniz\", \"1646-1716\", 244], [2957, 260, \"Milojica Jacimovic  is a Montenegrin mathematician whose work is in the area of operations research, mathematical programming, calculus of variations and optimal control. He was the first president of the Society of Mathematicians and Physicists of Montenegro.\", \"Milojica Jacimovic\", \"1950-\", 2941], [2093, 261, \"E T Davies  graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations.\", \"Evan (Ianto) Davies\", \"1904-1973\", 1908], [211, 261, \"Blaise Pascal  was a very influential French mathematician and philosopher who contributed to many areas of mathematics. He worked on conic sections and projective geometry and in correspondence with Fermat he laid the foundations for the theory of probability.\", \"Blaise Pascal\", \"1623-1662\", 209], [536, 261, \"Augustin-Louis Cauchy  pioneered the study of analysis, both real and complex, and the theory of permutation groups. He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.\", \"Augustin-Louis Cauchy\", \"1789-1857\", 515], [2575, 261, \"Chaim Samuel H\\u00f6nig  was born in Berlin but became a Brazilian citizen. He was the founder of the Brazilian Mathematics Colloquium in  1957  and its first organiser. He was also a founder of the Brazilian Mathematical Society in  1969  and its first president.\\\\n \", \"Chaim Samuel H\\u00f6nig\", \"1926-2018\", 2549], [1595, 262, \"Finlay Freundlich  was a distinguished German astronomer who worked with Einstein on measurements of the orbit of Mercury to confirm the general theory of relativity. He left Germany to avoid Nazi rule and became the Napier Professor of Astronomy at St Andrews. \", \"Finlay Freundlich\", \"1885-1964\", 1471], [913, 262, \"William Clifford  was an English mathematician who studied non-euclidean geometry arguing that energy and matter are simply different types of curvature of space. He introduced what is now called a Clifford algebra which generalises Grassmann's exterior algebra.\", \"William Clifford\", \"1845-1879\", 857], [2788, 263, \"         Umirzak Sultangazin  was a Kazakhstan mathematician who\\\\n          did excellent work on kinetic transport theory. He was an important figure in building up\\\\n          mathematics in Kazakhstan and was involved in the Mir and Soyuz space programmes.       \", \"Umirzak Sultangazin\", \"1936-2005\", 2797], [2932, 263, \"Ricardo Ma\\u00f1\\u00e9  was an outstanding Uruguayan mathematician, famed for his work in dynamical systems, especially for proving the Stability Conjecture. He worked for his whole career at the Instituto Nacional de Matem\\u00e1tica Pura e Aplicada in Rio de Janeiro, Brazil.\\\\n \", \"Ricardo Ma\\u00f1\\u00e9\", \"1948-1995\", 2927], [1498, 263, \"Ethel Elderton  was a statistician who worked for Francis Galton and Karl Pearson. Although her work was an important contribution applying statistics to social problems, much of it makes difficult reading today because it is written with a eugenic perspective.\\\\n \", \"Ethel Elderton\", \"1878-1954\", 1345], [3001, 264, \"Ruth Michler  was an American mathematician who became an expert in commutative algebra and algebraic geometry. She organised several special sessions at meetings of the American Mathematical Society. She was killed in a road accident in Boston at the age of  33 .\", \"Ruth Michler\", \"1967-2000\", 3000], [2370, 264, \"Vincent Vernon McRae  was an African American mathematician who worked as an operations analyst in the Operations Research Office of Johns Hopkins University. He became Technical Assistant to the President of the United States' Advisor on Science and Technology.\\\\n \", \"Vincent McRae\", \"1918-1998\", 2357], [2574, 265, \"Carol Karp  was an American mathematical logician whose research was closely linked to algebra. She made a reputation both as a teacher and researcher, and she was undertaking important work on infinitary logic and recursion theory when she died at the age of  46 .\", \"Carol Karp\", \"1926-1972\", 2548], [2203, 265, \"Elgy Sibley Johnson  was an African American mathematician   who was awarded a Ph.D. by the Catholic University of America. He served at the District of Columbia Teachers College, then joined the University of the District of Columbia when it was founded in  1976 .\", \"Elgy Johnson\", \"1912-1987\", 2179], [1276, 267, \"T J J See  was an American astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. \", \"T J J See\", \"1866-1962\", 1167], [2815, 268, \"John Conway  was an English mathematician who has produced many results  in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made many contributions to recreational mathematics, including the  Game of Life .\", \"John Conway\", \"1937-2020\", 2809], [887, 269, \"Paul Diene s was a Hungarian mathematician who, because of his political views, had to escape from Hungary in  1920 . He spent most of his career in Wales and England, was a highly effective Ph.D. supervisor, and wrote the influential book  The Taylor Series   (1931) .\", \"Paul Dienes\", \"1882-1952\", 1420], [2916, 269, \"Celia Hoyles  is a Professor of Mathematics Education at University College London. She has received many honours for her contributions to education such as an OBE, a DBE, and the first Hans Freudenthal Medal by the International Commission on Mathematical Instruction.\", \"Celia Hoyles\", \"1946-\", 2903], [1848, 269, \"Emil Post  was a Polish-born American mathematician and logician who is best known for his work on polyadic groups, recursively enumerable sets, and degrees of unsolvability, as well as for his contribution to the unsolvability of problems in combinatorial mathematics.\", \"Emil Post\", \"1897-1954\", 1720], [2278, 269, \"Paul Halmos  was a Hungarian-American mathematician who made fundamental advances in the areas of logic, probability, statistics, operator theory and functional analysis. He is best known for some of his text-books and for his collection of mathematicians' photographs.\", \"Paul Halmos\", \"1916-2006\", 2301], [1718, 270, \"Edward Ince  graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions.\", \"Edward Ince\", \"1891-1941\", 1594], [1669, 270, \"Selig Brodetsky  was educated at Cambridge and Leipzig. He became a lecturer at Bristol and later lecturer and professor at Leeds. He worked on fluid flow with particular emphasis on aerodynamics. He was President of the Hebrew University of Jerusalem for a short time. \", \"Selig Brodetsky\", \"1888-1954\", 1544], [2982, 270, \"Hajer Bahouri  was born in Tunisia and is an expert in partial differential equations. She became Director of Research at the National Centre for Scientific Research and the Laboratory of Analysis and Applied Mathematics at the University Paris-Est-Cr\\u00e9teil-Val-de-Marne.\", \"Hajer Bahouri\", \"1958-\", 2974], [1859, 272, \"Sylvia Skan  was an English applied mathematician who worked on fluid dynamics and aerodynamics. For most of her career, she worked for the Aerodynamics Department of the National Physical Laboratory. She wrote many papers and the two volume book  Handbook for computers .\", \"Sylvia Skan\", \"1897-1972\", 1730], [2049, 272, \"Gladys Mackenzie  graduated from the University of Edinburgh and became an assistant in the Natural Philosophy department. She moved to Newnham College Cambridge and late to Bristol University and Queen Elizabeth College London. She published papers on X-ray spectroscopy.\", \"Gladys Mackenzie\", \"1903-1989\", 1876], [2962, 272, \"Olabisi Ugbebor  is the first female professor of mathematics in Nigeria. She has written many papers on Brownian motion and on economics, and is a co-author of books such as  Further Mathematics, Analytical Geometry and Mechanics , and  Fundamentals of Abstract Algebra .\", \"Olabisi Ugbebor\", \"1951-\", 2946], [2226, 273, \"\\u00c1ngel Palacio Gros  was a Spanish mathematician who fought for the Republicans and spent  8  years in prison before being able to emigrate to Venezuela. There he did excellent work as a mathematics professor and wrote four mathematics books which ran to several editions.\\\\n \", \"\\u00c1ngel Gros\", \"1913-1990\", 2203], [2361, 273, \"Luiz Henrique Jacy Monteiro  was a Brazilian mathematician who played a major role in the development of Brazilian mathematics in the middle of the  20 th century. He did much to introduce modern mathematics to Brazilian school teachers as well as to university students.\\\\n \", \"Jacy Monteiro\", \"1918-1975\", 2344], [2906, 274, \"Jos\\u00e9phine Guidy-Wandja  was the first African woman with a Doctorat  3 \\u00e8me cycle  in mathematics  ( Paris VI ) , the first African woman with a Ph.D. in mathematics  ( Abidjan )  and the first African woman to become a professor of mathematics in a university  ( Abidjan ) .\", \"Jos\\u00e9phine Guidy-Wandja\", \"1945-\", 2893], [1618, 275, \"Lester Ford  was an American mathematician who lectured for several years in Edinburgh before moving back to the USA. He wrote some important text-books and is best known for his contributions to the Mathematical Association of America and the American Mathematical Monthly. \", \"Lester R Ford\", \"1886-1967\", 1495], [1783, 275, \"Xiong Qinglai  was a Chinese mathematician who served as a highly successful president of three major Chinese universities. His outstanding research as a function-theorist was claimed by a reviewer to be of the first rank even comparable with \\u00c9mile Borel and Rolf Nevanlinna.\", \"Xiong Qinglai\", \"1893-1969\", 1647], [1494, 275, \"Beulah Russell  taught mathematics at several colleges in the United States including William and Mary. She attended the Edinburgh Mathematical Society Colloquium held in St Andrews, Scotland, in  1930  becoming the first female professor to attend the St Andrews Colloquium.\", \"Beulah Russell\", \"1878-1940\", 1341], [1998, 276, \"Winifred Deans  graduated from Aberdeen and Cambridge. After a period in teaching she joined a Scottish publishing company and translated many important German scientific texts for them. After World War II she worked at the Commonwealth Bureau of Animal Nutrition in Aberdeen.\", \"Winifred Deans\", \"1901-1990\", 1830], [2659, 276, \"Branko Gr\\u00fcnbaum  was a Jewish Croatian mathematician who survived the Nazi invasion, later escaped to Israel where he obtained his doctorate, and had most of his career in the United States. He was a prolific author writing over  250  papers and four very influential books.\\\\n \", \"Branko Gr\\u00fcnbaum\", \"1929-2018\", 2643], [1672, 276, \"William Berwick  studied at Cambridge and lectured at Bristol, Bangor and Leeds before returning to Cambridge and eventually became Professor at Bangor. He worked in algebraic number theory. His widow endowed the Berwick prizes of the London Mathematical Society in his name. \", \"William Berwick\", \"1888-1944\", 1547], [1146, 276, \"Hilbert 's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose  21  such axioms and he analysed their significance. He made contributions in many areas of mathematics and physics.\", \"David Hilbert\", \"1862-1943\", 1067], [1711, 278, \"Olive Clio Hazlett  was an American mathematician who worked in algebra. Between  1914  and  1930  she published fourteen papers that were presented at meetings of the American Mathematical Society. She did outstanding work for the Cryptanalysis Committee during World War II.\\\\n \", \"Olive Clio Hazlett\", \"1890-1974\", 1587], [319, 278, \"Ramiro Rampinelli  was a member of the Olivetan Order and an outstanding teacher of mathematics, most famed as the teacher of Maria Gaetana Agnesi. He flourished in Italy in the early  18 th century at a time when much mathematical learning was led by those in religious Orders.\", \"Ramiro Rampinelli\", \"1697-1759\", 310], [1311, 278, \"Arthur Bowley  was a leading statistician with an international reputation for his work on poverty. His expertise in mathematics meant that he played an important part in developing the mathematical basis of economics. He was a prolific author publishing many influential books.\", \"Arthur Bowley\", \"1869-1957\", 1205], [2845, 278, \"Calixto Calder\\u00f3n  is an Argentinian mathematician who has spent much of his career in the United States. He has made major contributions to ordinary differential equations, partial differential equations, harmonic analysis, mathematical biology and the history of mathematics.\\\\n \", \"Calixto Calder\\u00f3n\", \"1939-\", 2838], [2758, 278, \"Soraya Sherif  is an Egyptian mathematician who was awarded a Ph.D. from the University of Birmingham, England, for her thesis on Tauberian theorems. She taught at the University College for Girls, Ain Shams University, Cairo and has published many papers on Tauberian theorems.\", \"Soraya Sherif\", \"1934-\", 2760], [2198, 278, \"Manuel Sadosky  is known today as the 'Father of computing in Argentina'. In addition he promoted applied mathematics, supported science, education and scientific popularisation. He lived though difficult political times and was forced to leave Argentina on several occasions.\\\\n \", \"Manuel Sadosky\", \"1914-2005\", 2243], [69, 279, \"Girolamo Cardan  or  Cardano  was an Italian doctor and mathematician who is famed for his work  Ars Magna   which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.\", \"Girolamo Cardano\", \"1501-1576\", 86], [1390, 280, \"Frances Hardcastle  was an English mathematician who held fellowships in the United States. She studied point groups and wrote some important works. She also was a major figure in the Women's Suffrage movement and was secretary of the National Union of Women's Suffrage Societies.\", \"Frances Hardcastle\", \"1866-1941\", 1158], [1294, 280, \"Annie MacKinnon  was the third woman to be awarded a Ph.D. in mathematics from an American university. She was a postdoctoral student at G\\u00f6ttingen with Felix Klein, then a Professor of Mathematics at Wells College, New York. She gave up her career when she married Edward Fitch.\\\\n \", \"Annie Fitch MacKinnon\", \"1868-1940\", 1182], [2811, 281, \"Enrique Planchart  worked at Sim\\u00f3n Bol\\u00edvar University in Venezuela for  47  years, first as a professor of mathematics, then as rector of the university. He fought for improvements in mathematical education, and was praised as a \\\"defender of democracy, the University and youth\\\".\\\\n \", \"Enrique Planchart\", \"1937-2021\", 2805], [2111, 281, \"Joseph James Dennis  was the eleventh African American to be awarded a Ph.D. in mathematics. He served as the chair of the\\u00a0department of mathematics at Clark College from  1930  to  1974 . From  1971  to  1977  he was Fuller E Calloway Chair of Mathematics at Albany State College.\", \"Joseph Dennis\", \"1905-1977\", 1954], [2849, 282, \"Fatma Moalla  is a Tunisian mathematician who has undertaken research on Finsler spaces. In  1961  she became the first Tunisian to have been awarded the Agr\\u00e9gation in Mathematics in France and, in  1965 , the first Tunisian woman to be awarded a doctorate in mathematics in France.\", \"Fatma Moalla\", \"1939-\", 2841], [826, 282, \"Thomas Barker  had an outstanding undergraduate career, being Senior Wrangler in the mathematical tripos at Cambridge and  1 st Smith's Prizeman in  1862 . He went on to play an important role in Owens College, Manchester where he was professor of pure mathematics for twenty years.\", \"Thomas Barker\", \"1838-1907\", 785], [116, 282, \"Galileo Galilei  was an Italian scientist who formulated the basic law of falling bodies, which he verified by careful measurements. He constructed a telescope with which he studied lunar craters, and discovered four moons revolving around Jupiter and espoused the Copernican cause.\", \"Galileo Galilei\", \"1564-1642\", 132], [2664, 283, \"Elon Lima  was a Brazilian mathematician who is famed as the most famous mathematics textbook writer in the Portuguese language. He also made important research contributions in topology and was a major contributor to the Brazilian Mathematics Colloquium between  1961  and  1983 .\\\\n \", \"Elon Lima\", \"1929-2017\", 2648], [2992, 283, \"Leopoldo Franca  was a Brazilian mathematician who had a major impact in the development and analysis of innovative finite element methods. He worked mainly on stabilised methods for fluids, acoustics and solids, residual-free methods, and enriched methods for transport equations.\\\\n \", \"Leopoldo Franca\", \"1959-2012\", 2977], [331, 284, \"Thomas Bayes  was an English clergyman who set out his theory of probability in  1764 . His conclusions were accepted by Laplace in  1781 , rediscovered by Condorcet, and remained unchallenged until Boole questioned them. Since then Bayes' techniques have been subject to controversy.\", \"Thomas Bayes\", \"1702-1761\", 322], [729, 286, \"William Thomson   ( Lord Kelvin )  became Professor of Natural Philosophy at Glasgow at a very young age. He made important contributions to many areas of Physics including electricity, magnetism and thermodynamics. His work on the first trans-Atlantic telegraph cable made his fortune.\", \"William Thomson\", \"1824-1907\", 700], [1434, 288, \"Edward Blades  graduated from Edinburgh University. He held posts at Moray House Training College, at Heriot Watt College and at George Watson's Ladies' College, all in Edinburgh. He became Director of Education for West Lothian. After he retired he made contributions to Army Education. \", \"Edward Blades\", \"1875-1953\", 1290], [1684, 288, \"Louise Doris Adams  was a school teacher and school inspector who did much to improve the teaching of mathematics in schools. She was enthusiastically involved with the Mathematical Association and in  1959 - 60  she served as its President, being only the second woman to hold this role.\", \"Doris Adams\", \"1889-1965\", 1556], [2469, 289, \"Leopoldo Nachbin  was an outstanding Brazilian mathematician who spent time as a Visiting Professor at many of the top institutions worldwide. He worked on ordered systems, topology, topological vector spaces, approximation theory, harmonic analysis, and infinite-dimensional holomorphy.\\\\n \", \"Leopoldo Nachbin\", \"1922-1993\", 2453], [2720, 289, \"Francis Allotey  was a mathematician and physicist from Ghana who was awarded a Ph.D. by Princeton University in  1966 . He returned to Ghana where he spent his career as a professor of mathematics and did outstanding work promoting mathematics and physics at all levels throughout Africa.\", \"Francis Allotey\", \"1932-2017\", 2710], [2862, 289, \"Jacob Palis  was a Brazilian mathematician who was a leading expert in dynamical systems. He gained many international prizes for his outstanding research contributions and also served as president of the International Mathematical Union as well as several other academies and societies.\\\\n \", \"Jacob Palis Jr\", \"1940-\", 2854], [333, 289, \"Jean-Louis Calandrini  was a mathematician working in Geneva, Switzerland in the first half of the  18 th century. A great supporter of Newton's theories, he was a major contributor, along with Thomas Le Seur and Fran\\u00e7ois Jacquier, to an highly annotated edition of Newton's  Principia .\\\\n \", \"Jean-Louis Calandrini\", \"1703-1758\", 325], [1841, 289, \"Alexander Weinstein  is famed for solving a variety of boundary value problems which have been used in a wide range of applications. He spent a large part of his life suffering discrimination and fleeing from persecution which he successfully survived physically but paid a price mentally.\", \"Alexander Weinstein\", \"1897-1979\", 1714], [213, 290, \"Ferdinand Verbiest  was a Flemish missionary to China in the  17 th century. He produced the first Manchu edition of the first six books of Euclid, a remarkable world map, and a steam automobile. He is also famed as an astronomer, designing astronomical instruments and producing calendars.\", \"Ferdinand Verbiest\", \"1623-1688\", 210], [369, 291, \"Mar\\u00eda Andresa Casamayor  was the first Spanish woman to publish a science book. In March  1738 , when only  17  years old, she published the arithmetic text  Tyrocinio arithm\\u00e9tico  designed to facilitate the learning of basic arithmetic: addition, subtraction, multiplication and division.\\\\n \", \"Mar\\u00eda Andresa Casamayor\", \"1720-1780\", 356], [1248, 291, \"Donald Sadler  was a mathematical astronomer who spent his career working at the Nautical Almanac Office. He made major contributions to the construction of mathematical tables. He served as President of the Royal Astronomical Society and worked tirelessly for international collaboration.\\\\n \", \"Donald Sadler\", \"1908-1987\", 2053], [2151, 293, \"Jean Dieudonn\\u00e9  was a French mathematician who worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. He was a founder member of Bourbaki and also wrote on the history of mathematics.\", \"Jean Dieudonn\\u00e9\", \"1906-1992\", 1998], [1264, 295, \"Clara Bacon  was the first woman to be awarded a Ph.D. in mathematics from Johns Hopkins University. She had an outstanding reputation as a teacher, and ten women to whom she taught mathematics at undergraduate level at Goucher College went on to be awarded a Ph.D. from a different institution.\", \"Clara Bacon\", \"1866-1948\", 1154], [2752, 296, \"Harvey Greenspan  played an important role in establishing Applied Mathematics as a subject in its own right in the United States. He studied fluid dynamics both from a theoretical and from an experimental perspective, making major contributions to fluid flow, wave motion and bio-fluid dynamics.\", \"Harvey Greenspan\", \"1933-\", 2740], [1022, 296, \"D D Kosambi  was an Indian mathematician who, in addition to many mathematics and mathematical physics papers, published on genetics, numismatics, Indology, Sanskrit studies, and Indian history. He brought mathematics, statistics, Marxism and critical analysis into his studies of historiography.\", \"D D Kosambi\", \"1907-1966\", 2020], [2533, 296, \"Eugene Alexander Graham Jr  was awarded the Silver Star for gallantry in the Italian campaign of World War II. He was the first African American to study for a Ph.D. in mathematics outside the United States. Because of discrimination in the United States, he spent most of his career in France.\\\\n \", \"Eugene Graham\", \"1925-1997\", 2524], [2023, 296, \"Jovan Karamata  was an outstanding mathematician who lived through the wars of the first half of the  20 th century in the Balkans. He gained international fame with a  2 -page proof of the Hardy-Littlewood theorem, and also did excellent work on slowly varying functions and on Tauberian theory.\", \"Jovan Karamata\", \"1902-1967\", 1843], [524, 296, \"Miles Bland  was a  19 th century mathematician, a fellow of St John's College, Cambridge, then later vicar of Lilley in Hertfordshire. He wrote a number of mathematical textbooks which proved very popular, one running to nine editions over nearly forty years. He also wrote some religious texts.\", \"Miles Bland\", \"1786-1867\", 504], [2344, 296, \"Luna Isaac Mishoe  was one of the first twenty African American to be awarded a Ph.D. in mathematics. He taught mathematics and physics at Morgan State College in Baltimore, did postdoctoral research at Oxford University in England and from  1960  served as president of Delaware State College.\\\\n \", \"Luna Isaac Mishoe\", \"1917-1989\", 2322], [2281, 297, \"Zoltan Dienes  was born in Hungary but spent much of his life in England and Canada. He was passionate about studying ways to teach mathematics to children and became a leading world expert carrying out numerous experiments in different countries. He was the author on many books on the subject.\\\\n \", \"Zolt\\u00e1n Dienes\", \"1916-2014\", 2304], [2857, 297, \"Cora Sadosky  was born in Argentina and became Professor of Mathematics at Howard University in the United States. She wrote over fifty papers in harmonic analysis and operator theory. She promoted women in mathematics as well encouraging greater participation of African-Americans in mathematics.\", \"Cora Sadosky\", \"1940-2010\", 2849], [2562, 299, \"Lloyd Kenneth Williams  was an African American mathematician who taught at the University of San Francisco while studying for his doctorate at University of California at Berkeley. He served as Chair of Mathematics at several universities, ending has career at Texas Southern University in Houston.\", \"Lloyd Williams\", \"1925-2001\", 2536], [1262, 301, \"John Carruthers Beattie  graduated from Edinburgh University and studied at Munich, Vienna, Berlin and Glasgow. He became Professor of Applied Mathematics and Experimental Physics at the University of Cape Town and was later Vice Chancellor and Principal of the University. He was knighted in  1920 . \", \"Carruthers Beattie\", \"1866-1946\", 1152], [1927, 302, \"Cecilia Payne-Gaposchkin  was a British mathematician and astronomer who did important work for her Ph.D. at Radcliffe College of Harvard University. She showed that stars were composed almost entirely of hydrogen and helium but, although completely correct, it was rejected by astronomers at the time.\", \"Cecilia Payne-Gaposchkin\", \"1900-1979\", 1780], [678, 302, \"Leslie Ellis  was a brilliant man with broad interests and abilities who suffered from ill health all his short life. Senior Wrangler in the Mathematical tripos at Cambridge in  1840 , he became a fellow of Trinity College and was interested in areas of mathematics which involved philosophical ideas. \", \"Leslie Ellis\", \"1817-1859\", 651], [2786, 302, \"         Anton Davidoglu  was a Romanian mathematician who\\\\n          studied for his doctorate in Paris. He was the founder of the Academy of Advanced\\\\n          Commercial and Industrial Studies in Bucharest, and laid the foundations of mathematical\\\\n          education of economists in Romania.       \", \"Anton Davidoglu\", \"1876-1958\", 1306], [1054, 302, \"E A Maxwell  wrote several popular textbooks and made many outstanding contributions to the teaching of mathematics, particularly through his contributions to the Mathematical Association. He was an outstanding lecturer at the Queens' College, Cambridge where he undertook many administrative duties.\\\\n \", \"Edwin Maxwell\", \"1907-1987\", 2026], [2637, 302, \"Charles Gladstone Costley  was an African American mathematician who was encouraged by Lee Lorch at Fisk University in Nashville, Tennessee. He was awarded a Ph.D. by the University of Illinois, served at McGill University in Montreal and published an excellent series of papers on integral eqations.\\\\n \", \"Charles Costley\", \"1928-1997\", 2611], [1904, 303, \"Florence Nightingale David  was an English statistician who worked to increase the opportunities for women to study statistics. She became head of the Statistics Department at the University of California, Riverside. Among her research interests were the history of probability and of statistical ideas.\", \"Florence Nightingale David\", \"1909-1993\", 2091], [2669, 303, \"Vera W de Spinadel  was the first woman to be awarded a mathematics Ph.D. by the University of Buenos Aires. She was an Argentine mathematician whose main contributions were to mathematics in architecture, art, and design. She introduced the \\\"metallic means family\\\" which generalises the Golden Ratio.\\\\n \", \"Vera Spinadel\", \"1929-2017\", 2658], [2444, 305, \"John Quill Taylor King  was an African American mathematician who was awarded a Ph.D. by the University of Texas. He was a professor of mathematics at Samuel Huston College continuing to serve at Huston-Tillotson College after it merged with Tillotson College where he was President for over twenty years.\", \"John Quill Taylor King\", \"1921-2011\", 2427], [2063, 307, \"Graham Sutton  was a mathematician who made important contributions applying mathematics to meteorology. He was elected a Fellow of the Royal Society in  1949 , appointed CBE in  1950  for distinguished service to government scientific work, and knighted in  1955  for services to mathematics and science.\\\\n \", \"Oliver Sutton\", \"1903-1977\", 1888], [2306, 308, \"Magdalena Mouj\\u00e1n  was an Argentine mathematician who became famed as a writer of science fiction. She taught mathematics and statistics at various Argentine universities: Universidad Cat\\u00f3lica de la Plata, Universidad Nacional de C\\u00f3rdoba, Universidad Nacional del Comahue, and Universidad Nacional de Luj\\u00e1n.\\\\n \", \"Magdalena Mouj\\u00e1n\", \"1926-2005\", 2569], [1928, 308, \"Cecily Tanner  was the daughter of the mathematicians William Henry Young and Grace Emily Chisholm. She published excellent papers on Riemann-Stieltjes integrals, then she became interested in the history of mathematics. Her efforts led to Thomas Harriot's work being much more widely known and understood.\\\\n \", \"Cecily Tanner\", \"1900-1992\", 1781], [1141, 308, \"William Briggs  was the founder and first Principal of the University Correspondence College and the University Tutorial College in London. He set up the University Tutorial Press with printing and book-binding works. He co-authored many mathematics texts designed for private study published by his Press.\\\\n \", \"William Briggs\", \"1861-1932\", 1063], [2999, 309, \"Katherine Okikiolu  was born in England, the daughter of a Nigerian mathematician. She went to the United States where she was awarded a Presidential Early Career Award for Scientists and Engineers for both her mathematical research and her development of mathematics curricula for inner-city school children.\", \"Katherine Okikiolu\", \"1965-\", 2994], [2747, 309, \"Dorothy Foster  studied at Bedford College and was awarded a Ph.D. by the University of London in  1960 . Except for a few years as an Assistant Lecturer in Mathematics at Royal Holloway College, London, she spent her whole career at the University of St Andrews. She was an expert on geometric number theory.\", \"Dorothy Foster\", \"1933-2021\", 2735], [2531, 310, \"Cecilia Berdichevsky  was a mathematician who played a major role in developing work with the first computer to be installed in Argentina in  1961 . This work ended in  1966  with the coup which caused many academics to leave Argentina. She remained in the country taking on numerous accounting and IT roles.\\\\n \", \"Cecilia Berdichevsky\", \"1925-2010\", 2521], [2850, 310, \"Henda Swart  was the first person to be awarded a doctorate in mathematics from Stellenbosch University. She worked on the geometry of projective planes and graph theory. She became professor of mathematics at the University of KwaZulu-Natal and served as editor-in-chief of the journal  Utilitas Mathematica .\", \"Hendrika Swart\", \"1939-2016\", 2842], [1295, 310, \"Annie Scott Dill Maunder  was a Northern Irish astronomer and mathematician who studied the mathematical tripos at Cambridge then worked at the Royal Observatory Greenwich. She was the first to find evidence of the movement of sunspot emergence from the poles toward the equator over the sun's  11 -year cycle.\", \"Annie Scott Dill Maunder\", \"1868-1947\", 1183], [1742, 310, \"Octav Onicescu  was a Romanian mathematician with research interests that included many areas such as probability, Riemannian manifolds, absolute differential calculus, functional analysis, algebra, and the topological theory of functions. He is considered as the founder of the Romanian school of probability.\", \"Octav Onicescu\", \"1892-1983\", 1621], [2891, 311, \"Georgia Benkart  was an outstanding mathematician who received many honours for her research on Lie algebras and related topics. She served the American Mathematical Society and the Association for Women in Mathematics in severable roles  ( she was President of the AWM )  and was an inaugural fellow of each.\\\\n \", \"Georgia Benkart\", \"1947-2022\", 2914], [2401, 311, \"Edwin Hewitt  made fundamental contributions to functional analysis, measure theory, and topology as well as Diophantine approximation, the structure of semigroups and abstract harmonic analysis. He is well-known for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt-Savage zero-one law.\", \"Edwin Hewitt\", \"1920-1999\", 2390], [2410, 314, \"Jeremiah Certaine  was an African American mathematician who was awarded a Ph.D. by Harvard University for a thesis on algebra in  1945 . He taught at Howard University for a few years but for most of his career he was an applied mathematician for Nuclear Development Associates and the United Nuclear Corporation.\", \"Jeremiah Certaine\", \"1920-1993\", 2397], [1655, 314, \"Joseph Proudman  was a mathematician who made major contributions to oceanography, particularly to the theory of tides. He was Professor of Applied Mathematics, then Professor of Oceanography at the University of Liverpool. He headed the Liverpool Tidal Institute, now called the Proudman Oceanographic Laboratory.\", \"Joseph Proudman\", \"1888-1975\", 1535], [1331, 316, \"Ion Ionescu  was a Romanian mathematician and engineer. He was one of the founders of the  Gazeta Matematica  and contributed a remarkable number of articles and problems to the journal. One of these problems is now known as the Ionescu-Weitzenb\\u00f6ck inequality. He is also famed as an engineer for building bridges.\\\\n \", \"Ion Ionescu\", \"1870-1946\", 1225], [1745, 316, \"Cypra Cecilia Krieger Dunaj  was the first woman to earn a PhD in mathematics from a Canadian university and only the third person to be awarded a mathematics doctorate in Canada. She is best known for her English translation of Sierpinski's  Introduction to General Topology   (1934)  and  General Topology   (1952)\", \"Cecilia Krieger\", \"1894-1974\", 1651], [2436, 318, \"Harry Reuter  was born in Germany but came to England as a refugee in  1935 . His career was at the University of Manchester, the University of Durham and Imperial College, London. He contributed to a wide range of topics but is best know for outstanding contributions to probability, particularly to Markov processes.\", \"Harry Reuter\", \"1921-1992\", 2422], [1954, 319, \"Bento Cara\\u00e7a  was a Portuguese mathematician who was very active in supporting mathematics and also organisations which supported democracy against Salazar's authoritarian government. He wrote the interesting book  Fundamental Concepts of Mathematics  and was one of the founders of the journal  Gazeta de Matem\\u00e1tica.  \", \"Bento Cara\\u00e7a\", \"1901-1948\", 1801], [998, 321, \"Albert Badoureau  discovered  37  of the  75  non-prismatic uniform polyhedra in  1878 . These were in addition to the  22  known at the time  (5  Platonic solids,  13  Archimedean solids, and  4  Kepler-Poinsot polyhedra ) . He is also famed for his work in geology and for being the mathematical advisor to Jules Verne.\", \"Albert Badoureau\", \"1853-1923\", 942], [134, 321, \"Pilar Ribeiro  was a co-founder of the journal  Gazeta de Matem\\u00e1tica  and co-founder of the Portuguese Mathematical Society, serving as its First Secretary. Along with her husband, the mathematician Hugo Ribeira, she spent  30  years in exile because of her opposition to the authoritarian Estado Novo regime in Portugal.\", \"Pilar Ribeiro\", \"1911-2011\", 2159], [2448, 323, \"Mar\\u00edlia Chaves Peixoto  was the first Brazilian woman to be awarded a Ph.D. in mathematics. In  1951  she was the first Brazilian woman to be elected a member of the Brazilian Academy of Sciences. She made substantial contributions to what is now known as Peixoto's Theorem on the structural stability of dynamical systems.\", \"Mar\\u00edlia Peixoto\", \"1921-1961\", 2431], [3008, 325, \"Maryna Viazovska  is a Ukrainian mathematician who is professor at the Chair of Number Theory at the Institute of Mathematics of the \\u00c9cole Polytechnique F\\u00e9d\\u00e9rale de Lausanne in Switzerland. She solved the sphere-packing problem in dimension  8  and, in collaboration with others, the sphere-packing problem in dimension  24 .\", \"Maryna Viazovska\", \"1984-\", 3009], [2251, 326, \"Muriel Wales  was born in Northern Ireland but lived in Canada from the age of one. In  1941  she was awarded a Ph.D. in mathematics from the University of Toronto. She worked at the Montreal Laboratory of the National Research Council of Canada but from  1950  worked as a claims agent for her step-father's shipping company.\", \"Muriel Wales\", \"1913-2009\", 2217], [2730, 327, \"Joachim Neub\\u00fcser  was one of the first to create a computer package to study discrete mathematics, in particular group theory. The system GAP, development of which bgan in  1985 , was awarded the ACM/SIGSAM Richard Dimick Jenks Memorial Prize for Excellence in Software Engineering applied to Computer Algebra in July  2008 .\\\\n \", \"Joachim Neub\\u00fcser\", \"1932-2021\", 2718], [1345, 330, \"Alberto Gonz\\u00e1lez Dom\\u00ednguez  was a major figure in the development of mathematical sciences in Argentina. He worked on analytic functions, the theory of distributions and their application to quantum theory, the representation of functions by Fourier integrals, Laplace integrals and orthogonal series, and on probability theory.\\\\n \", \"Gonz\\u00e1lez Dom\\u00ednguez\", \"1904-1982\", 1913], [450, 330, \"Franti\\u0161ek Josef Gerstner  was a Czech mathematician, astronomer and engineer. He is famed for transforming the Prague School of Engineers into the Prague Polytechnic Institute in  1806 . It is now the Polytechnic University of Prague. He also produced a non-linear wave solution, known today as Gerstner waves or trochoidal waves.\", \"Franti\\u0161ek Josef Gerstner\", \"1756-1832\", 431], [1439, 330, \"Henry Plummer  was a mathematician and astronomer who for some years was Royal Astronomer of Ireland and Andrews Professor of Astronomy at Trinity College, Dublin. He left Ireland to take up the Professorship of Mathematics at the Military College of Science at Woolwich. He made important contributions to mathematical astronomy.\", \"Henry Plummer\", \"1875-1946\", 1295], [1454, 333, \"Frances Evelyn Cave-Browne-Cave  was home educated, then studied the mathematical tripos at the University of Cambridge, being ranked next to G H Hardy. She was the first recipient of a research grant from Girton College, worked with Karl Pearson and published two papers. She spent the rest of her career teaching at Girton College.\", \"Evelyn Cave-Browne-Cave\", \"1876-1965\", 1311], [2022, 335, \"Joseph Pierce  was the sixth African American to be awarded a Ph.D. in mathematics. He taught mathematics in universities for most of his career, undertook research in statistics, and is most famed for the classic book  Negro Business and Business Education   (1947)  which was reprinted almost  50  years after it was first published.\", \"Joseph Pierce\", \"1902-1969\", 1842], [390, 335, \"Samuel Vince  came from a working class family but, with the support of several priests, was able to study the mathematical tripos at Cambridge and he was Senior Wrangler in  1775 . He wrote many works on mathematics, physics and astronomy. He was Plumian professor of astronomy and experimental philosophy at Cambridge for  25  years.\", \"Samuel Vince\", \"1749-1821\", 414], [1766, 339, \"Elza Furtado Gomide  was the second Brazilian woman to be awarded a doctorate in mathematics. She served for many years as Head of Mathematics at the Institute of Mathematics and Statistics in the University of S\\u00e3o Paulo. She was influential in promoting a debate on the role of the university in the training of qualified professionals.\\\\n \", \"Elza Furtado Gomide\", \"1925-2013\", 2523], [1465, 340, \"Margaret Barr Moir  was a Scottish mathematical physicist who became a lecturer in mathematics at the University of Western Australia in Perth. She may be the first woman appointed as a university lecturer in mathematics in Australia. She lost her job after the University had to make substantial cut-backs following the Great Depression.\\\\n \", \"Margaret Barr Moir\", \"1883-1975\", 1441], [904, 342, \"Elizaveta Litvinova  was the second woman to receive a Ph.D. in mathematics. A competent mathematician, she was denied the possibility to teach and research at high levels in Russia. She was a friend of Sofia Kovalevskaya and wrote a biography of her and of other mathematicians. She also wrote around  70  articles on teaching mathematics.\\\\n \", \"Elizaveta Litvinova\", \"1845-1919\", 848], [2530, 342, \"Adelina Guti\\u00e9rrez  was a Chilean professor, scientist and academic who was the main force behind setting up the first Bachelor's degree in Astronomy in Chile and later the first Master's degree in Astronomy. She was the first Chilean to obtain a doctorate in astrophysics and also the first woman elected to the Chilean Academy of Sciences.\\\\n \", \"Adelina Guti\\u00e9rrez Moreno\", \"1925-2015\", 2520], [2778, 343, \"Gonzalo P\\u00e9rez Iribarren  was a Uruguayan mathematician and statistician who was forced to spend ten years in exile during the right-wing dictatorship beginning in  1973 . He returned to Uruguay in  1983  and was the main force in rebuilding the Institute of Mathematics and Statistics and setting up the Basic Sciences Development Programme.\\\\n \", \"Gonzalo P\\u00e9rez Iribarren\", \"1936-1998\", 2781], [2248, 343, \"Marie-H\\u00e9l\\u00e8ne Schwartz  was the daughter of Paul L\\u00e9vy and the wife of Laurent Schwartz. She lived through very difficult times but went on to have an outstanding career at the University of Lille. She worked on functions of a complex variable, Ahlfors theory, the Poincar\\u00e9-Hopf theorem, and finally characteristic classes of singular varieties.\", \"Marie-H\\u00e9l\\u00e8ne Schwartz\", \"1913-2013\", 2214], [2649, 346, \"Marion Ilse Walter  was born in Berlin and escaped the Nazis on the Kindertransport to England. She emigrated to the United States in  1948  and after earning her doctorate, founded the Mathematics Department at Simmons College. She published over  40  journal articles, several children's books, and the popular book  The Art of Problem Posing .\", \"Marion Walter\", \"1928-2021\", 2633], [2628, 348, \"Charles Bernard Bell Jr  was an African American whose specialties were nonparametric statistics, stochastic processes, and related areas. He was professor of mathematics at Tulane University, then professor of Biostatistics at the University of Washington in Seattle, and finally professor of Mathematical Sciences at San Diego State University.\\\\n \", \"Charles Bell\", \"1928-2010\", 2610], [1074, 348, \"Alice Lee  was awarded a D.Sc. in  1899 , and had an outstanding career as a statistician working in both Bedford College and University College in London. Her work was important in disproving the belief that skull size was related to intelligence, the argument that was being used at that time to \\\"prove\\\" women were intellectually inferior to men.\", \"Alice Lee\", \"1858-1939\", 1003], [2485, 348, \"Dan Mostow  was an outstanding mathematician winning the Leroy Steele Prize in  1993  and the Wolf Prize in Mathematics in  2013  for his fundamental and pioneering contribution to geometry and Lie group theory. He also played a major role in supporting mathematics as president of the American Mathematical Society and in many other leading roles.\", \"Dan Mostow\", \"1923-2017\", 2465], [2641, 349, \"Elizabeth Fennema  was an American mathematician who worked on mathematical education. She received many honours such as the first Annual Award for Outstanding Contribution to Research on Women and Education from the American Educational Research Association, and the Dora Helen Skypek Award from the Association for Women and Mathematics Education.\", \"Elizabeth Fennema\", \"1928-2021\", 2615], [1228, 361, \"Alice Everett  was a mathematician and astronomer who studied the mathematical tripos at Girton College, worked at the Royal Observatory Greenwich and then at the Potsdam Astrophysical Observatory. She had a second career working on optics at the National Physical Laboratory. Her final career was working on the early developments of television broadcasting.\\\\n \", \"Alice Everett\", \"1865-1949\", 1130], [2244, 365, \"Israel Everett Glover  was the first African American to be awarded a Ph.D. in mathematics by Oklahoma State University. He was appointed as Chairman of the Department of Mathematics at Florida A &amp; M University in Tallahassee, Florida where he presided at the General Session of the five hundred and ninety-fourth meeting of the American Mathematical Society.\\\\n \", \"Israel Everett Glover\", \"1913-1975\", 2210], [1897, 366, \"Yewande Olubummo  is a Nigerian mathematician who works in the United States. In  2006 - 2010  she was chair of the mathematics department at Spelman College. She publishes papers on functional analysis and dynamical systems. With National Science Foundation support she led a programme to encourage minority undergraduates in mathematics to go on to graduate study.\", \"Yewande Olubummo\", \"1960-\", 2983], [2998, 367, \"Karen Smith  is an American mathematician who works on commutative algebra and algebraic geometry. She is the Keeler Professor of Mathematics at the University of Michigan. She won the Ruth Lyttle Satter Prize in Mathematics for her development of tight closure methods in commutative algebra and especially for her application of these methods in algebraic geometry.\", \"Karen Smith\", \"1965-\", 2993], [1687, 371, \"E H Neville  was professor of mathematics at the University of Reading. He played an important role in mathematical education, particularly with the British Association for the Advancement of Science, with the Mathematical Association and with the International Commission on Mathematical Instruction. He wrote a number of important texts and many interesting articles.\\\\n \", \"Eric Harold Neville\", \"1889-1961\", 1559], [2688, 372, \"Juan Jorge\\u00a0Sch\\u00e4ffer  was born in Austria, became a citizen of Uruguay where he had most of his schooling and undergraduate studies, and worked at Carnegie Mellon University in Pittsburgh, USA from  1968 . His outstanding research papers on functional analysis and ordinary differential equations made important contributions to the development of mathematics in Uruguay.\\\\n \", \"Juan Jorge Sch\\u00e4ffer\", \"1930-2017\", 2678], [2636, 375, \"G\\u00fcnter Lumer  was born in Germany but his Jewish family were forced to flee from the Nazis in  1933 , eventually going to Uruguay where G\\u00fcnter was educated. He spent half his career in the United States and half in Belgium. He was a creative and prolific mathematician whose works have great influence on the research community in functional analysis and evolution equations.\", \"G\\u00fcnter Lumer\", \"1929-2005\", 2650], [1964, 379, \"Jerzy Rozycki  was a Polish mathematician who, along with his colleagues Marian Adam Rejewski and Henryk Michal Zygalski, did amazingly valuable work decoding messages sent by the German Enigma machines. Although impossible to quantify, many lives must have been saved since, it is claimed, their work contributed to the shortening of World War II by between three to five years.\", \"Jerzy Rozycki\", \"1909-1942\", 2097], [3005, 386, \"Talitha Washington  is an American mathematician who, in  2001 , became the first African American to graduate with a doctorate in mathematics from the University of Connecticut. She became co-leader of the National Science Foundation's 'Improving Undergraduate STEM Education: Hispanic-Serving Institutions' programme and won the  2019  Black Engineer of the Year STEM Innovator Award.\", \"Talitha Washington\", \"1974-\", 3005], [2853, 391, \"Mario Wschebor  was a Uruguayan mathematician and statistician who has a remarkable record of outstanding papers, and an international reputation of speaking at conferences around the world. Yet his career was disrupted by having to flee because of political events. He was also passionate about political and social issues and fought throughout his career for an improved university system.\", \"Mario Wschebor\", \"1939-2011\", 2845], [846, 392, \"Allen Whitworth  became an editor of the newly founded journal  Messenger of Mathematics  while still an undergraduate at St John's College, Cambridge. He was later elected a fellow of the College and wrote several popular teaching books. He later had a career in the Church and, because of his proposal and encouragement, St John's College set up a Mission for the disadvantaged in London.\\\\n \", \"Allen Whitworth\", \"1840-1905\", 797], [2152, 395, \"Wade Ellis Sr  was the twelfth African American to be awarded a Ph.D. in mathematics. He worked on radar and taught at Boston University before being appointed as a professor at Oberlin College in Oberlin, Ohio, where he served for  19  years. From  1967  he served as professor of mathematics at the University of Michigan and Associate Dean of the Horace H Rackham School of Graduate Studies. \", \"Wade Ellis\", \"1909-1989\", 2109], [2854, 397, \"Marjorie Senechal  is an American mathematician who worked on tessellations and quasicrystals. She won the Mathematical Association of America's Carl B Allendoerfer Award for excellence in expository writing in  Mathematics Magazine  for her article,  Which Tetrahedra Fill Space?  Her book  American Silk  1830 - 1930  won the Millia Davenport Publication Award of the Costume Society of America.\", \"Marjorie Senechal\", \"1939-\", 2846], [2045, 423, \"Evan James Williams  was a mathematician and physicist who made outstanding contributions to atomic physics, especially when working with Niels Bohr. During World War II he worked for the Admiralty applying methods of Operations Research to deal with the problem of German U-boats. It is claimed that his contributions led to the defeat of the U-boat campaign which made planning for the Allies to invade Europe possible.\\\\n \", \"Evan James Williams\", \"1903-1945\", 1872], [1419, 432, \"Beatrice Mabel Cave-Browne-Cave  studied the mathematical tripos at Girton College Cambridge. She the taught mathematics at a High School for eleven years before becoming an assistant to Karl Pearson in the Galton Laboratory of University College, London. She later became an assistant to Leonard Bairstow in the Department of Aeronautics at the Imperial College, London. She published two papers with Pearson and two with Bairstow.\", \"Beatrice Mabel Cave-Browne-Cave\", \"1874-1947\", 1276], [2984, 432, \"Joshua Allensworth Leslie  was an African American mathematician born in Jamaica. He studied for his Ph.D. at the University of Paris advised by Henri Cartan. He was a professor at the University of Ibadan in Nigeria, Northwestern University in Evanston, Illinois, and Howard University. He was awarded a Major Research Instrumentation grant to study the application of topology and group theory to solving differential equations.\\\\n \", \"Joshua Leslie\", \"1933-\", 2743], [341, 437, \"Augustin Hallerstein  was born in Ljubljana  ( now in Slovenia )  and entered the Jesuit Order.\\\\n          After studying and teaching in Europe he went to China as a Jesuit missionary. He became head of the\\\\n          Mathematics and Astronomy Board of the Imperial Court but maintained extensive contacts with the Royal Society\\\\n          in London, the Imperial Observatory in Vienna and the Academy of St Petersburg.\\\\n                   \", \"Jorge Juan\", \"1713-1773\", 345], [2587, 453, \"Lonnie Grafton Cross  was an African American mathematician who took the name  Abdulalim Abdullah Shabazz . With an outstanding record working to increase the participation of women, minorities, and individuals with physical disabilities into science and engineering, he was awarded the Mentor Award of the American Association for the Advancement of Science and the Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring.\\\\n \", \"Abdulalim Shabazz\", \"1927-2014\", 2579], [1678, 453, \"         Augustin Hallerstein  was born in Ljubljana  ( now in Slovenia )  and entered\\\\n          the Jesuit Order. After studying and teaching in Europe he went to China as a Jesuit\\\\n          missionary. He became head of the Mathematics and Astronomy Board of the Imperial Court\\\\n          but maintained extensive contacts with the Royal Society in London, the Imperial\\\\n          Observatory in Vienna and the Academy of St Petersburg.                 \", \"Augustin Hallerstein\", \"1703-1774\", 324], [1244, 465, \"Gilbert Walker  was an English mathematician who was Senior wrangler in the Mathematical Tripos at Cambridge in  1889 , and elected a fellow of Trinity College. His interest moved to meteorology and he worked in India from  1903  to  1924  becoming Director-General of the Indian Observatories. Returning to England, he was appointed Professor of Meteorology at Imperial College of Science and Technology. His interests included boomerangs, and the flight of birds.\", \"Gilbert Walker\", \"1868-1958\", 1192], [2481, 470, \"Beauregard Stubblefield  was an African American mathematician who, despite his excellent undergraduate record, was turned down for graduate work at several universities. He showed great determination and eventually was awarded a Ph.D. from the University of Michigan. He served at several universities including Oakland University in Michigan, the Appalachian State University in Boone, North Carolina and then at the U.S. Department of Commerce in Boulder, Colorado.\\\\n \", \"Beauregard Stubblefield\", \"1923-2013\", 2461]];\n",
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    "### https://github.com/mwouts/itables/blob/main/docs/advanced_parameters.md\n",
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    "     scrollCollapse=True, paging=False, column_filters=\"footer\", dom=\"lrtip\")"
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