bios.yaml

# ==============================================================================
# MATHIGON BIOGRAPHIES
# ==============================================================================


abel:
  born: 1802
  died: 1829
  name: Abel
  overflow: true
  bio: |
    __Niels Henrik Abel__ (1802 – 1829) was an important Norwegian
    mathematician. Even though he died at the age of 26, he made groundbreaking
    contributions to a wide range of topics.

    At the age of 16, Abel proved the binomial theorem. Three years later, he
    proved that it is impossible to solve quintic equations – by independently
    inventing group theory. This had been an open problem for over 350 years! He
    also worked on elliptic functions and discovered _Abelian_ functions.

    Abel spent his life in poverty: he had six siblings, his father died when he
    was 18, he was unable to find a job at a university, and many mathematicians
    initially dismissed his work. Today, one of the highest awards in
    mathematics, the _Abel Prize_ is named after him.
  links:
    - title: Group Theory
      url: /course/transformations-and-symmetry/symmetry-groups

al-haytham:
  born: 965
  died: 1050
  name: Al-Haytham
  bio: |
    __Hasan Ibn al-Haytham__ (أبو علي، الحسن بن الحسن بن الهيثم, c. 965 – 1050)
    lived in Cairo during the Islamic Golden Age, and studied mathematics,
    physics, astronomy, philosophy and medicine. He was a proponent of the
    _scientific method_: the belief that any a scientific hypothesis must be
    verified using experiments or mathematical logic – centuries before
    European scientists during the Renaissance.

    Al-Haytham was particularly interested in optics and visual perception. He
    also derived a formula for the sum of fourth powers (`1^4 + 2^4 + 3^4 + … +
    n^4`), and he studied the link between algebra and geometry.

al-karaji:
  born: 953
  died: 1029
  name: Al-Karaji
  bio: __Muhammad Al-Karaji__ (ابو بکر محمد بن الحسن الکرجی, c. 953 – 1029) was
    a Persian mathematician and engineer. He was the first person to use _prove
    by induction_, which allowed him to prove the binomial theorem.
  links:
    - title: Proof by Induction
      url: /world/Axioms_and_Proof

al-khwarizmi:
  born: 780
  died: 850
  name: Al-Khwarizmi
  overflow: true
  bio: |
    The Persian mathematician __Muhammad Al-Khwarizmi__ (محمد بن موسى الخوارزمي‎,
    780 – 850) lived during the golden age of the Muslim Abbasid regime in
    Baghdad. He worked at the “House of Wisdom”, which contained the first large
    collection of academic books since the destruction of the Library of
    Alexandria.

    Al-Khwarizmi has been called the “father of algebra” – in fact, the word
    _algebra_ comes from the Arabic title of his most important book: “The
    Compendious Book on Calculation by Completion and Balancing”. In it, he
    showed how to solve linear and quadratic equations, and for many centuries,
    it was the main mathematics textbook at European universities.

    Al-Khwarizmi also worked in astronomy and geography, and the word
    “algorithm” is named after him.

apollonius:
  name: Apollonius
  born: -262  # ???
  died: -190  # ???
  bio: __Apollonius of Perga__ (c. 200 BC) was a Greek mathematician and
    astronomer best known for his work on the four _conic sections_.
  links:
    - title: Conic Sections
      url: /course/circles-and-pi/conic-sections

appel:
  name: Appel
  bio: |
    __Kenneth Appel__ (1932 – 2013) was an American mathematician, known for his
    proof of the Four Colour Theorem with Wolfgang Haken.

    In recognition, he and Haken received the Fulkerson Prize of the American
    Mathematical Society.

    Appel studied at Queens College, New York, and the University of Michigan.
    He taught at the University of Illinois, and the University of New
    Hampshire.

archimedes:
  name: Archimedes
  born: -287
  died: -212
  bio: |
    __Archimedes__ (c. 287 – c. 212 BC) was an ancient Greek scientist and
    engineer, and one of the greatest mathematicians of all time. He discovered
    many concepts of calculus, and worked in geometry, analysis and mechanics.

    While taking a bath, Archimedes discovered a way to determine the volume of
    irregular objects using the amount of water they displaced when submerged.
    He was so excited by this discovery that he ran out on the street, still
    undressed, yelling _“Eureka!”_ (Greek for _“I have found it!”_).

    As engineer he built ingenious defence machines during the siege of his home
    city Syracuse in Sicily. After two years, the Romans finally managed to
    enter and Archimedes was killed. His last words were _“Do not disturb my
    circles”_ – which he was studying at the time.
  links:
    - title: Archimedean Solids
      url: /course/polygons-and-polyhedra/more-on-polyhedra

aristotle:
  born: -384
  died: -322
  name: Aristotle
  bio: |
    __Aristotle__ (Ἀριστοτέλης, c. 384 – 322 BC) was a philosopher in Ancient
    Greece. Together with his teacher _Plato_, he is considered the “Father of
    Western Philosophy”. He was also the private tutor of Alexander the Great.

    Aristotle wrote about science, mathematics, philosophy, poetry, music,
    politics, rhetoric, linguistics, and many other subjects. His work was
    highly influential during the Middle Ages and into the Renaissance, and his
    views on ethics and other philosophical questions are still being discussed
    today.

    Aristotle is also the first known person to formally study _logic_,
    including its applications in science and mathematics.

aryabhata:
  born: 476
  died: 550
  name: Aryabhata
  overflow: true
  bio: __Aryabhata__ (आर्यभट) was one of the first mathematicians and astronomers
    in the golden age of Indian mathematics. He defined trigonometric functions,
    solved simultaneous quadratic equations, found approximations for _π_, and
    realised that _π_ is irrational.
  links:
    - title: Trigonometry
      url: /course/triangles-and-trigonometry/trigonometry
    - title: Quadratic Equations
      url: /course/quadratics/introduction

babbage:
  born: 1791
  died: 1871
  name: Babbage
  small: true
  bio: |
    __Charles Babbage__ (1791 – 1871) was a British mathematician, philosopher
    and engineer. He is often called the “father of the computer”, having
    invented the first mechanical computer (the _Difference engine_), and an
    improved, programmable version (the _Analytical Engine_).

    In theory, these machines could automatically perform certain calculations
    stored on cards or tape. However, due to the high production costs, they
    were never fully completed during Babbage’s lifetime. In 1991, a functional
    replica was constructed at the Science Museum in London.

bernoulli-1:
  born: 1654
  died: 1705
  name: Bernoulli
  bio: |
    __Jacob Bernoulli__ (1655 – 1705) was a Swiss mathematician, and one of the
    many important scientists in the Bernoulli family. In fact, he had a deep
    academic rivalry with several of his brothers and sons.

    Jacob made significant advances to the calculus that was invented by Newton
    and Leibnitz, created the field of _calculus of variations_, discovered the
    fundamental constant _e_, developed techniques for solving differential
    equations, and much more.

    He published the first substantial work about probability, including
    permutations, combinations and the law of large numbers, he proved the
    binomial theorem, and derived many of the properties of Bernoulli numbers.

bernoulli-2:
  born: 1700
  died: 1782
  name: Bernoulli
  bio: |
    __Daniel Bernoulli__ (1700 – 1782) was a Swiss mathematician and physicist.
    He was one of the many famous scientists from the Bernoulli family –
    including his father Johann, his uncle Jacob, and his brother Nicholas.

    Daniel Bernoulli showed that as the speed of a fluid increases, its pressure
    decreases. Now called _Bernoulli’s principle_, this is the mechanism used by
    airplane wings and combustion engines. He also made important discoveries
    in probability and statistics, and first encountered _Bessel functions_.

    At the age of 34, he was banned from his father’s house for beating him at
    an award from the Paris Academy, for which they both submitted an entry.

bhaskara:
  born: 1114
  died: 1185
  name: Bhaskara
  bio: __Bhaskara II__ (1114 – 1185) was an Indian mathematician and astronomer.
    He discovered some of the basic concepts of calculus, more than 500 years
    before Leibnitz and Newton. Bhaskara also established that division by zero
    yields infinity, and solved various quadratic, cubic, quartic and
    Diophantine equations.

blackwell:
  born: 1919
  died: 2010
  name: Blackwell
  small: true
  bio: |
    __David Blackwell__ (1919 – 2010) was an American statistician and
    mathematician. He worked on game theory, probability theory, information
    theory and dynamic programming, and wrote one of the first textbooks on
    Bayesian statistics. The _Rao-Blackwell Theorem_ shows how to improve
    estimators of certain quantities in statistics.

    Blackwell was the first African-American elected to join the American
    _National Academy of Sciences_, and he was one of the first to receive a
    PhD in mathematics.

bolyai:
  born: 1802
  died: 1860
  name: Bolyai
  small: true
  bio: |
    __János Bolyai__ (1802 – 1860) was a Hungarian mathematician, and one of
    the founders of non-Euclidean geometry – a geometry in which Euclid’s fifth
    axiom about parallel lines does not hold. This was a significant
    breakthrough in mathematics. Unfortunately for Bolyai, the mathematicians
    Gauss and Lobachevsky discovered similar results at the same time, and
    received most of the credit.
  links:
    - title: Non-Euclidean Geometry
      url: /world/Dimensions_and_Distortions

boole:
  born: 1815
  died: 1864
  name: Boole
  bio: __George Boole__ (1815 – 1864) was an English mathematician. As a child,
    he taught himself Latin, Greek and mathematics, hoping to escape his lower
    class life. He created _Boolean algebra_, which uses operators like AND, OR
    and NOT (rather than addition or multiplication) and can be used when
    working with sets. This was the foundation for formal mathematical logic,
    and has many applications in computer science.

brahmagupta:
  born: 598
  died: 668
  name: Brahmagupta
  overflow: true
  bio: The Indian mathematician __Brahmagupta__ (c. 598 – 668 AD) invented the
    rules for addition, subtraction and multiplication with zero and negative
    numbers. He was also an astronomer and made many other discoveries in
    mathematics. Unfortunately, his writings did not contain any proofs, so we
    don’t know how he derived his results.

cantor:
  born: 1845
  died: 1918
  name: Cantor
  bio: |
    The German mathematician __Georg Cantor__ (1845 – 1918) was the inventor of
    set theory, and a pioneer in our understanding of infinity. For most of his
    life, Cantor's discoveries were fiercely opposed by his colleagues. This may
    have contributed to his depression and nervous breakdowns, and he spent many
    decades in a mental institution.

    Cantor proved that there are _different sizes_ of infinity. The set of real
    numbers, for example, is _uncountable_ – meaning that it cannot be paired up
    with the set of real numbers.

    Only towards the end of his life, Cantor started to receive the recognition
    he deserved. David Hilbert famously declared that “No one shall expel us
    from the paradise that Cantor has created”.
  links:
    - title: Infinity
      url: /world/Infinity
    - title: Set Theory
      url: /world/Axioms_and_Proof

cardano:
  born: 1501
  died: 1576
  name: Cardano
  bio: |
    The Italian __Gerolamo Cardano__ (1501 – 1576) was one of the most
    influential mathematicians and scientists of the Renaissance. He
    investigated hypercycloids, published Tartaglia’s and Ferrari’s solution for
    cubic and quartic equations, was the first European to systematically use
    negative numbers, and even acknowledged the existing of imaginary numbers
    (based on `sqrt(-1)`).

    Cardano also made some early progress in probability theory and introduced
    binomial coefficients and binomial theorem to Europe. He invented many
    mechanical devices, including combination locks, gyroscopes with three
    degrees of freedom, and drive shafts (or Cardan shafts) that are still used
    in vehicles today.
  links:
    - title: Imaginary Numbers
      url: /world/Real_Irrational_Imaginary

carroll:
  born: 1832
  died: 1898
  name: Carroll
  bio: |
    __Charles Lutwidge Dodgson__ (1832 – 1898) is best know under his pen name
    __Lewis Carroll__, as the author of _Alice’s Adventures in Wonderland_ and
    its sequel _Through the Looking-Glass_.

    However, Carroll was also a brilliant mathematician. He always tried to
    incorporate puzzles and logic into his children’s stories, making them more
    enjoyable and memorable.

cauchy:
  born: 1789
  died: 1857
  name: Cauchy
  small: true
  bio: |
    __Augustin-Louis Cauchy__ (1789 – 1857) was a French mathematician and
    physicist. He contributed to a wide range of areas in mathematics, and
    dozens of theorems and named after him.

    Cauchy formalised calculus and analysis, by reformulating and proving
    results where previous mathematicians were much more careless and imprecise.
    He founded the field of _complex analysis_, studied permutation groups, and
    worked on optics, fluid dynamics and elasticity theory.

cavalieri:
  name: Cavalieri
  born: 1598
  died: 1647
  bio: |
    __Bonaventura Cavalieri__ (1598 – 1647) was an Italian mathematician and
    monk. He developed a precursor to infinitesimal calculus, and is remembered
    for Cavalieri’s principle to find the volume of solids in geometry.

    Cavalieri also worked optics and motion, introduction logarithms to Italy,
    and exchanged many letters with Galileo Galilei.
  links:
    - title: Cavalieri’s Principle
      url: /course/circles-and-pi/spheres-cones-cylinders#cavalieri

cayley:
  born: 1821
  died: 1895
  name: Cayley
  bio: __Arthur Cayley__ (1821 – 1895) was a British mathematician and lawyer.
    He was one of the pioneers of _group theory_, first proposed the modern
    definition of a “group”, and generalised them to encompass many more
    applications in mathematics. Cayley also developed matrix algebra, and
    worked on higher-dimensional geometry.
  links:
    - title: Group Theory
      url: /course/transformations-and-symmetry/symmetry-groups

collatz:
  name: Collatz
  bio: __Lothar Collatz__ (1910 – 1990) was a German mathematician working on
    differential equations and optimisation problems. The _Collatz conjecture_
    or `3x+1` problem is named after him – and still unsolved.

conway:
  name: Conway
  born: 1937
  died: 2020
  bio: |
    __John Horton Conway__ (born 1937) is a British mathematician and currently
    Professor Emeritus at Princeton University.

    He is best known for inventing “Conway’s Game of Life”, a _cellular
    automaton_ with fascinating properties. He explored the underlying
    mathematics of everyday objects like knots and games, as well as
    contributing to group theory, number theory and many other areas of
    mathematics.
  links:
    - title: Look-and-say Sequence
      url: /course/sequences/special#look-and-say

copernicus:
  born: 1473
  died: 1543
  name: Copernicus
  bio: |
    __Nicolaus Copernicus__ (1473 – 1543) was a Polish mathematician,
    astronomer and lawyer. During his life, most people believed in the
    _Geocentric_ model of the universe, with Earth at the centre and
    everything else rotating around it.

    Copernicus created a new model, where the sun is at the centre, and Earth
    moves around it on a circle. He also predicted that Earth rotates around its
    axis once every day. Afraid that it would upset the Catholic church, he
    only published the model just before his death – triggering what is now
    called the _Copernican Revolution_.

    Copernicus also worked as a diplomat and physician, and made important
    contributions to economist.
  links:
    - title: Planetary Orbits
      url: /course/circles-and-pi/conic-sections#orbits

de-moivre:
  born: 1667
  died: 1754
  name: De Moivre
  bio: |
    __Abraham de Moivre__ (1667 – 1754) was a French mathematician who worked
    in probability and analytic geometry. He is most remembered for _de Moivre's
    formula_, which linkes trigonometry and complex numbers.

    De Moivre discovered the formula for the normal distribution in probability,
    and first conjectured the _central limit theorem_. He also found a
    non-recursive formula for Fibonacci numbers, linking them to the golden
    ratio `φ`.
  links:
    - title: Probability
      url: /course/probability/predicting-the-future
    - title: Fibonacci Numbers
      url: /course/sequences/fibonacci

dedekind:
  born: 1831
  died: 1916
  name: Dedekind
  small: true
  bio: __Richard Dedekind__ (1831 – 1916) was a German mathematician and one of
    the students of Gauss. He developed many concepts in set theory, and
    invented _Dedekind cuts_ as the formal definition of real numbers. He also
    gave the first definitions of _number fields_ and _rings_, two important
    constructs in abstract algebra.

democritus:
  born: -460
  died: -370
  name: Democritus
  bio: The Greek mathematician __Democritus__ (c. 460 – 370 BC), may be the
    first person to speculate that all matter was made up of tiny _atoms_ and
    is considered the “father of modern science”. He also made many discoveries
    in geometry, including the formula for the volume of prisms and cones.
  links:
    - title: Volume of a Cone
      url: /course/circles-and-pi/spheres-cones-cylinders#cone-volume

desargues:
  born: 1591
  died: 1661
  name: Desargues
  bio: |
    __Girard Desargues__ (1591 – 1661) was a French mathematician, engineer,
    and architect. He designed numerous buildings in Paris and Lyon, helped
    construct a dam, and invented a mechanism for raising water using
    epicycloids.

    In mathematics, Desargues is considered the father of _projective geometry_.
    This is a special kind of geometry in which parallel lines meet at at “point
    at infinity”, the size of shapes does not matter (only their proportions),
    and all four conic sections (circle, ellipse, parabola and hyperbola) are
    essentially the same.
  links:
    - title: Conic Sections
      url: /course/circles-and-pi/conic-sections

descartes:
  born: 1596
  died: 1650
  name: Descartes
  bio: |
    __René Descartes__ (1596 – 1650) was a French mathematician and philosopher,
    and one of the key figures in the Scientific Revolution. He refused to
    accept the authority of previous philosophers, and one of his best-known
    quotes is “I think, therefore I am”.

    Descartes is the father of _analytical geometry_, which allows us to
    describe geometric shapes using algebra. This was one of the prerequisites,
    which allowed Newton and Leibnitz to invent _calculus_ a few decades later.

    He is credited with the first use of superscripts for powers or exponents,
    and the _cartesian coordinate system_ is named after him.

diophantus:
  born: 200
  died: 284
  name: Diophantus
  overflow: true
  bio: |
    __Diophantus__ was a Hellenistic mathematician who lived in Alexandria.
    Most of his works are about solving polynomial equations with several
    unknowns. These are now called _Diophantine equation_ and remain an
    important area of research today.

    It was while reading one of Diophantus’ books, many centuries later, that
    _Pierre de Fermat_ proposed one of these equations had no solution. This
    became known as “Fermat’s Last Theorem”, and was only solved in 1994.

dirac:
  name: Dirac
  bio: |
    __Paul Dirac__ (1898 – 1972) was an English theoretical physicist, who
    shared the 1933 Nobel Prize with Erwin Schrödinger. Dirac was one of the
    pioneers of Quantum Mechanics, formulated the famous _Dirac equation_ and
    first predicted the existence of antimatter.

    He taught at Cambridge University, before moving to America. Dirac was
    famously shy and, according to Einstein, _“balancing on the dizzying path
    between genius and madness”_.

einstein:
  name: Einstein
  born: 1879
  died: 1955
  small: true
  bio: |
    __Albert Einstein__ (1879 – 1955) was a German physicist, and one of the
    most influential scientists in history. He received the Nobel Prize for
    physics and TIME magazine called him the _person of the 20th century_.

    Einstein triggered the most significant transformation in our view of the
    universe since Newton. He realised that classical, _Newtonian_ physics was
    no longer enough to explain certain physical phenomenons.

    At the age of 26, during his “miracle year”, he published four
    groundbreaking scientific papers that explained the photoelectric effect
    and Brownian motion, introduced special relativity, and derived the formula
    `E = m c^2`, which states that energy (_E_) and mass (_m_) are equivalent.

eratosthenes:
  name: Eratosthenes
  born: -276
  died: -195
  bio: __Eratosthenes of Cyrene__ (c. 276 BC – 195 BC) was a Greek
    mathematician, geographer, astronomer, historian, and poet. He spent much
    of his life in Egypt, as head of the library of Alexandria.

    Among many other achievements, Eratosthenes calculated the circumference of
    the Earth, measured the tilt of the Earth’s axis of rotation, estimated the
    distance to the sun, and created some of the first maps of the world.

    He also invented the “Sieve of Eratosthenes”, an efficient way to
    calculate _prime numbers_.
  links:
    - title: Radius of the Earth
      url: /course/circles-and-pi/tangets-chords-arcs#eratosthenes
    - title: Sieve of Eratosthenes
      url: /course/divisibility-and-primes/prime-numbers#eratosthenes

erdos:
  born: 1913
  died: 1996
  name: Erdős
  bio: |
    __Paul Erdős__ (1913 – 1996) was one of the most productive mathematicians
    in history. Born in Hungarian, he solved countless problems in graph theory,
    number theory, combinatorics, analysis, probability, and other parts of
    mathematics.

    During his life, Erdős published around 1,500 papers and collaborated with
    more than 500 other mathematicians. In fact, he spent most of his life
    living out of a suitcase, travelling to seminars, and visiting colleagues!

escher:
  name: Escher
  born: 1898
  died: 1972
  bio: |
    __Maurits Cornelis Escher__ (1898 – 1972) was a Dutch artist who created
    sketches, woodcuts and lithographs of mathematically inspired objects and
    shapes: including polyhedra, tessellations and impossible shapes. He
    graphically explored concepts like symmetry, infinity, perspective and
    non-euclidean geometry.
  small: true
  links:
    - title: Tessellations in Art
      url: /course/polygons-and-polyhedra/tessellations#escher

euclid:
  name: Euclid
  born: -330
  died: -270
  bio: __Euclid of Alexandria__ (around 300 BC) was a Greek mathematician and
    is often called the _father of geometry_. He published a book _Elements_
    that first introduced Euclidean geometry and contained many important proofs
    in geometry and number theory. It was the main mathematics textbook until
    the 19th century. He taught mathematics in Alexandria, but very little else
    is known about his life.
  links:
    - title: Euclid’s Axioms
      url: /course/euclidean-geometry/euclids-axioms
    - title: Infinitely many Primes
      url: /course/divisibility-and-primes/prime-numbers#primes3

euler:
  name: Euler
  born: 1707
  died: 1783
  bio: |
    __Leonhard Euler__ (1707 – 1783) was one the greatest mathematicians of all
    times. His work spans all areas of mathematics, and he wrote 80 volumes of
    research.

    Euler was born in Switzerland and studied in Basel, but lived most of his
    life in Berlin, Prussia, and St. Petersburg, Russia.

    Euler invented much of the modern mathematical terminology and notation, and
    made important discoveries in calculus, analysis, graph theory, physics,
    astronomy, and many other topics.
  links:
    - title: Königsberg Bridges Problem
      url: /course/graphs-and-networks/bridges-of-koenigsberg
    - title: Euler’s Formula
      url: /course/graphs-and-networks/eulers-formula
    - title: Polyhedrons
      url: /course/polygons-and-polyhedra/polyhedra

fermat:
  name: Fermat
  born: 1607
  died: 1665
  bio: |
    __Pierre de Fermat__ (1607 – 1665) was a French mathematician and lawyer. He
    was an early pioneer of calculus, as well as working in number theory,
    probability, geometry and optics.

    In 1637, he wrote a short note in the margin of one of his textbooks,
    claiming that the equation `a^n + b^n = c^n` has no integer solutions for
    `n > 2`, and that he had a “marvellous proof, which this margin is too
    narrow to contain”. This became known as _Fermat’s Last Theorem_, and one of
    the most famous unsolved problems in mathematics – until it was finally
    proven in 1994.
  links:
    - title: Probability
      url: /course/probability/introduction

fibonacci:
  name: Fibonacci
  born: 1175
  died: 1250
  bio: |
    __Leonardo Pisano__, commonly known as __Fibonacci__ (1175 – 1250) was an
    Italian mathematician. He is best known for the number sequence named after
    him: 1, 1, 2, 3, 5, 8, 13, …

    Fibonacci is also responsible for popularising the Arabic numerals (0, 1, 2,
    3, 4, …) in Europe, which was still using Roman numerals (I, V, X, D, …) in
    the 12th century AD. He explained the decimal system in a book called “Liber
    Abaci”, a practical textbook for merchants.
  links:
    - title: Fibonacci Numbers
      url: /course/sequences/fibonacci

fourier:
  born: 1768
  died: 1830
  name: Fourier
  bio: |
    __Joseph Fourier__ (1768 – 1830) was a French mathematician, and a friend
    and advisor of Napoleon. In addition to his mathematical research, he is
    also credited with the discovery of the greenhouse effect.

    While travelling to Egypt, Fourier became particularly fascinated with
    _heat_. He studied heat transfer and vibrations, and discovered that any
    periodic function can be written as an infinite sum of trigonometric
    functions: a _Fourier series_.

fuller:
  name: Fuller
  bio: __Richard Buckminster “Bucky” Fuller__ (1895 – 1983) was an American
    architect, designer and inventor. He is famous for constructing _geodesic
    dome_ – large, spherical structures. Similar looking Carbon molecules, the
    _fullerenes_, were later named after him.

galileo:
  born: 1564
  died: 1642
  name: Galileo
  bio: |
    __Galileo Galilei__ (1564 – 1642) was an Italian astronomer, physicist and
    engineer. He used one of the first telescopes to make observations of the
    night sky, where he discovered the four largest moons of Jupiter, the phases
    of Venus, sunspots, and much more.

    Galileo, sometimes called the “father of modern science”, also studied the
    motion of objects in free fall, kinematics, material science, and invented
    the thermoscope (an early thermometer).

    He was a vocal proponent of _Heliocentrism_, the idea that the Sun was at
    the centre of our solar system. This eventually led to him being tried by
    the Catholic Inquisition: Galileo was forced to recant and spent the rest
    of his life under house arrest.

galois:
  born: 1811
  died: 1832
  name: Galois
  overflow: true
  bio: |
    The French mathematician __Évariste Galois__ (1811 – 1832) had a short and
    tragic life, yet he invented two entirely new fields of mathematics: _Group
    theory_ and _Galois theory_.

    While still in his teens, Galois proved that there is no general solution
    for polynomial equations of degree five or higher – simultaneously with
    Niels Abel.

    Unfortunately, other mathematicians who he shared these discoveries with
    repeatedly misplaced or simply returned his work, and he failed his school
    and university exams while concentrating on much more complex work.

    At the age of 21, Galois was shot in a duel (some say a feud over a woman),
    and later died of his wounds. In the night before his death, he summarised
    his mathematical discoveries in a letter to a friend. It would take other
    mathematicians many years to fully realise the true impact of his work.
  links:
    - title: Group Theory
      url: /course/transformations-and-symmetry/symmetry-groups

gauss:
  name: Gauss
  born: 1777
  died: 1855
  bio: |
    __Carl Friedrich Gauss__ (1777 – 1855) was arguably the greatest
    mathematician in history. He made groundbreaking discoveries in just about
    every field of mathematics, from algebra and number theory to statistics,
    calculus, geometry, geology and astronomy.

    According to legend, he corrected a mistake in his father‘s accounting at
    the age of 3, and found a way to quickly add up all integers from 1 to 1000
    at the age of 8. He made his first important discoveries while still a
    teenager, and later tutored many other famous mathematicians as Professor.
  links:
    - title: Prime Number Theorem
      url: /course/divisibility-and-primes/the-distribution-of-primes#riemann
    - title: Non-Euclidean Geometry
      url: /world/Dimensions_and_Distortions
    - title: Sums of Triangle Numbers
      url: /course/sequences/figurate#triangle-sums

germain:
  born: 1776
  died: 1831
  name: Germain
  small: true
  bio: |
    __Marie-Sophie Germain__ (1776 – 1831) decided that we wanted to be a
    mathematician at the age of 13, after reading about Archimedes.
    Unfortunately, as a woman, she was faced with significant opposition.
    Her parents tried to prevent her from studying when she was young, and she
    never received a post at a university.

    Germain was a pioneer in understanding the mathematics of elastic surfaces,
    for which she won the grand prize from the Paris Academy of Sciences. She
    also made considerable progress in solving Fermat's Last Theorem, and
    regularly corresponded with Carl Friedrich Gauss.

godel:
  born: 1906
  died: 1978
  name: Gödel
  small: true
  bio: |
    __Kurt Gödel__ (1906 – 1978) was an Austrian mathematician who later
    immigrated to America, and is considered one of the greatest logicians in
    history.

    At the age of 25, just after finishing his doctorate in Vienna, he published
    his two _incompleteness theorems_. These state that any (consistent and
    sufficiently powerful) mathematical system contains certain statements that
    are true but cannot be proven. In other words, mathematics contains certain
    problems that are impossible to solve.

    This result had a profound impact on the development and philosophy of
    mathematics. Gödel also found an example of these “impossible theorems”:
    the _continuum hypothesis_.
  links:
    - title: Unprovable Theorems
      url: /world/Axioms_and_Proof
    - title: Continuum Hypothesis
      url: /world/Infinity

goldbach:
  name: Goldbach
  born: 1690
  died: 1764
  bio: __Christian Goldbach__ (1690 – 1764) was a Prussian mathematician and
    contemporary of Euler, Leibniz and Bernoulli. He was tutor of Russian Tsar
    Peter II, and is remembered for his “Goldbach Conjecture“.
  links:
    - title: Goldbach Conjecture
      url: /course/divisibility-and-primes/the-distribution-of-primes#goldbach1

grothendieck:
  born: 1928
  died: 2014
  name: Grothendieck
  small: true
  bio: The French mathematician __Alexander Grothendieck__ (1928 – 2014) was one
    of the key figures in the development of _algebraic geometry_. He extended
    the scope of the field to apply to many new problems in mathematics,
    including, eventually, Fermat’s last theorem. In 1966, he was awarded the
    Fields medal.

guthrie:
  name: Guthrie
  bio: __Francis Guthrie__ (1831 – 1899) was a South African botanist and
    mathematician, who first stated the Four Colour Problem in 1852. He was a
    student of Augustus De Morgan, one of the greatest British mathematicians.
    In addition to being a mathematics professor and teacher, Guthrie worked as
    a lawyer and did research in solar power and aeronautics.

haken:
  name: Haken
  bio: __Wolfgang Haken__ (born 1928) is a German mathematician, known for his
    proof the _Four Colour Theorem_ with Kenneth Appel. In recognition, he and
    Appell received the Fulkerson Prize of the American Mathematical Society. In
    1990, Haken became a member of the Center for Advanced Study at the
    University of Illinois, where he is now an Emeritus Professor.

halley:
  name: Halley
  bio: __Edmond Halley__ (1656 – 1742) was an English mathematician and
    physicist, and the second _Astronomer Royal_. He calculated the orbit of
    Halley’s Comet, which is named after him.

hamilton:
  born: 1805
  died: 1865
  name: Hamilton
  small: true
  bio: |
    __William Rowan Hamilton__ (1805 – 1865) was an Irish mathematician and
    child prodigy. He invented _quaternions_, the first example of a
    “non-commutative algebra”, which has important applications in mathematics,
    physics and computer science.

    He first came up with the idea while walking along the Royal Canal in
    Dublin, and carved the fundamental formula into a stone bridge he passed:
    `"i"^2 = "j"^2 = "k"^2 = "ijk" = -1`.

    Hamilton also made significant contributions to physics, including optics
    and Newtonian mechanics.

hardy:
  born: 1877
  died: 1947
  name: Hardy
  small: true
  bio: |
    __G.H. Hardy__ (1877 – 1947) was a leading English pure mathematician.
    Together with _John Littlewood_, he made important discoveries in analysis
    and number theory, including the distribution of prime numbers.

    In 1913, Hardy received a letter from _Srinivasa Ramanujan_, an unknown,
    self-taought clerk from India. Hardy immediately recognised his genius, and
    arranged for Ramanujan to travel to Cambridge where he was working.
    Together, they made important discoveries and authord numerous paper.

    Hardy always dislkied applied mathematics and expressed this in his personal
    account of mathematical thinking, the 1940 book _A Mathematician’s Apology_.

hilbert:
  name: Hilbert
  born: 1862
  died: 1943
  bio: |
    __David Hilbert__ (1862 – 1943) was one of the most influential
    mathematicians of the 20th century. He worked on almost every area of
    mathematics, and was particularly interested in building a formal, logical
    foundation for maths.

    Hilbert worked in Göttingen (Germany), where he tutored numerous students
    who later became famous mathematicians. During the International Congress of
    Mathematicians in 1900, he presented a list of 23 unsolved problems. These
    set the course for future research – and four of them are still unsolved
    today!
  links:
    - title: Hilbert’s Hotel
      url: /world/Infinity

hypatia:
  born: 360
  died: 415
  name: Hypatia
  overflow: true
  bio: |
    __Hypatia__ (c. 360 – 415 AD) was a prominent astronomer and mathematician
    in ancient Alexandria. She was also the first female mathematician whose
    life is work is reasonably well recorded. She edited or wrote commentaries
    on many of the scientific books of her time, and constructed astrolabes and
    hydrometers.

    She was renowned during her life as a great teacher, and she advised
    Orestes, the Roman prefect of Alexandria. Orestes’ feud with Cyril, the
    bishop of Alexandria, led to Hypadia being murdered by a mob of Christians.

jacobi:
  born: 1809
  died: 1851
  name: Jacobi
  small: true
  bio: __Carl Jacobi__ (1804 – 1851) was a German mathematician. He worked on
    analysis, differential equations and number theory, and was one of the
    pioneers in the study of _elliptic functions_.

jefferson:
  name: Jefferson
  bio: |
    __Thomas Jefferson__ (1743 – 1826), was one of the Founding fathers of the
    United States, their third president, and the principal author of the
    Declaration of Independence.

    In addition to his work in politics, he studied mathematics, horticulture,
    mechanics, and worked as an architect. After retiring from public office,
    Jefferson founded the University of Virginia.

jiushao:
  born: 1202
  died: 1261
  name: Qin Jiushao
  overflow: true
  bio: |
    __Qin Jiushao__ (秦九韶, c. 1202 – 1261) was a Chinese mathematician,
    inventor and politician. In his book _Shùshū Jiǔzhāng_, he published
    numerous mathematical discoveries, including the important _Chinese
    remainder theorem_, and wrote about surveying, meteorology and the military.

    Qin first developed a method for numerically solving polynomial equations,
    which is now known as _Horner’s method_. He found a formula for the area of
    a triangle based on the length of its three sides, calculated the sum of
    arithmetic series, and introduced a symbol for “zero” into Chinese
    mathematics.

    Qin also invented _Tianchi basins_, which were used to measure rainfall and
    gather meteorological data important for farming.

johnson:
  born: 1918
  died: 2020
  name: Johnson
  bio: |
    __Katherine Johnson__ (born 1918) is an African-American mathematician.
    While working at NASA, Johnson calculated the orbits taken by American
    astronauts – including Alan Shepard, the first American in space, the Apollo
    Moon landing program, and even the Space Shuttle.

    Her extraordinary ability to calculate orbital trajectories, launch windows
    and emergency return paths was widely known. Even after the arrival of
    computers, astronaut John Glenn asked her to personally re-check the
    electronic results.

    In 2015, Johnson received the Presidential Medal of Freedom.

karinthy:
  name: Karinthy
  bio: __Frigyes Karinthy__ (1887 – 1938) was a Hungarian author, poet and
    journalist. He is best known for the 1929 short story “Chains”, which first
    introduced the concept of _six degrees of separation_.

kepler:
  name: Kepler
  born: 1571
  died: 1630
  bio: __Johannes Kepler__ (1571 – 1630) was a German astronomer and
    mathematician. He was the _imperial mathematician_ in Prague, and he is best
    known for his three _laws of planetary motion_. Kepler also worked in
    optics, and invented an improved telescope for his observations.
  links:
    - title: Elliptical Orbits
      url: /course/circles-and-pi/conic-sections#kepler

khayyam:
  name: Khayyam
  born: 1048
  died: 1131
  bio: __Omar Khayyam__ (عمر خیّام‎, 1048 – 1131) was a Persian mathematician,
    astronomer and poet. He managed to classify and solve all cubic equations,
    and found new ways to understand Euclid’s _parallel axiom_. Khayyam also
    designed the _Jalali calendar_, a precise solar calendar that is still used
    in some countries.
  links:
    - title: Pascal’s Triangle
      url: /course/sequences/pascals-triangle

lagrange:
  born: 1736
  died: 1813
  name: Lagrange
  bio: |
    __Joseph-Louis Lagrange__ (1736 – 1813) was an Italian mathematician who
    succeeded Leonard Euler as the director of the Academy of Sciences in
    Berlin.

    He worked on analysis and the calculus of variations, invented new
    methods for solving differential equations, proved theorems in number
    theory, and laid the foundations of group theory.

    Lagrange also wrote about classical and celestial mechanics, and helped
    establish the metric system in Europe.

lambert:
  born: 1728
  died: 1777
  name: Lambert
  bio: __Johann Lambert__ (1728 – 1777) was a Swiss mathematician, physicist,
    astronomer and philosopher. He was the first to prove that _π_ is an
    irrational number, and he introduced hyperbolic trigonometric functions.
    Lambert also worked on geometry and cartography, created map projections,
    and foreshadowed the discovery of non-Euclidean spaces.

laplace:
  born: 1749
  died: 1827
  name: Laplace
  small: true
  bio: |
    __Pierre-Simon Laplace__ (1749 – 1827) was a French mathematician and
    scientist. He is sometimes called the “Newton of France”, because of his
    wide range of interests, and the enormous impact of his work.

    In a five-volume book, Laplace translated problems in celestial mechanics
    from _geometry_ to _calculus_. This opened up a wide range of new strategies
    for understanding our universe. He proposed that the solar system developed
    from a rotating disk of dust.

    Laplace also pioneered the field of probability, and showed how probability
    can help us understand data from the physical world.

leibniz:
  name: Leibniz
  born: 1646
  died: 1716
  bio: |
    __Gottfried Wilhelm Leibniz__ (1646 – 1716) was a German mathematician
    and philosopher. Among many other achievements, he was one of the inventors
    of calculus, and created some of the first mechanical calculators.

    Leibniz believed that our universe is the “best possible universe” that God
    could have created, while allowing us to have a free will. He was a great
    advocate of _rationalism_, and also made contributions to physics, medicine,
    linguistics, law, history, and many other subjects.

leonardo:
  born: 1452
  died: 1519
  name: Da Vinci
  bio: |
    __Leonardo da Vinci__ (1452 – 1519) was an Italian artist and polymath. His
    interests ranged from painting, sculpting and architecture to engineering,
    mathematics, anatomy, astronomy, botany and cartography. He is often seen
    as the prime example of a “Universal Genius” and was one of the most
    diversely talented individuals ever to have lived.

    Leonardo was born in Vinci, educated in Florence, and worked in Milan,
    Rome, Bologna, and Venice. Only 15 of his paintings have survived, but among
    them are some of the best known and most reproduced works in the world,
    including the _Mona Lisa_ and _The Last Supper_.

    His notebooks contain a vast number of drawings, inventions, and scientific
    diagrams – including the first flying machines and helicopters, hydraulic
    pumps, bridges, and much more.

lie:
  born: 1842
  died: 1899
  name: Lie
  small: true
  bio: The Norwegian mathematician __Marius Sophus Lie__ (1842 – 1899) made
    significant advances in the study of _continuous transformation groups_ –
    now called _Lie groups_. He also worked on differential equations and
    non-Euclidean geometry.

lobachevsky:
  born: 1792
  died: 1856
  name: Lobachevsky
  small: true
  bio: __Nikolai Lobachevsky__ (Никола́й Лобаче́вский) was a Russian
    mathematician, and one of the founders of non-Euclidean geometry. He managed
    to show that you can build up a consistent type of geometry in which
    Euclid’s fifth axiom (about parallel lines) does not hold.
  links:
    - title: Non-Euclidean Geometry
      url: /world/Dimensions_and_Distortions

lorenz:
  name: Lorenz
  born: 1917
  died: 2008
  bio: __Edward Lorenz__ (1917 – 2008) was an American mathematician and
    meteorologist. He pioneered _chaos theory_, discovered _strange attractor_,
    and coined the term “butterfly effect”.

lovelace:
  born: 1815
  died: 1852
  name: Lovelace
  overflow: true
  bio: |
    __Ada Lovelace__ (1815 – 1852) was an English writer and mathematician.
    Together with Charles Babbage, she worked on the _Analytical Engine_ an
    early, mechanical computer. She also wrote the first algorithm to run on
    such a machine (to calculate Bernoulli numbers), making her the first
    computer programmer in history.

    Ada described her approach as “poetical science”, and spent much time
    thinking about the impact of technology on society.

madhava:
  born: 1340
  died: 1425
  name: Madhava
  bio: |
    __Madhava of Sangamagramma__ (c. 1340 – 1425) was a mathematician and
    astronomer from southern India. All of his original work has been lost, but
    he had a great impact on the development of mathematics.

    Madhava first used infinite series to approximate trigonometric functions,
    which was a significant step towards the development of calculus many
    centuries later. He also studied geometry and algebra, and found an exact
    formula for _π_ (also using infinite series).
  links:
    - title: Trigonometry
      url: /course/triangles-and-trigonometry/trigonometry
    - title: Pi
      url: /course/circles-and-pi/introduction

mandelbrot:
  born: 1924
  died: 2010
  name: Mandelbrot
  bio: |
    The mathematician __Benoît Mandelbrot__ was born in Poland, grew up in
    France, and eventually moved to the United States. He was one of the
    pioneers of _fractal geometry_, and particularly interested in how
    “roughness” and “chaos” appear in the real world (e.g. clouds or
    coastlines).

    While working at IBM, he used early computers to create graphical
    representations of fractals, and in 1980 he discovered the famous
    _Mandelbrot set_.
  links:
    - title: Fractals
      url: /world/Fractals

mersenne:
  born: 1588
  died: 1648
  name: Mersenne
  bio: |
    __Marin Mersenne__ (1588 – 1648) was a French mathematician and priest.
    Because of the frequent exchanges with his contacts in the scientific world
    during the 17th century, he has been called the “the post-box of Europe”.

    Today we mostly remember him for the _Mersenne primes_, prime numbers that
    can be written as `2^n - 1`. Most of the largest known primes are of this
    type. He also studied acoustics and the harmonics of a vibrating string,
    and wrote about theology and philosophy.
  links:
    - title: Large Primes
      url: /course/divisibility-and-primes/the-distribution-of-primes#prime-test-1

milgram:
  name: Milgram
  bio: __Stanley Milgram__ (1933 – 1984) was a famous social psychologist. He is
    best known for experiments on _obedience_, testing how willing adults are to
    follow orders, even when hurting others, and for the _small-world
    experiment_, which tests the degree of connectedness of societies.

mirzakhani:
  born: 1977
  died: 2017
  name: Mirzakhani
  overflow: true;
  bio: |
    __Maryam Mirzakhani__ (مریم میرزاخانی‎, 1977 – 2017) was an Iranian
    mathematician and professor at Standford University. She is the only woman
    to have received the _Fields Medal_, the highest award in mathematics.

    Maryam worked at the intersection of dynamical systems and geometry. She
    studied objects like _hyperbolic surfaces_ and _complex manifolds_, but
    also contributed to many other areas of mathematics.

    When solving problems, Maryam would draw doodles and diagrams on large
    sheets of paper, to see the underlying patterns and beauty. Her daughter
    even described Maryam’s work as “painting”. At the age of 40, Maryam died
    of breast cancer.

monge:
  born: 1746
  died: 1818
  name: Monge
  bio: |
    __Gaspard Monge__ (1746 – 1818) was a French mathematician. He is considered
    the father of _differential geometry_, having introduced the concept of
    _lines of curvature_ on surfaces in three-dimensional space (e.g. on a
    sphere). Monge also invented _orthographic projection_ and _descriptive
    geometry_, which allows the representation of three-dimensional objects
    using two-dimensional drawings.

    During the French Revolution, Monge served as Minister of the Marine. He
    helped reform the French education system and found the École Polytechnique.
  small: true
  links:
    - title: Map Projections
      url: /world/Dimensions_and_Distortions

monsky:
  name: Monsky
  bio: __Paul Monsky__ (born 1936) is an American mathematician and professor at
    Brandeis University. He proved that a square cannot be divided into an odd
    number of equal-area triangles – this is known as “Monsky’s theorem”.

napier:
  born: 1550
  died: 1617
  name: Napier
  bio: __John Napier__ (1550 – 1617) was a Scottish mathematician, physicist,
    and astronomer. He invented logarithms, popularised the use of the decimal
    point, and created “Napier’s bones”, a manual calculating device that
    helped with multiplication and division.

nash:
  born: 1928
  died: 2015
  name: Nash
  bio: |
    __John Forbes Nash__ (1928 – 2015) was an American mathematician who worked
    on game theory, differential geometry and partial differential equations.
    He showed how mathematics can explain the decision-making in complex,
    real-life systems – including economics and the military.

    In his 30s, Nash was diagnosed with paranoid schizophrenia, but he managed
    to recover and return to his academic work. He is the only person to receive
    both the Nobel Prize for economics and the _Abel Prize_, one of the highest
    awards in mathematics.
  links:
    - title: Game Theory
      url: /world/Game_Theory

neumann:
  born: 1903
  died: 1957
  name: von Neumann
  small: true
  bio: |
    __John von Neumann__ (1903 – 1957) was a Hungarian-American mathematician,
    physicist and computer scientist. He made important contributions to pure
    mathematics, was a pioneer of quantum mechanics, and developed concepts like
    game theory, cellular automata, self-replicating machines, and linear
    programming.

    During World War II, von Neumann was a key member of the _Manhattan
    Project_, working on the development of the hydrogen bomb. He later
    consulted for the Atomic Energy Commission and the US Air Force.

newton:
  name: Newton
  born: 1642
  died: 1726
  bio: |
    __Sir Isaac Newton__ (1642 – 1726) was an English physicist, mathematician,
    and astronomer, and one of the most influential scientists of all time. He
    was a professor at Cambridge University, and president of the Royal Society
    in London.

    In his book _Principia Mathematica_, Newton formulated the laws of motion
    and gravity, which laid the foundations for classical physics and dominated
    our view of the universe for the next three centuries.

    Among many other things, Newton was one of the inventors of calculus, built
    the first reflecting telescope, calculated the speed of sound, studied the
    motion of fluids, and developed a theory of colour based on how prisms split
    sunlight into a rainbow-coloured spectrum.
  links:
    - title: Gravity
      url: /course/circles-and-pi/conic-sections#newton
    - title: Digits of Pi
      url: /course/circles-and-pi/introduction#pi-record

nicomachus:
  name: Nicomachus
  born: 60
  died: 120
  overflow: true
  bio: __Nicomachus of Gerasa__ (c. 60 – 120) was an ancient Greek mathematician
    who also spent much time thinking about the mystical properties of numbers.
    His book _Introduction to Arithmetic_ contains the first mention of perfect
    numbers.
  links:
    - title: Perfect Numbers
      url: /course/sequences/special#perfect

nightingale:
  born: 1820
  died: 1910
  name: Nightingale
  small: true
  bio: |
    __Florence Nightingale__ (1820 – 1910) was an English nurse and
    statistician. During the Crimean War, she nursed wounded British soldiers,
    and later founded the first training school for nurses. As the “The Lady
    with the Lamp”, she bacame a cultural icon, and new nurses in the US still
    take the _Nightingale pledge_.

    One of her most important contributions to medicine was the use of
    statistics to evaluate treatments. She created numerous infographics, and
    was one of the first to use pie charts. Nightingale also worked to improve
    sanitation and hunger relief in India, helped abolish prostitution laws, and
    promoted new careers for women.

noether:
  name: Noether
  born: 1882
  died: 1935
  bio: __Amalie Emmy Noether__ (1882 – 1935) was a German mathematician who made
    important discoveries in abstract algebra and theoretical physics, including
    the connection between symmetry and conservation laws. She is often
    described as the most influential female mathematician.
  small: true
  links:
    - title: Symmetry in Physics
      url: /course/transformations-and-symmetry/symmetry-in-physics

oresme:
  born: 1323
  died: 1382
  name: Oresme
  bio: __Nicole Oresme__ (c. 1323 – 1382) was an important French mathematician,
    philosopher and bishop, living in the late Middle Ages. He invented
    coordinate geometry, long before Descartes, was the first to use fractional
    exponents, and worked on infinite series. He wrote about economics, physics,
    astronomy and theology, and was an advisor to King Charles V of France.

pacioli:
  born: 1446
  died: 1517
  name: Pacioli
  bio: __Luca Pacioli__ was an influential Italian friar and mathematician, who
    invented the standard symbols for plus and minus (+ and –). He was one of
    the first accountants in Europe, where he introduced double-entry
    book-keeping. Pacioli collaborated with Leonardo da Vinci, and also wrote
    about arithmetic and geometry.

pascal:
  name: Pascal
  born: 1623
  died: 1662
  bio: |
    __Blaise Pascal__ (1623 – 1662) was a French mathematician, physicist and
    philosopher. He invented some of the first mechanical calculators, as well
    as working on projective geometry, probability and the physics of the
    vacuum.

    Most famously, Pascal is remembered for naming _Pascal’s Triangle_, an
    infinite triangle of numbers with some amazing properties.
  links:
    - title: Probability
      url: /course/probability/introduction
    - title: Pascal’s Triangle
      url: /course/sequences/pascals-triangle

peano:
  born: 1858
  died: 1932
  name: Peano
  small: true
  bio: |
    The Italian mathematician __Giuseppe Peano__ (1858 – 1932) published over
    200 books and papers about logic and mathematics. He formulated the _Peano
    axioms_, which became the basis for rigorous algebra and analysis, developed
    the notation for logic and set theory, constructed continuous, space-filling
    curves (_Peano curves_), and worked on the method of proof by induction.

    Peano also developed a new, international language, _Latino sine flexione_,
    which was a simplified version of Latin.
  links:
    - title: Proof by Induction
      url: /world/Axioms_and_Proof

pearson:
  name: Pearson
  bio: __Karl Pearson__ (1857 – 1936) was an English mathematician and
    statistician. He worked on biometrics, meteorology, and eugenics, among many
    other topics, and founded the world’s first university statistics
    department, at University College London.

penrose:
  name: Penrose
  born: 1931
  died: 2020
  bio: |
    __Sir Roger Penrose__ (born 1931) is a British mathematician and physicist
    who is known for his groundbreaking work in general relativity and cosmology
    – often collaborating with other famous scientists like Stephen Hawking and
    Michael Atiyah. He also discovered _Penrose Tilings_: self-similar,
    non-periodic tessellations.
  links:
    - title: Penrose Tilings
      url: /course/polygons-and-polyhedra/tessellations#penrose

perelman:
  born: 1966
  died: 2020
  name: Perelman
  bio: |
    In 2003, the Russian mathematician __Grigori Perelman__ (Григо́рий
    Перельма́нborn, born 1966) proved the _Poincaré Conjecture_, which, until
    then, was one of the most famous unsolved problems in mathematics.

    The complex proof was verified by 2006, but Perelman declined two big awards
    that came with it: the $1 million Clay Millennium Prize, and the _Fields
    Medal_ which is the highest recognition in mathematics. In fact, he said:
    _“I’m not interested in money or fame; I don’t want to be on display like an
    animal in a zoo.”_

    Perelman also made contributions to Riemannian geometry and geometric
    topology, and the Poincaré Conjecture is still the only one of the seven
    Millennium Prize problems to have been solved.

pingala:
  name: Pingala
  born: -330
  died: -270
  bio: __Pingala__ (पिङ्गल) was an ancient Indian poet and mathematician who
    lived around 300BC, but very little is known about his life. He wrote the
    Chandaḥśāstra, where he analysed Sanskrit poetry mathematically. It also
    contained the first known explanations of binary numbers, Fibonacci numbers
    and Pascal’s triangle.
  links:
    - title: Pascal’s Triangle
      url: /course/sequences/pascals-triangle

planck:
  name: Plank
  bio: __Max Plank__ (1858 – 1947) was a German physicist and one of the
    original developers of Quantum Mechanics – for which received the Nobel
    Prize in 1918.

plato:
  name: Plato
  born: -425
  died: -347
  bio: |
    __Plato__ (c. 425 – 347 BC) was a philosopher in ancient Greece, and –
    together with his teacher Socrates and his student Archimedes – laid the
    very foundation of Western philosophy and science.

    Plato founded the Academy of Athens, the first higher learning institution
    in the Western world. His many writings on philosophy and theology, science
    and mathematics, politics and justice, make him one of the most influential
    thinkers of all time.
  links:
    - title: Platonic Solids
      url: /course/polygons-and-polyhedra/platonic-solids

poincare:
  born: 1854
  died: 1912
  name: Poincaré
  bio: |
    The French mathematician __Henri Poincaré__ (1854 – 1912) is often
    described as _the last universalist_, meaning that he worked in every field
    of mathematics known during his lifetime.

    Poincaré is one of the founders of the field of _Topology_, and he came up
    with the _Poincaré conjecture_. This was one of the famous unsolved problems
    in mathematics, until it was proven in 2003 by Grigori Perelman

    He also found a partial solution for the “three body problem”, and
    discovered that the motion of three stars or planets in space can be
    completely unpredictable. This laid the foundation for modern _Chaos
    theory_.

    Poincaré was the first to propose _gravitational waves_, and his work on
    Lorentz transformations was the basis upon which Albert Einstein built his
    theory of special relativity.
  links:
    - title: Chaos Theory
      url: /course/chaos/introduction
    - title: Topology
      url: /world/Dimensions_and_Distortions

ptolemy:
  born: 90
  died: 168
  name: Ptolemy
  bio: |
    __Claudius Ptolemy__ (c. 100 – 170 AD) was a Greco-Roman mathematician,
    astronomer, geographer and astrologer. He is best remembered for the
    _Ptolemaic_ or _Geocentric_ model of our universe – that Earth is in the
    centre and all planets and the sun revolve around this.

    While we know today this model is incorrect, Ptolemy’s scientific impact is
    indisputable. He developed trigonometric tables with many practical
    applications, which remained the most accurate for many centuries. He also
    created detailed maps of the Earth, and wrote about music theory and optics.
  links:
    - title: Trigonometry
      url: /course/triangles-and-trigonometry/trigonometry
    - title: Orbits
      url: /course/circles-and-pi/introduction

pythagoras:
  name: Pythagoras
  born: -570
  died: -495
  bio: |
    __Pythagoras of Samos__ (c. 570 – 495 BC) was a Greek philosopher and
    mathematician. He is best known for proving _Pythagoras’ Theorem_, but made
    many other mathematical and scientific discoveries.

    Pythagoras tried to explain music in a mathematical way, and discovered that
    two tones sound “nice” together (consonant) if the ratio of their
    frequencies is a simple fraction.

    He also founded a school in Italy where he and his students worshipped
    mathematics almost like a religion, while following a number of bizarre
    rules – but the school was eventually burned down by their adversaries.
  links:
    - title: Pythagoras’ Theorem
      url: /course/triangles-and-trigonometry/pythagoras-theorem

ramanujan:
  born: 1887
  died: 1920
  name: Ramanujan
  overflow: true
  bio: |
    __Srinivasa Ramanujan__ (1887 – 1920) grew up in India, where he received
    very little formal education in mathematics. Yet, he managed to develop new
    ideas in complete isolation, while working as a clerk in a small shop.

    After a few failed attempts to contact other mathematicians, he wrote a
    letter to the famous G.H. Hardy. Hardy immediately recognised Ramanujan's
    genius, and arranged for him to travel to Cambridge in England. Together,
    they made numerous discoveries in number theory, analysis, and infinite
    series.

    Unfortunately, Ramanujan soon fell ill and was forced to return to India,
    where he died at the age of 32. During his short life, Ramanujan proved over
    3000 theorems and equations, on a wide range of topics. His work created
    entirely new areas of maths, and his notebooks were studied by other
    mathematicians for many decades after his death.

regiomontanus:
  born: 1436
  died: 1476
  name: Regiomontanus
  overflow: true
  bio: __Johann Müller Regiomontanus__ (1436 – 1476) was a German mathematician
    and astronomer. He made great advances in both fields, including creating
    detailed astronomical tables and publishing multiple textbooks.

riemann:
  name: Riemann
  born: 1826
  died: 1866
  overflow: true
  bio: __Bernhard Riemann__ (1826 – 1866) was a German mathematician working in
    the fields of analysis and number theory. He came up with the first rigorous
    definition of integration, studied differential geometry which laid the
    foundation for general relativity, and made groundbreaking discoveries
    regarding the distribution of prime numbers.
  links:
    - title: Riemann Hypothesis
      url: /course/divisibility-and-primes/the-distribution-of-primes#riemann

russell:
  born: 1872
  died: 1970
  name: Russell
  small: true
  bio: |
    __Bertrand Russell__ (1872 – 1970) was a British philosopher, mathematician
    and author. He is widely considered to be one of the most important
    logicians of the 20th century.

    Russell co-wrote the “Principia Mathematica”, where he attempted to create a
    formal foundation for mathematics using logic. His work has had a
    significant impact not just on maths and philosophy, but also on
    linguistics, artificial intelligence and metaphysics.

    Russell was a passionate pacifist and anti-war activist. In 1950, he
    received the Nobel Prize in Literature, for his work “in which he champions
    humanitarian ideals and freedom of thought”.

shannon:
  name: Shannon
  born: 1898
  died: 1972
  bio: __Claude Shannon__ (1898 – 1972) was an American mathematician and
    electrical engineer, remembered as the “father of information theory”. He
    worked on cryptography, including codebreaking for national defence during
    World War II, but he was also interested in juggling, unicycling and chess.
    In his spare times, he built machines that could juggle or solve the Rubik’s
    Cube puzzle.
  small: true
  links:
    - title: Computers for Gambling
      url: /course/probability/casino-mathematics#dealer

shijie:
  born: 1249
  died: 1314
  name: Zhu Shijie
  bio: |
    __Zhu Shijie__ (朱世杰, 1249 – 1314) was one of the greatest Chinese
    mathematicians. In is book _Jade Mirror of the Four Unknowns_, he showed how
    to solve 288 different problem using systems of polynomial equations and
    four variables (called _Heaven_, _Earth_, _Man_ and _Matter_).

    Zhu made extensive use of Pascal’s triangle. He also invented rules for
    solving systems of linear equations – predating our modern matrix methods
    by many centuries.
  links:
    - title: Pascal’s Triangle
      url: /course/sequences/pascals-triangle

sikdar:
  name: Sikdar
  bio: __Radhanath Sikdar__ (1813 – 1870) was an Indian mathematician. He was
    the first to measure the height of Mount Everest, and to show that it is
    the tallest mountain on Earth.

singmaster:
  name: Singmaster
  bio: __David Singmaster__ (born 1939) is an American mathematician who is
    particularly well known for his mathematical puzzles and brain teasers. He
    was the first to come up with mathematical algorithms for analysing and
    solving the _Rubik’s Cube_.

stevin:
  born: 1548
  died: 1620
  name: Stevin
  bio: __Simon Stevin__ (1548 – 1620) was Flemish mathematician and engineer. He
    was one of the first people to use and write about decimal fractions, and
    made many other contributions to science and engineering.

tartaglia:
  born: 1499
  died: 1557
  name: Tartaglia
  bio: __Niccolò Fontana Tartaglia__ (1499 – 1557) was an Italian mathematician,
    engineer and bookkeeper. He published the first Italian translations of
    Archimedes and Euclid, found a formula for solving any cubic equation
    (including the first real application of complex numbers), and used
    mathematics to investigate the projectile motion of cannonballs.

thales:
  name: Thales
  born: -624
  died: -546
  bio: |
    __Thales of Miletus__ (c. 624 – 546 BC) was a Greek mathematician and
    philosopher.

    Thales is often recognised as the first scientist in Western civilisation:
    rather than using religion or mythology, he tried to explain natural
    phenomena using a scientific approach. He is also the first individual in
    history that has a mathematical discovery named after him: Thales’ theorem.
  links:
    - title: Thales’ Theorem
      url: /course/euclidean-geometry/introduction

thorp:
  name: Thorp
  bio: __Edward Thorp__ (born 1932) is an American hedge fund manager and
    blackjack player, known for inventing _card counting_ and for building the
    first _wearable computer_ to beat casinos at Roulette. He worked at MIT, is
    a professor of mathematics, and pioneered modern applications of probability
    theory.

turing:
  born: 1912
  died: 1954
  name: Turing
  bio: |
    __Alan Turing__ (1912 – 1954) was an English mathematician and is often
    called the “father of computer science”.

    During the Second World War, Turing played a critical role in breaking the
    Enigma code used by the German military, as part of the “Government Code and
    Cypher School” at Bletchley Park. This helped the Allies win the war, and
    may have saved millions of lives.

    He also invented the _Turing machine_, a mathematical model of a general
    purpose computer, and the _Turing test_, which can be used to judge the
    ability of artificial intelligence.

    Turing was gay, which was still a crime during his life, and meant that his
    groundbreaking accomplishments were never fully recognised. He committed
    suicide at the age of 41.

ulam:
  name: Ulam
  bio: __Stanisław Ulam__ (1909 – 1984) was a Polish-American mathematician. He
    played an important part in the American _Manhatten Project_ that developed
    the first nuclear weapons. He also worked on rocket propulsion using nuclear
    pulses, and developed the _Monte Carlo method_ – and important concept in
    statistics.

venn:
  name: Venn
  bio: __John Venn__ (1834 – 1923) was an English mathematician and philosopher
    who introduced the _Venn diagram_ used in set theory and probability. He
    taught at Cambridge University and was a Fellow of the Royal Society in
    London.

viete:
  born: 1540
  died: 1603
  name: Viète
  bio: |
    __François Viète__ (1540 – 1603) was a French mathematician, lawyer, and
    advisor to Kings Henry III and IV of France. He made significant advances
    in Algebra, and first introduced the use of letters to represent variables.

    Viète discovered the connection between the roots and coefficients of a
    polynomial, called _Viète's formula_. He also wrote books about geometry
    and trigonometry, including calculating _π_ to 10 decimal places using a
    polygon with 393216 sides.

wallis:
  born: 1616
  died: 1703
  name: Wallis
  bio: The English mathematician __John Wallis__ (1616 – 1703) contributed to
    the development of calculus, invented the number line and the symbol ∞ for
    infinity, and served as chief cryptographer for Parliament and the royal
    court.

wiles:
  born: 1953
  died: 2020
  name: Wiles
  bio: |
    The British mathematician Sir __Andrew Wiles__ (born 1953) is best known for
    proving Fermat’s Last Theorem, which, until then, was one of the most famous
    unsolved problems in mathematics.

    In 1637, Pierre de Fermat, wrote in the margin of a textbook that he had a
    wonderful proof that the equation `a^n + b^n = c^n` has no integer
    solutions for `n > 2`. Unfortunately, no one was able to find a proof –
    until Wiles, some 400 years later.

    Wiles had been fascinated by the problem since the age of 10, and spent
    seven years working on it in solitude. He announced his solution in 1993,
    although a small gap in his argument took two more years to fix.

    He was too old to receive the _Fields medal_, the highest award in
    mathematics, which has an age limit of 40. Instead, Wiles was awarded a
    special silver plaque for his work.