diff --git a/Pipfile b/Pipfile
index bd12c73..aefe599 100644
--- a/Pipfile
+++ b/Pipfile
@@ -16,6 +16,7 @@ mkdocs-glightbox = "*"
 mkdocs-jupyter = "*"
 mkdocs-material = "*"
 mkdocs-redirects = "*"
+sympy = "*"
 
 [dev-packages]
 
diff --git a/Pipfile.lock b/Pipfile.lock
index 66c07bd..3f6946e 100644
--- a/Pipfile.lock
+++ b/Pipfile.lock
@@ -1,7 +1,7 @@
 {
     "_meta": {
         "hash": {
-            "sha256": "f7bb15e8bab7129c94f2ab5422e31fbc8c56dffb83fb1488c018c415f7e71b3f"
+            "sha256": "793c96810a6a725ea92a1d628561380744eba9d976cf1ffedeb22ddb22340fa2"
         },
         "pipfile-spec": 6,
         "requires": {
@@ -21,7 +21,7 @@
                 "sha256:1de3860566df9caf38f01f86f65e0e13e379af54f9e4bee1e66b48f2efffd1ee",
                 "sha256:502575ee11cd7a28c0205f379b525beefebab9d161b7c964670864014ed7213c"
             ],
-            "markers": "platform_system == 'Darwin'",
+            "markers": "python_version >= '3.6'",
             "version": "==0.1.4"
         },
         "asttokens": {
@@ -33,19 +33,19 @@
         },
         "attrs": {
             "hashes": [
-                "sha256:935dc3b529c262f6cf76e50877d35a4bd3c1de194fd41f47a2b7ae8f19971f30",
-                "sha256:99b87a485a5820b23b879f04c2305b44b951b502fd64be915879d77a7e8fc6f1"
+                "sha256:5cfb1b9148b5b086569baec03f20d7b6bf3bcacc9a42bebf87ffaaca362f6346",
+                "sha256:81921eb96de3191c8258c199618104dd27ac608d9366f5e35d011eae1867ede2"
             ],
             "markers": "python_version >= '3.7'",
-            "version": "==23.2.0"
+            "version": "==24.2.0"
         },
         "babel": {
             "hashes": [
-                "sha256:08706bdad8d0a3413266ab61bd6c34d0c28d6e1e7badf40a2cebe67644e2e1fb",
-                "sha256:8daf0e265d05768bc6c7a314cf1321e9a123afc328cc635c18622a2f30a04413"
+                "sha256:368b5b98b37c06b7daf6696391c3240c938b37767d4584413e8438c5c435fa8b",
+                "sha256:d1f3554ca26605fe173f3de0c65f750f5a42f924499bf134de6423582298e316"
             ],
             "markers": "python_version >= '3.8'",
-            "version": "==2.15.0"
+            "version": "==2.16.0"
         },
         "beautifulsoup4": {
             "hashes": [
@@ -58,115 +58,130 @@
         },
         "bleach": {
             "hashes": [
-                "sha256:0a31f1837963c41d46bbf1331b8778e1308ea0791db03cc4e7357b97cf42a8fe",
-                "sha256:3225f354cfc436b9789c66c4ee030194bee0568fbf9cbdad3bc8b5c26c5f12b6"
+                "sha256:117d9c6097a7c3d22fd578fcd8d35ff1e125df6736f554da4e432fdd63f31e5e",
+                "sha256:123e894118b8a599fd80d3ec1a6d4cc7ce4e5882b1317a7e1ba69b56e95f991f"
             ],
-            "markers": "python_version >= '3.8'",
-            "version": "==6.1.0"
+            "markers": "python_version >= '3.9'",
+            "version": "==6.2.0"
         },
         "certifi": {
             "hashes": [
-                "sha256:5a1e7645bc0ec61a09e26c36f6106dd4cf40c6db3a1fb6352b0244e7fb057c7b",
-                "sha256:c198e21b1289c2ab85ee4e67bb4b4ef3ead0892059901a8d5b622f24a1101e90"
+                "sha256:922820b53db7a7257ffbda3f597266d435245903d80737e34f8a45ff3e3230d8",
+                "sha256:bec941d2aa8195e248a60b31ff9f0558284cf01a52591ceda73ea9afffd69fd9"
             ],
             "markers": "python_version >= '3.6'",
-            "version": "==2024.7.4"
+            "version": "==2024.8.30"
         },
         "charset-normalizer": {
             "hashes": [
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-                "sha256:0a55554a2fa0d408816b3b5cedf0045f4b8e1a6065aec45849de2d6f3f8e9786",
-                "sha256:0b2b64d2bb6d3fb9112bafa732def486049e63de9618b5843bcdd081d8144cd8",
-                "sha256:10955842570876604d404661fbccbc9c7e684caf432c09c715ec38fbae45ae09",
-                "sha256:122c7fa62b130ed55f8f285bfd56d5f4b4a5b503609d181f9ad85e55c89f4185",
-                "sha256:1ceae2f17a9c33cb48e3263960dc5fc8005351ee19db217e9b1bb15d28c02574",
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-                "sha256:1f79682fbe303db92bc2b1136016a38a42e835d932bab5b3b1bfcfbf0640e519",
-                "sha256:2127566c664442652f024c837091890cb1942c30937add288223dc895793f898",
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@@ -194,31 +209,35 @@
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@@ -241,16 +260,16 @@
                 "sha256:3111b9d131c238bec2f8f516e123e14ba243563fb135d3fe885990585aa7795b",
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@@ -284,11 +303,11 @@
         },
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-            "version": "==3.7"
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@@ -300,11 +319,11 @@
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@@ -332,19 +351,19 @@
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@@ -389,69 +408,70 @@
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             "markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2, 3.3, 3.4, 3.5'",
-            "version": "==6.0.0"
+            "version": "==6.1.0"
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@@ -708,7 +736,7 @@
                 "sha256:37dd54208da7e1cd875388217d5e00ebd4179249f90fb72437e91a35459a0ad3",
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+            "markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2'",
             "version": "==2.9.0.post0"
         },
         "python-markdown-document-offsets-injection-extension": {
@@ -722,67 +750,69 @@
         },
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@@ -794,97 +824,118 @@
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@@ -990,119 +1056,119 @@
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+                "sha256:c14937af98c4cc362a1d4374806204dd51b1e12dded1ae30645c298e5a5c4cb1",
+                "sha256:ca449520e7484534a2a44faf629362cae62b660601432d04c482283c47eaebab",
+                "sha256:cd945871335a639275eee904caef90041568ce3b42f402c6959b460d25ae8732",
+                "sha256:d0b937b2a1988f184a3e9e577adaa8aede21ec0b38320d6009e02bd026db04fa",
+                "sha256:d126b52e4a473d40232ec2052a8b232270ed1f8c9571aaf33f73a14cc298c24f",
+                "sha256:d8761c3c891cc51e90bc9926d6d2f59b27beaf86c74622c8979380a29cc23ac3",
+                "sha256:d9ecb51120de61e4604650666d1f2b68444d46ae18fd492245a08f53ad2b7711",
+                "sha256:da584ff96ec95e97925174eb8237e32f626e7a1a97888cdd27ee2f1f24dd0ad8",
+                "sha256:dbcf360c9e3399b056a238523146ea77eeb2a596ce263b8814c900263e46031a",
+                "sha256:dbddc10776ca7ebf2a299c41a4dde8ea0d8e3547bfd731cb87af2e8f5bf8962d",
+                "sha256:dc73505153798c6f74854aba69cc75953888cf9866465196889c7cdd351e720c",
+                "sha256:e13de156137b7095442b288e72f33503a469aa1980ed856b43c353ac86390519",
+                "sha256:e1791c4aabd117653530dccd24108fa03cc6baf21f58b950d0a73c3b3b29a350",
+                "sha256:e75ba609dba23f2c95b776efb9dd3f0b78a76a151e96f96cc5b6b1b0004de66f",
+                "sha256:e79059d67bea28b53d255c1437b25391653263f0e69cd7dec170d778fdbca95e",
+                "sha256:ecd27a66740ffd621d20b9a2f2b5ee4129a56e27bfb9458a3bcc2e45794c96cb",
+                "sha256:f009c69bc8c53db5dfab72ac760895dc1f2bc1b62ab7408b253c8d1ec52459fc",
+                "sha256:f16bc1334853e91ddaaa1217045dd7be166170beec337576818461268a3de67f",
+                "sha256:f19169781dddae7478a32301b499b2858bc52fc45a112955e798ee307e294977",
+                "sha256:fa3060d885657abc549b2a0f8e1b79699290e5d83845141717c6c90c2df38311",
+                "sha256:fa41a64ac5b08b292906e248549ab48b69c5428f3987b09689ab2441f267d04d",
+                "sha256:fbf15aff64a163db29a91ed0868af181d6f68ec1a3a7d5afcfe4501252840bad",
+                "sha256:fe00a9057d100e69b4ae4a094203a708d65b0f345ed546fdef86498bf5390982"
             ],
             "markers": "python_version >= '3.8'",
-            "version": "==0.19.1"
+            "version": "==0.20.1"
         },
         "six": {
             "hashes": [
                 "sha256:1e61c37477a1626458e36f7b1d82aa5c9b094fa4802892072e49de9c60c4c926",
                 "sha256:8abb2f1d86890a2dfb989f9a77cfcfd3e47c2a354b01111771326f8aa26e0254"
             ],
-            "markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2, 3.3'",
+            "markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2'",
             "version": "==1.16.0"
         },
         "smmap": {
@@ -1115,11 +1181,11 @@
         },
         "soupsieve": {
             "hashes": [
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-                "sha256:eaa337ff55a1579b6549dc679565eac1e3d000563bcb1c8ab0d0fefbc0c2cdc7"
+                "sha256:e2e68417777af359ec65daac1057404a3c8a5455bb8abc36f1a9866ab1a51abb",
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             ],
             "markers": "python_version >= '3.8'",
-            "version": "==2.5"
+            "version": "==2.6"
         },
         "stack-data": {
             "hashes": [
@@ -1128,21 +1194,30 @@
             ],
             "version": "==0.6.3"
         },
+        "sympy": {
+            "hashes": [
+                "sha256:54612cf55a62755ee71824ce692986f23c88ffa77207b30c1368eda4a7060f73",
+                "sha256:b27fd2c6530e0ab39e275fc9b683895367e51d5da91baa8d3d64db2565fec4d9"
+            ],
+            "index": "pypi",
+            "markers": "python_version >= '3.8'",
+            "version": "==1.13.3"
+        },
         "tinycss2": {
             "hashes": [
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-                "sha256:54a8dbdffb334d536851be0226030e9505965bb2f30f21a4a82c55fb2a80fae7"
+                "sha256:10c0972f6fc0fbee87c3edb76549357415e94548c1ae10ebccdea16fb404a9b7",
+                "sha256:3a49cf47b7675da0b15d0c6e1df8df4ebd96e9394bb905a5775adb0d884c5289"
             ],
             "markers": "python_version >= '3.8'",
-            "version": "==1.3.0"
+            "version": "==1.4.0"
         },
         "tomli": {
             "hashes": [
-                "sha256:939de3e7a6161af0c887ef91b7d41a53e7c5a1ca976325f429cb46ea9bc30ecc",
-                "sha256:de526c12914f0c550d15924c62d72abc48d6fe7364aa87328337a31007fe8a4f"
+                "sha256:2ebe24485c53d303f690b0ec092806a085f07af5a5aa1464f3931eec36caaa38",
+                "sha256:d46d457a85337051c36524bc5349dd91b1877838e2979ac5ced3e710ed8a60ed"
             ],
-            "markers": "python_version < '3.11'",
-            "version": "==2.0.1"
+            "markers": "python_version >= '3.8'",
+            "version": "==2.0.2"
         },
         "tornado": {
             "hashes": [
@@ -1174,54 +1249,52 @@
                 "sha256:04e5ca0351e0f3f85c6853954072df659d0d13fac324d0072316b67d7794700d",
                 "sha256:1a7ead55c7e559dd4dee8856e3a88b41225abfe1ce8df57b7c13915fe121ffb8"
             ],
-            "markers": "python_version < '3.12'",
+            "markers": "python_version >= '3.8'",
             "version": "==4.12.2"
         },
         "urllib3": {
             "hashes": [
-                "sha256:a448b2f64d686155468037e1ace9f2d2199776e17f0a46610480d311f73e3472",
-                "sha256:dd505485549a7a552833da5e6063639d0d177c04f23bc3864e41e5dc5f612168"
+                "sha256:ca899ca043dcb1bafa3e262d73aa25c465bfb49e0bd9dd5d59f1d0acba2f8fac",
+                "sha256:e7d814a81dad81e6caf2ec9fdedb284ecc9c73076b62654547cc64ccdcae26e9"
             ],
             "markers": "python_version >= '3.8'",
-            "version": "==2.2.2"
+            "version": "==2.2.3"
         },
         "watchdog": {
             "hashes": [
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diff --git a/docs/math/analysis/attention-is-all-you-need.md b/docs/math/analysis/attention-is-all-you-need.md
new file mode 100644
index 0000000..46f3e1d
--- /dev/null
+++ b/docs/math/analysis/attention-is-all-you-need.md
@@ -0,0 +1,164 @@
+# 注意力惊人
+
+构造定积分 $\displaystyle \int_{0}^{1} f(x) \mathrm{d} x = \pi - \frac{p}{q} \geq 0$ 来比较 $\pi$ 和 $\displaystyle \frac{p}{q}$ 的大小。
+
+不经过函数，所有能构造出来的数字：
+
+$$
+\mathbb{K} := \left\{\left( \frac{p}{q} \right)^{\dfrac{r}{s}} \Big|\ p,q,r,s \in \mathbb{Z} \right\}
+$$
+
+考虑 $\pi$ 的构造，其实也就是原函数 $F(b) - F(a)$ 能在 $\mathbb{K}$ 上给出 $\pi$。
+
+> 因为上下限被固定在了 $[0,1]$，因此其实能选取的函数并不多，考虑反三角函数：
+
+-   $\arcsin(x)$:
+
+$$
+\int_{0}^{1} \frac{1}{\sqrt{1-x^2}} \mathrm{d} x = \arcsin(1) = \frac{\pi}{2}
+$$
+
+-   $\arctan(x)$:
+
+$$
+\int_{-\infty}^{\infty} \frac{1}{1+x^2} \mathrm{d} x = \left[ \arctan(x) \right]_{-\infty}^{\infty} = \pi
+$$
+
+$$
+\int_{0}^{1} \frac{1}{1+x^2} \mathrm{d} x = \arctan(1) = \frac{\pi}{4}
+$$
+
+额外的：
+
+$$
+\int_0^1 \sqrt{1-x^2}\ \mathrm{d} x = \frac{\pi}{4}
+$$
+
+以这个想法来先证明：
+
+$$
+\begin{aligned}
+\pi - 2 &= \int_0^1 4\left(\sqrt{1-x^2} - (1-x)\right) \mathrm{d} x \\
+&= \int_0^1 4\left(\sqrt{1-x}\left(\sqrt{1+x} - \sqrt{1-x}\right)\right) \mathrm{d} x
+\end{aligned}
+$$
+
+不过性质不是很好（你可以尝试 Taylor Series，虽然很紧，但是 Sympy 其实难以判断大小，而且长度也不符合题目要求），回到 $\displaystyle \frac{1}{1+x^2}$，尝试一点别的：
+
+$$
+\pi - \frac{p}{q} = \int_0^1 \left(\frac{4}{1+x^2} - \frac p q \cdot g(x)\right)\mathrm{d} x
+$$
+
+启发我们考虑一个更一般的 $g(x)$：
+
+$$
+\int_0^1 g(x) \mathrm{d} x = \int_0^1 \left( a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \dots \right)\mathrm{d} x = a_0 + \frac 12 a_1 + \frac 13 a_2 + \dots = 1
+$$
+
+积分内形式：
+
+$$
+\frac{4q - p(1+x^2)(a_0 + a_1 x + a_2 x^2 + ...)}{1+x^2}
+$$
+
+考虑分子：
+
+$$
+k(x) = (4q - p a_0) - p a_1 x - p (a_2 + a_0) x^2 - p(a_3 + a_1) x^3  - p(a_4 + a_2) \geq 0
+$$
+
+不妨令（真的不妨吗）：
+
+$$
+a_0 =4q/p > 4/\pi > 1\\
+a_1 = 2(1- a_0) = 2 (1- 4q/p) < 0
+$$
+
+代入：
+
+$$
+k(x) = -2(p - 4q) x - 4q x^2 - 2(p - 4q) x^3 = 2x (-(p-4q) - 2q x - (p-4q)x^2)
+$$
+
+验证以后会发现实际上不能满足条件，更一般的，考虑 $a_1, a_0$ 的条件
+
+$$
+k(x) = (4q - p a_0) - 2p(1 - a_0) x - p a_0 x^2 - 2p (1-a_0)x^3\\
+k(0) = 4q - p a_0 \geq 0 \\
+k(1) = (4q - p a_0) - 2p + 2 pa_0 -p a_0 - 2p + 2p a_0 = 2p a_0 + 4q - 4p \geq 0
+$$
+
+即
+
+$$
+a_0 \leq 4 q/p \Rightarrow a_0 \leq 1 \\
+a_0 \geq 2 - 2q/p = 2 (p - q)/p
+$$
+
+也难以满足要求，实际上也就要求更高 Taylor Series 的展开，但是盲目打开到 $a_2$ 其实是不必要的，更一般的，直接考虑构造这样一个显然更容易恒正的函数：
+
+$$
+f(x) = \frac{{x}^n {(1-x)}^m {(a+b\ x + c\ x^2)}}{1 + x^2}
+$$
+
+代入到符号计算软件可以直接得到一个关于 $\pi, \ln 2$ 的 $\mathbb{Q}$ 线性组合（我在说什么？），注意带着 $m,n$ 可能会得到一堆关于 $m,n$ 的 $\Gamma$ 函数，考虑直接代入几个值进去（比如 $m=n=3$ 进去）
+
+接下来只需要令 $\pi, \ln 2$ 前面的系数为 $0$，然后剩余有理数的部分 $\displaystyle =\frac{p}{q}$ 即可，一元三次方程，而且均为有理数，解显然也是有理数。
+
+其实容易注意，随着 $m,n$ 的增加，能得到的解其实更紧，接下来需要的数学准备已经差不多了，剩下的就是题目本身的限制了：
+
+- 有部分 $a,b,c$ 的解并不能满足在 $[0,1]$ 上二次函数恒正，需要调高 $m,n$
+- 有部分 $m,n$ 会超出题目长度要求
+- 复制粘贴的手速大概率会超时
+
+嘛，总之用到的脚本在这里，可以参考：
+
+```python
+import sympy as sp
+import pyperclip
+
+
+x = sp.symbols("x")
+a = sp.symbols("a")
+b = sp.symbols("b")
+c = sp.symbols("c")
+
+n = 80
+
+while True:
+    f = x**n * (1 - x) ** n * (a + b * x + c * x**2) / (1 + x**2)
+
+    p, q = input("p/q:").split("/")
+    pq = sp.Rational(int(p), int(q))
+
+    sol = sp.solve(
+        [
+            sp.Rational(
+                -264625355360516117450008340198714638981492191523281648346833579224158082061028,
+                306437384083077799057007332399381984236948705737346929421798748875,
+            )
+            * a
+            + sp.Rational(
+                1067625583461964288587691136180185035077897741239121612103106082260802255650717,
+                2801713225902425591378352753365778141594959595312886211856445704000,
+            )
+            * b
+            + sp.Rational(
+                3175504264326193409400100082384575667777906298279379780162003198829635728211061,
+                3677248608996933588684087988792583810843384468848163153061584986500,
+            )
+            * c
+            + pq,
+            b,
+            274877906944 * a - 274877906944 * c - 1,
+        ],
+        (a, b, c),
+    )
+
+    f = f.subs(sol)
+    print(f)
+    pyperclip.copy(str(f))
+
+    integrate_result = sp.integrate(f, (x, 0, 1))
+    print(integrate_result)
+```