1. Primes and the zeta function:

∏_{p} \frac{1}{1 − \frac{1}{p^{s}}} = ∑_{n=1}^{∞} \frac{1}{n^{s}}

3. Yang-Baxter Equation

R_{12}R_{23}R_{12} = R_{23}R_{12}R_{23}

7. Newton’s Law of Gravitation:

F = \frac{Gm_{1}m_{2}}{r^{2}}

8. Pythagoras’ Theorem with no-word proof:

c^{2} = a^{2} + b^{2}

10? Euler’s Equation:

eiπ + 1 = 0

11? Schrödinger’s Equation:

iℏ\frac{∂ψ}{∂t} = −\frac{ℏ^{2}}{2m}∇^{2}ψ + V ψ

12. Maxwell’s Equations in Vacuum:

\begin{matrix}∇ · B = 0 \\ ∇ × B = \frac{1}{c} \frac{∂E}{∂t} \end{matrix} \begin{matrix}∇ · E = 0 \\ ∇ × E = −\frac{1}{c} \frac{∂B}{∂t} \end{matrix}

14. Einstein’s General Relativity Equation:

R_{μν} − \frac{1}{2}Rg_{μν} = 8πT_{μν}

16. Heisenberg Uncertainty Principle:

ΔxΔp ≥ \frac{ℏ}{2}

17. Dynkin diagram of E_{8}:

22. Stokes’ Theorem

∫_{M} dω = ∫_{∂M} ω

24. Atiyah-Singer Theorem for Twisted Dirac Operator: dim ker / D_{E} − dim coker / D_{E} = ∫_{M^{4k}} Â(M) · ch(E)

26. Classical Gauss-Bonnet Theorem:

χ(M^{2}) = \frac{1}{2π} ∫_{M} K dA

27. Chern-Simons Action:

S_{CS} = \frac{k}{2π} ∫_{M} Tr (\frac{1}{2}A ∧ dA + \frac{1}{3}A ∧ A ∧ A)

29. Snell’s (Pascal’s) Law:

sin i = n sin r

32. Virasoro algebra:

[L_{m}, L_{n}] = (m − n)L_{m+n} + \frac{c}{12}(m^{3} − m)δ_{m+n}

34. Yang-Mills equations:

F = dA + A ∧ A
∇ ∧ ⋆F = 0

37. Dirac Equation:

\begin{aligned}(−iℏγ^{μ}∇_{μ} + mc) ψ & = & 0 \\ γ^{μ}γ^{ν} + γ^{ν}γ^{μ} & = & 2g^{μν} \end{aligned}

(i ∂̸ − m) ψ = 0

(i D̸ − m) ψ = 0

39. Cauchy’s Integral Formula:

f(z) = \frac{1}{2πi} ∮_{C} \frac{f(ζ)}{ζ − z} dζ

41. Graphic with Feynman diagrams and surfaces [insert graphic] 42? Navier-Stokes equation:

∂_{t}v_{i} + v_{j}∂_{j}v_{i} = −∂_{i}p + ν∂_{j}∂_{j}v_{i}

43. Kolmogorov Law:

E(k) ∼ ε^{2/3}k^{−5/3}

47. The entropy formula:

S = − ∑_{i} p_{i} log p_{i}

49. Bott Periodicity:

π_{i}(U) = π_{i+2}(U)
π_{i}(O) = π_{i+8}(O)
ℤ_{2}, ℤ_{2}, 0, ℤ, 0, 0, 0, ℤ

50. Ricci flow:

\frac{∂g_{t}}{∂t} = −2Ric(g_{t})

51. Apollonian fractal:

53? Pascal’s triangle, Fibonacci numbers:

55. Aharonov-Bohm Effect:

∫_{C_{2}} A⃗ · dℓ⃗ − ∫_{C_{1}} A⃗ · dℓ⃗ = \frac{1}{2π} Φ

[insert figure]

56. Group law on cubic:

a + b + c = 0

57? Riemann-Roch-Hirzebruch:

∑_{k=0}^{n}(−1)^{k}dim H^{k}(X, E) = ∫_{X} ch E ∪ T odd(X)

58. Platonic solids, Euler characteristic:

V − E + F = 2

61? Mandelbrot Set:

63. Eratosthenes’ measurement of radius of Earth: 64? Prime number Theorem:

π(x) ∼ \frac{x}{ln x}

65. Supergravity:

ℒ = R − ψ̄_{μ}γ^{μρσ}D_{ρ}ψ_{σ}

66. Fourier transform:

f̂(ξ) = ∫ f(x)e^{2πix·ξ}dx f(x) = ∫ f̂(ξ)e^{−2πix·ξ}dξ 67. Euler’s summation for ζ(2):

1 + \frac{1}{4} + \frac{1}{9} + ⋯ = \frac{π^{2}}{6}

68. Kepler’s laws:

70. dd

∂ ∘ ∂ = 0

[insert graphic? exploded tetrahedron?]

71. Poincaré

π_{1}M^{3} = 0 ⇒ M^{3} ≈ S^{3}

72. Fermat

x^{n} + y^{n} ≠ z^{n}