I. LARGE FORMULAS

1. Primes and the zeta function:

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

7. Newton’s Law of Gravitation:

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

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

14. Einstein’s General Relativity Equation:

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

16. Heisenberg Uncertainty Principle:

ΔxΔp ≥ ℏ/2

22. Stokes’ Theorem

∫_{M} dω = ∫_{∂M} ω

∫_{M} dω

= ∫_{∂M} ω

26. Classical Gauss-Bonnet Theorem:

χ(M^{2}) = \frac{1}{2π} ∫_{M} K dA

xy. Kepler’s Laws:

r\frac{dθ}{dt} = C

∮ dt ∝ (rmin + rmax)^{\frac{3}{2}}

∮ dt ∝ (\overline{r} + \underline{r})^{\frac{3}{2}}

∮ dt ∝ (\overline{r} + \underline{r})^{3/2}

T = ka^{\frac{2}{3}}

T = ka^{2/3}

xz. Hamilton’s quaternion eq.:

i^{2} = j^{2} = k^{2} = ijk = −1

xw. Conservation of energy-momentum:

T_{, ν}^{μν} = 0

35. Yang-Mills equation

F = dA + A ∧ A

xu. Self-dual

∗F = F

II SMALL FORMULAS IN IMAGE CAPTIONS 8. Pythagoras’ Theorem with no-word proof:

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

xt. knot polynomial

q + q^{3} − q^{4}
V_{K}(q) = q + q^{3} − q^{4}

xs. Babylonian tablet

1; 24; 51; 10 = 1.414213 …

xr. Schwartzschild radius

r_{S} = 2Gm/c^{2}

xx. Equation for Lorenz attractor:

\frac{dx}{dt} = σ(y − x)

\frac{dy}{dt} = x(ρ − z) − y

\frac{dz}{dt} = xy − βz

58. Platonic solids, Euler characteristic: V − E + F = 2

42. Navier-Stokes equation:

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

2. Archimedes. Volume of Sphere:

v = \frac{2}{3}V

19. Limiting ratio of Fibonacci numbers = golden mean = partial fraction expansion:

lim_{n→∞} \frac{F_{n+1}}{F_{n}} = \frac{1 + \sqrt{5}}{2} = 1 + \frac{1}{1 + \frac{1}{1+ \frac{1}{1+...}}}

\frac{1 + \sqrt{5}}{2} = 1 + \frac{1}{1 + \frac{1}{1+ \frac{1}{1+...}}}

55. Aharonov-Bohm Effect:

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

20. Wilson loop average w.r.t Chern-Simons action gives knot invariant:

\frac{1}{Z} ∫_{𝒜} Tr_{2}P exp(− ∮_{K} A) e^{\frac{ik}{4π} CS(A)}𝒟A

\frac{1}{Z} ∫_{𝒜} (Tr_{2}P ∮_{K} A) e^{\frac{ik}{4π} CS(A)}𝒟A

\frac{1}{Z} ∫_{𝒜} (Tr_{2}P ∮_{K} A) e^{\frac{ik}{4π} ∫_{M} Tr(A∧dA+ \frac{2}{3} A∧A∧A)}𝒟A

xq. Volume of frustum of pyramid (from Moscow Papyrus:)

V = \frac{1}{3} · 6(2^{2} + 4^{2} + 2 · 4) = 56

3. Yang-Baxter Equation

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