Paywalling the laws of the universe.

The Authorea Team

Pythagoras’ Theorem \(a^{2}+b^{2}=c^{2}\) Pythagoras, 530 BC Clay tablet
Logarithms \(\log{xy}=\log{x}+log{y}\) John Napier, 1610 Book
Calculus \(\frac{\mathrm{d}f}{\mathrm{d}t}=\lim_{h\to 0}\frac{f(t~{}+~{}h)~{}-~{}f(t)}{h}\) Newton, 1668 Book
Law of Gravity \(F=G\frac{m_{1}m_{2}}{r^{2}}\) Newton, 1687 Book
The Square Root of Minus One \(\mathrm{i}^{2}=-1\) Euler, 1750 Open
Euler’s Formula for Polyhedra \(V-E+F=2\) Euler, 1751 Open
Normal Distribution \(\psi(x)=\frac{1}{\sqrt{2\pi\rho}}e^{\frac{(x~{}-~{}\mu)^{2}}{2~{}\rho^{2}}}\) C. F. Gauss, 1810 Open
Wave Equation \(\frac{\partial^{2}u}{\partial t^{2}}=c^{2}\frac{\partial^{2}u}{\partial x^{2}}\) J. D‘Ambert, 1746
Fourier Transform \(f(\omega)=\int_{-\infty}^{\infty}f(x)e^{-2~{}\pi~{}\mathrm{i}~{}x~{}\omega}\mathrm{d}x\) J. Fourier, 1822 Book
Navier-Stokes Equation \(\rho\left(\frac{\partial\mathbf{v}}{\partial t}+\mathbf{v}\cdot\nabla\mathbf{v}\right)=-\nabla p+\nabla\cdot T+f\) C. Navier, G. Stokes, 1845
Maxwell’s Equations \(\nabla\cdot E=0\) J. C. Maxwell, 1865 Open
\(\nabla\times E=-\frac{1}{e}\frac{\partial H}{\partial t}\)
\(\nabla\cdot H=0\)
\(\nabla\times H=\frac{1}{e}\frac{\partial E}{\partial t}\)
Second Law of Thermodynamics \(\mathrm{d}S\geq 0\) L. Boltzmann, 1874 PAYWALL
Relativity \(E=mc^{2}\) Einstein, 1905 PAYWALL
Schrödinger’s Equation \(\mathrm{i}\hbar\frac{\partial}{\partial t}\psi=H\psi\) E. Schrödinger, 1927 PAYWALL
Information Theory \(H=-\sum p(x)\log{p(x)}\) C. Shannon, 1949 PAYWALL
Chaos Theory \(x_{t+1}=k~{}x_{t}(1-x_{t})\) Robert May, 1975 PAYWALL
Black-Scholes Equation \(\frac{1}{2}\sigma^{2}S^{2}\frac{\partial^{2}V}{\partial S^{2}}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0\) F. Black, M. Scholes, 1990 PAYWALL
Euler’s Transformation \(\sum_{n=0}^{\infty}(-1)^{n}a_{n}=\sum_{n=0}^{\infty}(-1)^{n}\frac{\Delta^{n}a_{0}}{2^{n+1}}\) Euler, 1755 PAYWALL
Russell’s Paradox Let \(R=\{x\mid x\not\in x\}\), then \(R\in R\iff R\not\in R\) Russell, 1902 Letter
Gödel’s Incompleteness Theorem \(G(x):=\neg\text{Prov}(\text{sub}(x,x))\Rightarrow\text{PA}\vdash G(\ulcorner G\urcorner)\leftrightarrow\neg\text{Prov}(\ulcorner G(\ulcorner G\urcorner)\urcorner)\) Gödel, 1931 Open