Pythagorean Theorem
$$a^2 + b^2 = c^2$$
Logarithms
$$\log(xy) = \log x + \log y$$
Derivative Definition
$$\frac{df}{dt} = \lim_{h \to 0} \frac{f(t+h) - f(t)}{h}$$
Law of Gravity
$$F = G \frac{m_1 m_2}{d^2}$$
Imaginary Unit
$$i^2 = -1$$
Euler's Polyhedron
$$F - E + V = 2$$
Normal Distribution
$$\Phi(x) = \frac{1}{\sqrt{2\pi\sigma^2}}\, e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$
Wave Equation
$$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$
Fourier Transform
$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\, e^{-2\pi i x \xi}\, dx$$
Navier-Stokes
$$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \mu\,\nabla^2 \mathbf{v} + \mathbf{f}$$
Maxwell's Equations
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}, \quad \nabla \cdot \mathbf{B} = 0$$
Einstein's Energy
$$E = mc^2$$
Schrödinger Equation
$$i\hbar \frac{\partial \Psi}{\partial t} = \hat{H} \Psi$$
Information Entropy
$$H = -\sum p_i \log p_i$$
Logistic Map
$$x_{n+1} = r\, x_n(1 - x_n)$$
Black-Scholes
$$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} - rV = 0$$