Today, I stumbled upon an article highlighting the world’s most transformative equations. It was a bit like a trip down memory lane, but instead of nostalgia, it felt like trying to decipher hieroglyphics. Remembering some of these equations from school gave me a headache and made me question all my life choices. Thought I’d share the joy (and the pain :)
1.Pythagoras’s Theorem: $$a^2 + b^2 = c^2$$
2.Logarithms: $$\log xy = \log x + \log y$$
3.Calculus: $$\frac{df}{dt} = \lim_{h \to 0} \frac{f(t+h) - f(t)}{h}$$
4.Law of Gravity: $$F = G\frac{m_1 m_2}{r^2}$$
5.The Square Root of Minus One: $$i^2 = -1$$
6.Euler’s Formula for Polyhedra: $$V - E + F = 2$$
7.Normal Distribution: $$\Phi(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{\frac{-(x-\mu)^2}{2\sigma^2}}$$
8.Wave Equation: $$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$
9.Fourier Transform: $$f(\omega) = \int_{-\infty}^{\infty} f(x)e^{-2\pi i \omega x}dx$$
10.Navier-Stokes Equation: $$\rho \left( \frac{\partial v}{\partial t} + v \cdot \nabla v \right) = - \nabla p + \nabla \cdot \mathbf{T} + f$$
11.Maxwell’s Equations: $$\nabla \cdot \mathbf{E} = 0$$ $$\nabla \cdot \mathbf{H} = 0$$ $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{H}}{\partial t}$$ $$\nabla \times \mathbf{H} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}$$
12.Second Law of Thermodynamics: $$dS \geq 0$$
13.Relativity: $$E = mc^2$$
14.Schrödinger’s Equation: $$i\hbar \frac{\partial \psi}{\partial t} = H \psi$$
15.Information Theory: $$H = - \sum p(x) \log p(x)$$
16.Chaos Theory: $$x_{t+1} = k x_t (1 - x_t)$$
17.Black-Scholes Equation: $$\frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r S \frac{\partial V}{\partial S} + \frac{\partial V}{\partial t} - r V = 0$$