The 20 Most Important Mathematical Equations
A journey through the most elegant and influential formulas in mathematics
1. Euler's Identity

$e^{i\pi} + 1 = 0$

Connects five fundamental constants (e, i, π, 1, 0), revealing the
profound relationship between exponential functions and
trigonometry.
3. The Fundamental Theorem of Calculus

$\int_a^b f(x)dx = F(b) – F(a)$

Establishes that differentiation and integration are inverse
operations. If F is an antiderivative of f, the definite integral
equals F(b) - F(a). Revolutionized mathematical problem-solving.
2. Pythagorean Theorem

$a^2 + b^2 = c^2$

In right triangles, the hypotenuse squared equals the sum of the
squares of the other sides. Cornerstone of geometry with
applications in navigation and architecture.
4. Maxwell's Equations

$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$

$\nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$

$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$

Unified electricity and magnetism as manifestations of the same
force. Describes electromagnetic field behavior, predicting waves
traveling at light speed. Enabled technologies from radio to
smartphones.
