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.
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.
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.
4. Maxwell's Equations

$\nabla \cdot E = \frac{ρ}{ε_0}$

$\nabla \cdot B = 0$

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

$\nabla \times B = μ_0J + μ_0ε_0 \frac{\partial E}{\partial t}$

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.
