The most beautiful equation in mathematics. "[It] is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth"

Euler’s identity is the equation links five fundamental mathematical constants: e, i, π, 1, and 0. It follows from Euler’s formula, e^ix = cos(x) + i sin(x), by setting x equal to π. The result shows that exponential functions, complex numbers, and trigonometry are deeply connected rather than separate ideas. Its compact form is famous for combining addition, multiplication, exponentiation, and equality in a single expression. Mathematicians often admire it for its elegance and unexpected unity. It is used in complex analysis, quantum mechanics, and calculations involving waves and rotations.