Fermat's Last Theorem

No positive integers satisfy aⁿ + bⁿ = cⁿ for any power n greater than two.

Specifications & Metrics

proved

Andrew Wiles, 1994 (announced 1993, gap closed 1994–95)

Core Principles & Analysis

• Fermat scribbled in a book margin that he had a proof too large to fit — almost certainly mistaken.
• Euler proved n = 3, Fermat himself n = 4; the general case took 358 years.
• Wiles's proof ran 109 pages and built a bridge from elliptic curves to modular forms.