Fermat’s Last Theorem – The Taniyama–Shimura Conjecture

Andrew Wiles proved Fermat’s Last Theorem in 1994 by proving a special case of the Taniyama–Shimura conjecture: every elliptic curve is modular. Elliptic curves are cubic equations y² = x³ + ax + b; modular forms are highly symmetric complex functions. The connection seemed impossible until Wiles built a bridge over 200 pages. He announced it in 1993, but a flaw appeared; with Richard Taylor, he fixed it in 1994. The proof unites number theory, algebraic geometry, and complex analysis.