Andrew Wiles

Fermat's Last Theorem

Wiles proved Fermat’s Last Theorem by establishing the modularity theorem for semistable elliptic curves — a result that, combined with Ribet’s theorem, ruled out integer solutions to a^n + b^n = c^n for n > 2. His initial 1993 proof contained a flaw in the Selmer group argument; he and Taylor repaired it in 1994 using Galois representations and Iwasawa theory. The complete proof appeared in the Annals of Mathematics in 1995.