Andrew Wiles Spent Six Years in His Attic Proving Fermat's Last Theorem and Got It Wrong

Pierre de Fermat scribbled a marginal note in his 1637 copy of Diophantus's Arithmetica claiming he had "discovered a truly marvelous proof" that the equation xⁿ + yⁿ = zⁿ had no nontrivial integer solutions for any n greater than 2 — "which this margin is too narrow to contain." He never published the proof. Three and a half centuries of mathematical effort followed without finding one. By 1986, when the British number theorist Andrew Wiles, then at Princeton, became convinced the problem might fall to a recently established connection to elliptic curves, the theorem was the most famous unsolved problem in mathematics.

Wiles told essentially nobody. He cleared his teaching schedule, retreated to his attic study, and worked in secret for six years, releasing other small unrelated papers periodically to keep up appearances. In June 1993 he came out at the Isaac Newton Institute in Cambridge with a three-lecture series whose final blackboard line announced a proof of the modularity theorem for semistable elliptic curves and, as a corollary, of Fermat's Last Theorem. The conference erupted. The mathematical world spent the summer reading the manuscript he submitted to Annals of Mathematics.

The referees found a hole. In one specific argument involving a bound on Selmer groups, the inequality Wiles needed didn't actually go through. Wiles spent the next year trying to plug it. He brought in his former student Richard Taylor to work alongside him. They tried more or less every approach available. On September 19, 1994, Wiles wrote later, he sat at his desk and saw the gap close: a combination of his original Iwasawa-theory approach with the Kolyvagin-Flach machinery would work. The corrected proof was published in May 1995 in two papers, one solo and one with Taylor. Wiles received the 2016 Abel Prize, with €600,000 attached, for an argument that took 358 years to write down.