The Proof of Fermat's Last Theorem
Starting in the summer of 1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, Wiles realised that a proof of a limited form of the modularity theorem might then be in reach. He dedicated all of his research time to this problem in relative secrecy. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August 1993 it turned out that the proof contained a gap. Wiles tried to fill in this gap, but found out that the error he had made was significant. According to Wiles, the crucial idea for circumventing, rather than closing this gap, came to him on 19 September 1994. Together with his former student Richard Taylor, he published a second paper which circumvented the gap and thus completed the proof. Both papers were published in 1995 in a special volume of the Annals of Mathematics.
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