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An Introduction to Fermats Last Theorem Fermat claimed to have found a proof of the theorem at an early stage in his career. Much later he spent time and effort proving the cases n=4 and n=5. Had he had a proof to his theorem earlier, there would have been no need for him to study specific cases. It is likely that he found a mistake in his own "proof" before he had a chance to …

… Both manuscripts written by Wiles have been published. Thousands of people have a read them. About a hundred understand it very well. Faltings has simplified the argument already, so that ordinary people can read it. The immensely complicated geometry has mostly been replaced by simpler algebra. There was a gap in this second proof as well, but it has been filled since October 1994, and is now generally accepted as an outright proof.