"I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof"

Andrew Wiles is referring to the popular mathematician Pierre de Fermat, who notoriously composed in the margin of a book that he had a proof for a theorem, however never wrote it down. Wiles is suggesting that Fermat may have been misinterpreted in his belief that he had a proof, and rather may have been tricking himself into thinking he had an evidence. This might be since Fermat was so confident in his own mathematical capabilities that he believed he had a proof, but in truth he might not have had one. Wiles' quote indicates that Fermat may have been too confident in his own capabilities, which he may have been mistaken in his belief that he had a proof. This might be due to the fact that Fermat was so sure of himself that he thought he had a proof, however in reality he might not have had one. Wiles' quote is a tip that even the most dazzling of mathematicians can make errors, and that it is essential to be simple and to double-check one's work.