The story as told by math popularizer Simon Singh in a Numberphile video goes as follows: There’s this 17th century French mathematician, Pierre de Fermat, sitting in his private library reading a book. He excitedly records in the margin a new discovery he’s made — the assertion we now call Fermat’s Last Theorem, or FLT for short — but he writes that the margin is too small to contain his proof, and then, before he can communicate the details to anyone, “he drops dead.”

Pierre de Fermat.

I have two problems with this version of the FLT story, and the way it shows a character’s death preventing the revelation of a vital secret. First, we’ve all “seen that movie” many, many times (see the TV Tropes entry on the His Name Is … trope, as well as the related tropes Conveniently Interrupted Document and Lost in Transmission); it’s kind of hokey, isn’t it? Second, there’s no evidence that Fermat wrote the passage right before he died. We can’t go back and date the ink he used (or breathalyze the page for alcohol content, for that matter), as the book was lost after his annotations were transcribed, but we know from Fermat’s correspondence that he read the book fairly early in his career, in the 1630s. Most scholars agree that this particular remark was written two decades before he died. So Singh is putting an over-dramatic spin on things at the 02:15 mark. Still, he is right about Fermat dying without revealing a proof of his claim to anyone.

Andrew Wiles.

Thanks to modern-day mathematician Andrew Wiles, who this month receives the prestigious Abel Prize for his work on Fermat’s Last Theorem, we know that Fermat’s claim was correct. But did Fermat have a proof? That’s the question I want to explore today. And while we’re discussing the most famous proof Fermat never revealed, I’ll tell you about the proof method that Fermat did reveal — one that beautifully solves other problems of the same kind.

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