1
$\begingroup$

It's usually believed that Fermat's claim that he had a proof for the Last Theorem is false, and that it might have been more of a conjecture. Or considering it took many centuries and advanced mathematics to prove it, Fermat may have been mistaken in thinking he did have a proof.

But how did he come up with that theorem in the first place?

$\endgroup$
6
  • 2
    $\begingroup$ What is known is described in Wikipedia. The original motivation came from trying to generalize Pythagorean triples in Diophantus. A common speculation is that he originally thought that his method of infinite descent that worked for $n=4$ would work for all $n$, but later realized his mistake. He never stated the general case after the famous original note on the margins. $\endgroup$
    – Conifold
    Sep 4 at 23:08
  • 1
    $\begingroup$ As @Conifold said: Fermat never mentioned his claim to the public, so it is to be assumed he quickly realized that his reputed proof was faulty. $\endgroup$ Sep 4 at 23:39
  • $\begingroup$ He was evidently thinking about $x^2+y^2=z^2$ which he saw in the book of Diophantus. $\endgroup$ Sep 4 at 23:39
  • $\begingroup$ It cannot be true that "It's usually believed that Fermat's claim that he had a proof for the Last Theorem is false" since the theorem is provably false. $\endgroup$ Sep 5 at 21:38
  • 3
    $\begingroup$ @JeremyBoden To the best of our current knowledge, FLT has been proved (true) and has never been proved false. $\endgroup$
    – Gae. S.
    Sep 6 at 17:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.