The one theorem Fermat actually bothered to prove
Pierre de Fermat claimed dozens of theorems in the margins of his books without ever writing down a proof, leaving mathematicians centuries of homework. But for one claim -- that no right triangle with whole-number sides can have an area that's a perfect square -- did he ever actually show his work?
Reveal the answer
Yes -- this is one of the only proofs of Fermat's that survives in his own hand, using a method he called 'infinite descent': assuming a smallest solution exists, then constructing an even smaller one from it, a contradiction. It's a special case of a much broader claim that would later become Fermat's Last Theorem.
— Pierre de Fermat, Observations on Diophantus — marginal notes, c. 1637