Today is the birthday of Pierre de Fermat, and there’s a Google Doodle to celebrate! Today’s Doodle is a chalkboard showing Fermat’s Last Theorem, famously scribbled in the margins of Arithmetica, with a note that the proof of the theorem didn’t fit there — see the mouseover on the actual Doodle for a reference to this.
The theorem stated that there are no three positive, different integers a, b, and c such that an + bn = cn is true for any integer n greater than 2.
Fermat’s claim left mathematicians puzzled for over 350 years — as mathematicians proved it true for many sets of possible values of n — until the general case was finally proved by Andrew Wiles in 1995. The story about the proof is told in Simon Singh’s book Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem.
Did Fermat really have a proof? Most likely not, since the techniques Wiles used to prove it weren’t developed until several centuries after Fermat’s death — and since, in the 30 years he lived after writing the note, he never wrote about the general case of the proof again — but nobody will ever know for sure. I’ll leave that, as they say, as an exercise for the reader.
[Note: There is some dispute, apparently, over whether Fermat was actually born in 1601, as most prevailing biographies seem to say. His birth year has been reported anywhere from 1590 to 1608 in various sources.]