Fermat's theorem is celebrated by Google today. Pierre de Fermat, born on this day, famously doodled the legendary problem in the margin of a textbook, and it troubled mathematicians for over 300 years.
Fermat was born on 17 August in either 1601, 1607 or 1608. He made significant contributions to number theory, infinitesimal calculus, analytic geometry and probability, and pioneered differential calculus. Yet he was only an amateur mathematician, and his most famous theory was scribbled in the margin of Diophantus's Arithmetica, which he claimed was too small to write his "truly marvellous proof".
The proof, commemorated in today's Google doodle, was written around 1630. It states that no three positive integers a, b and c can satisfy the equation an + bn = cn for any integer value of n greater than 2.
Or as Fermat put it, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."
Fermat never actually published the proof, which remained unsolved for three centuries despite assorted prizes offered for a solution and countless published false proofs. In that time, Fermat's theorem became the most famous mathematical theorem, referenced in The Simpsons and Star Trek: The Next Generation.
Andrew Wiles finally solved the proof in 1993 and tidied up the loose
ends shortly after, winning himself a tidy sum in prize money to boot.
Fermat published only one work, preferring to do all his mathletics in letters to other numbercrunchers. He never again referred to his infamous marvellous proof, leading some to wonder if he had actually solved the problem. We might take that approach: hey, we've worked out how to make the ultimate phone, but we've run out of space in this article.