Fermat was a Toulouse judge who did world-class mathematics as a hobby
Pierre de Fermat spent his working life as a councillor in a regional high court in Toulouse. In spare hours he found tangents and maxima by a method close to calculus, co-founded probability with Pascal, and scribbled a claim in a book margin that took until 1994 to prove.
Born in 1601 in Beaumont-de-Lomagne in Gascony, son of a rich leather merchant who served as a town consul, Fermat studied civil law at Orléans and started serious mathematics in Bordeaux, influenced by François Viète's new algebra. In 1630 he bought a seat on the Parlement de Toulouse, which entitled him to add 'de' to his name, and he kept the post until he died. He spoke six languages, including Occitan and classical Greek, wrote verse, and was consulted on correcting ancient Greek texts.
His treatise on maxima, minima and tangents was circulating in manuscript by 1636, a year before Descartes published La géométrie. Fermat also became the first person known to integrate general power functions, reducing the task to summing a geometric series, and Newton later said his own early calculus came from Fermat's way of drawing tangents. In optics he generalised an ancient idea into the principle that light takes the quickest route between two points.
In 1654 letters with Blaise Pascal about dividing the stakes of an interrupted game laid the groundwork for probability. Fermat also explained to a gambler why betting on one six in four throws of a die wins over time, while betting on a double six in 24 throws of two dice loses. In number theory he found his little theorem while studying perfect numbers, promoted proof by infinite descent, and worked on sums of squares.
He rarely wrote out proofs, preferring to announce results in letters, and secrecy fuelled quarrels with Descartes and John Wallis. His son found the famous Last Theorem noted in the margin of his father's Diophantus, with a remark that there was no room for the proof; Andrew Wiles proved it with modern methods. Fermat was sometimes simply wrong: he believed every Fermat number was prime, but Euler showed 4,294,967,297 divides by 641. He died at Castres in January 1665.
Source: Pierre de Fermat
