Pierre de Fermat

Fermat was born in 1607 in Beaumont-de-Lomagne, a small town in southwestern France, the son of a wealthy leather merchant. He studied law at the University of Toulouse and in 1631 bought a seat as a magistrate in the parlement of Toulouse — a post he held for the rest of his life. Mathematics was, for him, a hobby. He never published a book, never held an academic position, and left his results scattered through private correspondence with Mersenne, Pascal, Huygens, and Descartes.

His mathematical range was absurd. With Descartes he independently co-invented analytic geometry — the identification of algebraic equations with curves. With Pascal he founded probability theory, in a correspondence from the summer of 1654 sparked by a gambling problem. He developed a method of 'adequality' that anticipated Newton and Leibniz's calculus by a full generation. And he effectively invented modern number theory single-handedly, proving theorems on prime decomposition and representations of integers. His most famous claim — the margin note in his copy of Diophantus asserting that xⁿ + yⁿ = zⁿ has no nontrivial integer solutions for n > 2 — went unproven for 358 years until Andrew Wiles finished it in 1994.

His contribution to physics is narrow but foundational. In 1662, replying to a challenge from the Cartesian physicist Claude Clerselier, Fermat published a letter stating that light travels between two points along the path that takes the least time. This principle of least time — Fermat's principle — correctly reproduced Snell's law of refraction. It was the first variational principle in physics, and the seed from which Maupertuis, Euler, and Lagrange would grow the principle of least action.