His method of finding the biggest and smallest ordinates of curved lines also makes him a contributor to differential calculus, which was not known at that time. His studies in the theory of numbers give him the rank of the founder of the modern theory. He also made notable contributions to analytic geometry, probability and optics.
He is also famous for making a simple mathematical statement (known as Fermat's Last Theorem) that he said he could prove, but he never wrote down his proof. Mathematicians tried to prove it for hundreds of years before finally managing it. Fermat probably did not really have a proof for this theorem, and only thought he did.
He proposed his principle on light which states that light selects the path which takes least time to travel.This principle was famous as Fermat principle.