French mathematician who founded number theory; contributed (with Pascal) to the theory of probability; author of Fermat's theorem (1601-1665).
(1601-1665) French mathematician who, with Blaise Pascal, founded the theory of probability and the modern theory of numbers. Fermat also made contributions to analytical geometry. In 1657, Fermat published a series of problems as challenges to other mathematicians, in the form of theorems to be proved.
Fermat’s last theorem states that equations of the form xn + yn = zn where x, y, z, and n are all integers have no solutions if n > 2. Fermat scribbled the theorem in the margin of a mathematics textbook and noted that he could have shown it to be true had he enough space in which to write the proof. The theorem remained unproven for 300 years (and therefore, strictly speaking, constituted a conjecture rather than a theorem). In 1993, Andrew Wiles of Princeton University, US, announced a proof; this turned out to be premature, but he put forward a revised proof 1994.
Fermat was born near Montauban and graduated in law from the University of Orléans. He became a magistrate in Toulouse, rising to the rank of King's Counselor for the local parliament 1648–65. He refused to publish any of his achievements in mathematics, which are known only from his letters.
Fermat’s technique in much of his work was “reduction analysis”, a reversible process in which a particular problem is “reduced” until it can be seen to be part of a group of problems for which solutions are already known. Analytical geometry was developed simultaneously both by Fermat (in letters written before 1636) and by René Descartes (who published his Géométrie 1637). There followed a protracted and bitter dispute over priority.
Fermat also derived what is now known as Fermat’s principle, which states that light travels by the path of least duration.