Fermat, Pierre de (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, the English mathematician of Princeton University, USA, announced a proof; this turned out to be premature, but he put forward a revised proof in 1994. Fermat's last theorem was finally laid to rest in June 1997 when Wiles collected the Wolfskehl prize (the legacy bequeathed in the 19th century for the problem's solution).

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 Counsellor 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 in 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.