A magistrate whose avocation was mathematics, Fermat is known as a founder of modern number theory and probability theory. He also did much to establish coordinate geometry (see Cartesian coordinates) and invented a number of methods for determining maxima and minima that were later of use to Newton in applying the calculus. He noted without proof, although he claimed to have discovered one, the assertion now known as **Fermat's Last Theorem,**. which states that the equation *x*^{n} + *y*^{n} = *z*^{n}, where *x,* *y,* *z,* and *n* are nonzero integers, has no solutions for *n* that are greater than 2. Prizes were offered for a proof of this theorem, and attempted proofs resulted in many developments in the theory of numbers. British mathematician Andrew Wiles described a proof of the conjecture in 1993, but a gap in the proof required additional work, which was completed in 1994. However, Wiles's proof involved mathematical concepts that were unknown in Fermat's lifetime, so whether Fermat had a valid proof remains conjecture. In optics Fermat recognized that of all possible paths, light takes the path that takes the least time; this fundamental rule is known as Fermat's principle.

**Bibliography:**

See M. S. Mahoney, *The Mathematical Career of Pierre de Fermat 1601–1665* (2d rev. ed. 1994); A. D. Aczel, *Fermat's Last Theorem* (1996); S. Singh and J. Lynch, *Fermat's Enigma* (1998).