Fermat, Pierre de (pyĕr də fĕrmä`), 1601–65, French mathematician. A magistrate whose avocation was mathematics, Fermat is known as a founder of modern number theory number theory, branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
..... Click the link for more information. and probability probability, in mathematics, assignment of a number as a measure of the "chance" that a given event will occur. There are certain important restrictions on such a probability measure.
..... Click the link for more information. theory. He also did much to establish coordinate geometry (see Cartesian coordinates Cartesian coordinates (kärtē`zhən)
..... Click the link for more information. ) 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 xⁿ + yⁿ = zⁿ, 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).

Fermat, Pierre de

Fermat, portrait by Roland Lefèvre; in the Narbonne City Museums, France

(credit: Courtesy of the Musees de la Ville de Narbonne, France)

(born Aug. 17, 1601, Beaumont-de-Lomagne, France—died Jan. 12, 1665, Castres) French mathematician. Of Basque origin, Fermat studied law at Toulouse and developed interests in foreign languages, Classical literature, ancient science, and mathematics. A jurist by profession, he produced major mathematical breakthroughs independently and collaboratively. A contemporary of René Descartes, he discovered independently the basic principles of analytic geometry, but, because Fermat's work was published posthumously, the field became known as Cartesian geometry. He found equations for tangent lines to curves through processes equivalent to differentiation and was coauthor (with Blaise Pascal) of probability theory. His work in number theory, especially divisibility, led to some of its most important theorems. He seldom demonstrated his results, which led to a centuries-long quest to prove a famous conjecture that Fermat claimed was easily shown (see Fermat's last theorem).