# Fermat, Pierre De

**FERMAT, PIERRE DE** (1601-1665), French mathematician, was born on the 17th of August 1601, at Beaumont-de-Lomagne near Montauban. While
still young, he, along with Blaise Pascal, made some discoveries in regard to the properties of numbers, on which he afterwards built his method of calculating
probabilities. He discovered a simpler method of quadrating parabolas than that of Archimedes, and a method of finding the greatest and the smallest ordinates
of curved lines analogous to that of the then unknown differential calculus. His great work *De maximis et minimis* brought him into conflict with
René Descartes, but the dispute was chiefly due to a want of explicitness in the statement of Fermat (see Infinitesimal Calculus). His brilliant
researches in the theory of numbers entitle him to rank as the founder of the modern theory. They originally took the form of marginal notes in a copy of
Bachet's *Diophantus*, and were published in 1670 by his son Samuel, who incorporated them in a new edition of this Greek writer. Other theorems were
published in his *Opera Varia*, and in John Wallis's *Commercium epistolicum* (1658). He died in the belief that he had found a relation which every
prime number must satisfy, namely 22n + 1 = a prime. This was afterwards disproved by Leonhard Euler for the case when n = 5. *Fermat's Theorem*, if p is
prime and a is prime to p then ap−1 − 1 is divisible by p, was first given in a letter of 1640. *Fermat's Problem* is that xn + yn = zn is
impossible for integral values of x, y and z when n is greater than 2.

Fermat was for some time councillor for the parliament of Toulouse, and in the discharge of the duties of that office he was distinguished both for legal knowledge and for strict integrity of conduct. Though the sciences were the principal objects of his private studies, he was also an accomplished general scholar and an excellent linguist. He died at Toulouse on the 12th of January 1665. He left a son, Samuel de Fermat (1630-1690) who published translations of several Greek authors and wrote certain books on law in addition to editing his father's works.

The *Opera mathematica* of Fermat were published at Toulouse, in 2 vols. folio, 1670 and 1679. The first contains the "Arithmetic of Diophantus," with
notes and additions. The second includes a "Method for the Quadrature of Parabolas," and a treatise "on Maxima and Minima, on Tangents, and on Centres of
Gravity," containing the same solutions of a variety of problems as were afterwards incorporated into the more extensive method of fluxions by Newton and
Leibnitz. In the same volume are treatises on "Geometric Loci, or Spherical Tangencies," and on the "Rectification of Curves," besides a restoration of
"Apollonius's Plane Loci," together with the author's correspondence addressed to Descartes, Pascal, Roberval, Huygens and others. The *OEuvres* of Fermat
have been re-edited by P. Tannery and C. Henry (Paris, 1891-1894).

See Paul Tannery, "Sur la date des principales découvertes de Fermat," in the *Bulletin Darboux* (1883); and "Les Manuscrits de Fermat," in the
*Annales de la faculté des lettres de Bordeaux*.

*Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)*