FERMAT, fil•mn', PIERRE nE (1(101-65). A French mathematician, born at Beaumont-de Lomagne, near Montauban. He was one of the moot versatile mathematicians of hit time, and was unsurpassed as a contributor to the theory of numbers. Fermat was educated privately, was of a retiring disposition, and published little dur ing his lifetime. At one time he turned his attention to law, and in 1631 became counselor for the Parliament of Toulouse. The first edition of his works, gathered from his papers, annota tions, and personal letters, was published in two volumes unter the title, Opera hlothcniatica (1670 ;9). Copies of this edition have become quite rare. The first volume contains the Arithmetic of Diophantus annotated, and the second. mono graphs on maxima and minima tangents. and centres of gravity, and copies of his correspon dence with Huygens. Pascal. Descartes, and others. His chief contributions to the theory of numbers are found in his commentaries on Dio phantus. Among them are such well-known propositions as follow: If a is prime to p, p being a prime number, then is divisible by p, or, expressed in the notation of congruences (q.v.), a (mod. p). A prime greater than 2 can be uniquely expressed as the difference of two squares, where p is prime to q, is not divisible by a prime of the form In — 1. If p, g, r, are integers such that q' then pq cannot be a square. The equation
2=y' has a unique solution, and the equation 4 — has two solutions. The equation x° 4-y° =z° has no integral root if n is integral and greater than 2. In the ease of particular curves, Fermat obtained the maximum and mini mum values of their functions; also the sub tangents of the ellipse. cycloid, eonehoid, and quadratrix. The methods employed so resembled those afterwards developed through the differen tial calculus that sonic mathematicians. espe cially Laplace and Lagrange, have suggested Fermat as the inventor of the calculus. The rise of the theory of probability (see PROBABILITY) may be dated practically from the correspondence of Fermat and Pascal (1654). Fermat's an swers to the problems suggested by Pascal re veal his firm grasp on the fundamental princi assistant engineer, on the construction of the Erie Canal in 1817-19; was assistant surveyor in the boundary commission appointed in accordance with the Treaty of Ghent from 1819 to 1822. and was astronomical surveyor of this commission from 1822 to 1527. From 1833 to 1847 he was first assistant in the United States Coast Survey. and from 1847 until his death was assistant as tronomer of the United States Naval Observa tory. He discovered several asteroids, and was a frequent contributor to scientific and other magazines.