LEGENDRE, ADRIEN-MARIE

born Sept. 18, 1752, Paris, France died Jan. 10, 1833, Paris French mathematician whose distinguished work on elliptic integrals provided basic analytic tools for mathematical physics. Legendre was professor of mathematics at the cole Militaire, Paris, from 1775 to 1780 and in 1795 became a professor at the cole Normale. Although he was appointed to several minor government positions, he was never offered offices commensurate with his ability because of the jealousy of his colleague Pierre-Simon Laplace, who appropriated some of Legendre's work with scant acknowledgment. One of the problems Legendre studied at an early age was the attraction of spheroids. In the first of his four great memoirs on this subject, published in 1783, he introduced the celebrated function that has been named after him. Legendre's Nouvelles mthodes pour la dtermination des orbites des comtes (1806; New Methods for the Determination of Comet Orbits) contains the first comprehensive treatment of the method of least squares. He also made important contributions to geodesy and was widely known for his lments de gomtrie (1794). In his lments Legendre greatly rearranged and simplified many of the propositions from Euclid's Elements to create a more effective textbook. Legendre's work replaced Euclid's Elements as a textbook in most of Europe and, in succeeding translations, in the United States and became the prototype of later geometry texts. In lments Legendre gave a simple proof that p (pi) is irrational, as well as the first proof that p2 is irrational, and conjectured that p is not the root of any algebraic equation of finite degree with rational coefficients. In 1786 Legendre took up research on elliptic integrals at the point that Leonhard Euler of Germany, John Landen of England, and Joseph-Louis Lagrange of France had left off. In his most important work, Trait des fonctions elliptiques (182537; Treatise on Elliptic Functions), he reduced elliptic integrals to three standard forms now known by his name. Shortly after his work appeared, the independent discoveries of Niels Henrik Abel and Karl Jacobi revolutionized the subject of elliptic integrals completely. Legendre published his own researches in number theory and those of his predecessors in a systematic form under the title Thorie des nombres, 2 vol. (1830). This work included his proof of the law of quadratic reciprocity. Regarded by the greatest mathematician of his day, Carl Friedrich Gauss, as the gem of arithmetic, this law was the most important general result in number theory since the work of Pierre de Fermat in the 17th century.