POINCARE, JULES HENRI ( ,1_54-1912), French mathe matician, was born at Nancy, on April 29, 1854. He studied at the Ecole Polytechnique, devoting himself to scientific mining, and took his degree in 1879. He was lecturer at Caen and then was transferred to the University of Paris in 1881, lecturing first on physical mechanics, then on mathematical physics, and ulti mately on astronomical mechanics.
Poincare's work falls into three main divisions : his work in pure mathematics, in astronomy and in physics. Most important is his work in pure analytical mathematics ; he took the main points of an existing theory, simplified it and then developed it beyond all recognition. In this way he opened up new fields for the mathematician and gave new material to the mathematical physicist. In pure analytical mathematics a good deal of his work is on the theory of functions. He developed automorphic functions and his work on the "Fuchsian" functions he applied to the non-Euclidean geometry of Lobatchevski ; he also wrote a number of papers on Abelian functions. Poincare's work on
differential equations is also important ; here he extended the work of Cauchy; he dealt with linear differential equations on the lines of Riemann and Fuchs and he wrote a number of papers on the differential equations which occur in physics. In astronomy he dealt chiefly with the theory of orbits; he began with an idea due to Hill and investigated the general problem of three bodies. In addition to his purely mathematical and scientific work he also wrote on philosophy. He died in Paris on July 17, 1912.
His works include Cours de physique mathematique, io vol. (1889, etc.) ; Lecons de la mecanique celeste (1905, etc.); Theorie de Maxwell et les oscillations hertziennes (1907); La theorie du patentiel newtonien (1899) ; Science d'hypothese (1903) ; La valeur de la science (1904); Science et methode (1908).