HADAMARD, JACQUES-SALOMON

born Dec. 8, 1865, Versailles, Fr. died Oct. 17, 1963, Paris French mathematician who proved the prime-number theorem, which states that as n approaches infinity, the limit of the ratio of p(n) and n/ln n is 1, where p(n) is the number of positive prime numbers not greater than n. He served as a professor at the Collge de France (18971935), the cole Polytechnique (191235), and the cole Centrales des Arts et Manufactures (192035), all in Paris. Hadamard's early work contained many important contributions to the theory of functions of a complex variable, in particular to the general theory of integral functions and to the theory of the singularities of functions represented by Taylor's series. In 1896 Hadamard proved the prime-number theorem, independently of the Belgian mathematician Charles Jean de la Valle Poussin. He also obtained important results in connection with the partial differential equations of mathematical physics. Hadamard's Leons sur le calcul des variations (1910; Lessons on the Calculus of Variations) helped to lay the foundations of the modern theory of functional analysis, in connection with which he introduced the term functional. Part of his work in determinants is important in the theory of integral equations.