SCHWARTZ, LAURENT

born March 5, 1915, Paris, France French mathematician who was awarded the Fields Medal in 1950 for his work in functional analysis. Schwartz received his early education at the cole Normale Suprieure and the Faculty of Science, Paris. He received his doctorate in mathematical sciences in Paris, after which he became a professor at the University of Nancy (194552). He joined the Faculty of Science (195383) and also served as professor of analysis at the cole Polytechnique, Palaiseau (195960, 196383). Schwartz was awarded the Fields Medal at the International Congress of Mathematicians in Cambridge, Mass., U.S., in 1950. Prior to the work of Schwartz, physicists concerned with mass distributions used something called the Dirac delta function, which had the following property: the function is 0 when x 0, is + for x = 0, and has integral equal to 1 over any interval containing 0. It was a useful but limited tool and, from a rigorously mathematical point of view, not a function. In a classic paper, Schwartz introduced a more mathematically satisfactory generalized function, which later found application in partial differential equations, potential theory, and spectral theory. Schwartz's publications include tude des sommes d'exponentielles relles (1943; Real Exponential Series), Thorie des distributions (195051; Theory of Distributions), Mthodes mathmatiques de la physique (1956; Mathematical Methods in Physics), Application des distributions l'tude de particules lmentaires en mcanique quantique rlativiste (1969; Applications of Distributions to the Theory of Elementary Particles in Quantum Mechanics), Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures (1973), Les Tenseurs (1975; Tensors), Analyse Hilbertienne (1979; Analysis on Hilbert Spaces), Semi-martingales sur des varits et martingales conformes sur des varits analytiques complexes (1980; Semi-Martingales and Martingales on Analytic Complex), and Pour sauver l'universit (1983; How to Save the University).