Laurent Schwartz
1915–2002, Paris, France, Paris, France
French mathematician, Fields Medalist 1950, creator of the theory of distributions that gave rigorous foundations to generalized functions and transformed the analysis of partial differential equations.
Laurent Schwartz was born in Paris into a family of doctors — his uncle was the surgeon Robert Debré — and studied mathematics at the École normale supérieure. During the Second World War, as a Trotskyist and Jew, he lived in hiding under the pseudonym Laurent Sélim Martin. Isolated in the provinces, he developed the ideas that became his theory of distributions: he later recalled formulating the basic definitions in a single night in 1944–45 while at the University of Grenoble.
His two-volume treatise Théorie des distributions (1950–51) gave analysis a new foundation: every continuous function has derivatives of all orders in the distributional sense, the Fourier transform extends to a perfect duality on tempered distributions, and linear differential operators act on a space where they can always be inverted in principle. The theory quickly proved indispensable — it underlies the modern theory of linear partial differential equations of Hörmander and the elementary solutions theorem of Malgrange and Ehrenpreis — and earned Schwartz the Fields Medal at the Harvard congress of 1950; he was initially denied a U.S. visa because of his Trotskyist past.
Schwartz taught at Nancy, then at the Faculty of Sciences in Paris, and spent his last two decades at the École polytechnique. He remained a committed activist — against the Algerian and Vietnam wars, for human rights — into old age, and wrote a memoir, A Mathematician Grappling with His Century. He died in Paris in 2002.
Workplaces: University of Nancy, Faculty of Sciences of Paris, École polytechnique
France