Laurent Schwartz

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Laurent Schwartz
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{{distinguish|Hermann Schwarz}}{{About|the mathematician|French oncologist|Laurent Schwartz (oncologist)}}

| birth_place = Paris, France20020403df=y}}| death_place = Paris, France| nationality = French| fields = Mathematics| workplaces = University of StrasbourgUniversity of NancyUniversity of GrenobleÃ‰cole PolytechniqueUniversitÃ© de Paris VII| alma_mater = Ã‰cole Normale SupÃ©rieure| doctoral_advisor = Georges Valiron| doctoral_students = Maurice AudinGeorges GlaeserAlexander GrothendieckJacques-Louis LionsBernard MalgrangeAndrÃ© MartineauBernard MaureyLeopoldo NachbinHenri Hogbe NlendGilles PisierFranÃ§ois TrevesDistribution (mathematics)>Theory of DistributionsSchwartz kernel theoremSchwartz spaceSchwartzâ€“Bruhat functionRadonifying operatorCylinder set measure| influenced = Per Enflo| awards = Fields Medal (1950)}}Laurent-MoÃ¯se Schwartz ({{IPA-fr|ÊƒvaÊts|lang}}; 5 March 1915 â€“ 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the Ã‰cole polytechnique.



Laurent Schwartz came from a Jewish family of Alsatian origin, with a strong scientific background: his father was a well-known surgeon, his uncle Robert DebrÃ© (who contributed to the creation of UNICEF) was a famous pediatrician, and his great-uncle-in-law, Jacques Hadamard, was a famous mathematician.During his training at LycÃ©e Louis-le-Grand to enter the Ã‰cole Normale SupÃ©rieure, he fell in love with Marie-HÃ©lÃ¨ne LÃ©vy, daughter of the probabilist Paul LÃ©vy who was then teaching at the Ã‰cole polytechnique. Later they would have two children, Marc-AndrÃ© and Claudine. Marie-HÃ©lÃ¨ne was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at the University of Lille.Angelo Guerraggio describes "Mathematics, politics and butterflies" as his "three great loves".A Guerraggio, Laurent Schwartz: political commitment and mathematical rigour, in Mathematical lives (Springer, Berlin, 2011), 157-164.


According to his teachers, Schwartz was an exceptional student. He was particularly gifted in Latin, Greek and mathematics. One of his teachers told his parents: "Beware, some will say your son has a gift for languages, but he is only interested in the scientific and mathematical aspect of languages: he should become a mathematician."In 1934, he was admitted at the Ã‰cole Normale SupÃ©rieure, and in 1937 he obtained the agrÃ©gation (with rank 2).

World War II

As a man of Trotskyist affinities and Jewish descent, life was difficult for Schwartz during World War II. He had to hide and change his identity to avoid being deported after Nazi Germany overran France. He worked for the University of Strasbourg (which had been relocated in Clermont-Ferrand because of the war) under the name of Laurent-Marie SÃ©limartin, while Marie-HÃ©lÃ¨ne used the name LengÃ© instead of LÃ©vy. Unlike other mathematicians at Clermont-Ferrand such as Feldbau, the couple managed to escape the Nazis.

Later career

Schwartz taught mainly at Ã‰cole Polytechnique, from 1958 to 1980. At the end of the war, he spent one year in Grenoble (1944), then in 1945 joined the University of Nancy on the advice of Jean Delsarte and Jean DieudonnÃ©, where he spent seven years. He was both an influential researcher and teacher, with students such as Bernard Malgrange, Jacques-Louis Lions, FranÃ§ois Bruhat and Alexander Grothendieck. He joined the science faculty of the University of Paris in 1952. In 1958 he became a teacher at the Ã‰cole polytechnique after having at first refused this position. From 1961 to 1963 the Ã‰cole polytechnique suspended his right to teach, because of his having signed the Manifesto of the 121 about the Algerian war, a gesture not appreciated by Polytechnique's military administration. However, Schwartz had a lasting influence on mathematics at the Ã‰cole polytechnique, having reorganized both teaching and research there.In 1973 he was elected corresponding member of the French Academy of Sciences, and was promoted to full membership in 1975.

Mathematical legacy

In 1950 at the ICM, Schwartz was a plenary speakerBOOK, Schwartz, Laurent, ThÃ©orie des noyaux, In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30â€“September 6, 1950, vol. 1, 220â€“230, 1950,weblink and was awarded the Fields medal for his work on distributions. He was the first French mathematician to receive the Fields medal. Because of his sympathy for Trotskyism, Schwartz encountered serious problems trying to enter the United States to receive the medal; however, he was ultimately successful.The theory of distributions clarifies the (then) mysteries of the Dirac delta function and Heaviside step function. It helps to extend the theory of Fourier transform and is now of capital importance to the theory of partial differential equations.

Popular science

Throughout his life, Laurent Schwartz actively worked to promote science and bring it closer to the general audience. Laurent says : What are mathematics helpful for ? Mathematics are helpful for physics. Physics helps us make fridges. Fridges are made to contain spiny lobsters, and spiny lobsters help mathematicians who eat them and have hence better abilities to do mathematics, which are helpful for physics, which helps us make fridges which..."Site de D. Michel-Amadry" {{webarchive|url= |date=2012-07-12 }}File:Clanis schwartzi Paratype MHNT both sides.jpg|thumb|Clanis schwartzi Paratype MHNTMHNT


His mother, who was passionate about natural science passed on her taste for entomology to Laurent. His personal collection of 20, 000 Lepidoptera specimens, collected during his various travels was bequeathed to theMusÃ©um national d'histoire naturelle), the Science Museum of Lyon, the Museum of Toulouse and the Museo de Historia Natural Alcide dâ€™Orbigny in Cochabamba (Bolivia). Several species discovered by Laurent Schwartz bear his name.

Personal ideology

Apart from his scientific work, Schwartz was a well-known outspoken intellectual. As a young socialist influenced by Leon Trotsky, Schwartz opposed the totalitarianism of the Soviet Union, particularly under Joseph Stalin. Schwartz ultimately rejected Trotskyism for democratic socialism.On his religious views, Schwartz called himself an atheist.BOOK, A Mathematician Grappling With His Century, 2001, Springer, 9783764360528, Laurent Schwartz, 193, My parents were atheists, I was an atheist, I never really felt Jewish.,


  • Ã‰tude des sommes d'exponentielles rÃ©elles. Hermann, 1943,JOURNAL, SzÃ¡sz, Otto, Otto SzÃ¡sz, Review Ã‰tude des sommes d'exponentielles rÃ©elles, by L. Schwartz, Bull. Amer. Math. Soc., 1946, 52, 11, Part 1, 976,weblink 10.1090/s0002-9904-1946-08674-7, new edn. 1959
  • ThÃ©orie des distributions. Hermann, 2 vols., 1950/1951,JOURNAL, Bochner, S., Salomon Bochner, Review: ThÃ©orie des distributions, by L. Schwartz, Bull. Amer. Math. Soc., 1952, 58, 1, 78â€“85,weblink 10.1090/s0002-9904-1952-09555-0, new edn. 1966
  • SÃ©minaire Schwartz in Paris 1953 bis 1961. Online edition: weblink" title="https:/-/">weblink
  • Mathematics for the physical sciences. Hermann, 1966
  • Analyse mathÃ©matique. 2 vols., Hermann, 1967
  • Tenseurs. Hermann, 1975
  • Analyse hilbertienne. Hermann, 1979
  • Semi-martingales sur des variÃ©tÃ©s et martingales conformes sur des variÃ©tÃ©s analytiques complexes. Springer, 1980
  • Geometry and probability in Banach Spaces. Springer, 1981
  • Cours d' Analyse. Hermann, 1981
  • Pour sauver lâ€™universitÃ©. Editions du Seuil, 1983
  • Semi-martingales and their stochastic calculus on manifolds. Presse de lÂ´Universitaire de Montreal, 1984
  • Un mathÃ©maticien aux prises avec le siÃ¨cle. Paris 1997, Autobiography, English translation: A mathematician grappling with his century. BirkhÃ¤user, 2001, {{isbn|3-7643-6052-6}}
  • Analyse. Hermann, 1998

See also




  • Schwartz, Laurent (2001). "A Mathematician Grappling with His Century." Birkhauser. {{isbn|3-7643-6052-6}}. (An English translation of Laurent Schwartz's autobiography, "Un mathÃ©maticien aux prises avec le siÃ¨cle," originally published in 1997.)

External links

{{Sister project links| wikt=no | commons=Category:Laurent Schwartz | b=no | n=no | q=Laurent Schwartz | s=no | v=no | voy=no | species=no | d=no}} {{Fields medalists}}{{Authority control}}

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