Laurent Schwartz
Laurent Schwartz  

Born 
Paris, France 
5 March 1915
Died  4 July 2002 Paris, France 
(aged 87)
Nationality  French 
Alma mater  École Normale Supérieure 
Known for 
Theory of Distributions Schwartz kernel theorem Schwartz space Schwartz–Bruhat function Radonifying operator Cylinder set measure 
Awards  Fields Medal (1950) 
Scientific career  
Fields  Mathematics 
Institutions 
University of Strasbourg University of Nancy University of Grenoble École Polytechnique Université de Paris VII 
Doctoral advisor  Georges Valiron 
Doctoral students 
Maurice Audin Georges Glaeser Alexander Grothendieck JacquesLouis Lions Bernard Malgrange André Martineau Bernard Maurey Leopoldo Nachbin Henri Hogbe Nlend Gilles Pisier François Treves 
Influenced  Per Enflo 
LaurentMoïse Schwartz (French: [ʃvaʁts]; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a welldefined 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 École polytechnique.
Contents
Biography
Family
Laurent Schwartz came from a Jewish family of Alsatian origin, with a strong scientific background: his father was a wellknown surgeon, his uncle Robert Debré (who contributed to the creation of UNICEF) was a famous pediatrician, and his greatuncleinlaw, Jacques Hadamard, was a famous mathematician.
During his training at Lycée LouisleGrand to enter the École Normale Supérieure, he fell in love with MarieHélène Lévy, daughter of the probabilist Paul Lévy who was then teaching at the École polytechnique. Later they would have two children, MarcAndré and Claudine. MarieHélène 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".^{[1]}
Education
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 École Normale Supérieure, and in 1937 he obtained the agrégation (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 ClermontFerrand because of the war) under the name of LaurentMarie Sélimartin, while MarieHélène used the name Lengé instead of Lévy. Unlike other mathematicians at ClermontFerrand such as Feldbau, the couple managed to escape the Nazis.
Later career
Schwartz taught mainly at École 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 Dieudonné, where he spent seven years. He was both an influential researcher and teacher, with students such as Bernard Malgrange, JacquesLouis Lions, François Bruhat and Alexander Grothendieck. He joined the science faculty of the University of Paris in 1952. In 1958 he became a teacher at the École polytechnique after having at first refused this position. From 1961 to 1963 the École 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 École 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 speaker^{[2]} 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...^{[3]}
Entomology
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 the Muséum national d'histoire naturelle), the Science Museum of Lyon, the Museum of Toulouse and the Museo de Historia Natural Alcide d’Orbigny in Cochabamba (Bolivia). Several species discovered by Laurent Schwartz bear his name.
Personal ideology
Apart from his scientific work, Schwartz was a wellknown 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.^{[4]}
Books
 Étude des sommes d'exponentielles réelles. Hermann, 1943,^{[5]} new edn. 1959
 Théorie des distributions. Hermann, 2 vols., 1950/1951,^{[6]} new edn. 1966
 Lectures on complex analytic manifolds. Springer, 1986 (Lectures at the Tata Institute, Bombay 1955)
 Séminaire Schwartz in Paris 1953 bis 1961. Online edition: [1]
 Mathematics for the physical sciences. Hermann, 1966
 Analyse mathématique. 2 vols., Hermann, 1967
 Application of distributions to the theory of elementary particles in quantum mechanics. Gordon and Breach, 1968, 1988
 Radon measures on arbitrary topological spaces and cylindrical measures. Oxford University Press, 1973 (Tata Lectures)
 Tenseurs. Hermann, 1975
 Analyse hilbertienne. Hermann, 1979
 Semimartingales sur des variétés et martingales conformes sur des variétés analytiques complexes. Springer, 1980
 Geometry and probability in Banach Spaces. Springer, 1981
 Cours d' Analyse. Hermann, 1981
 Pour sauver l’université. Editions du Seuil, 1983
 Semimartingales and their stochastic calculus on manifolds. Presse de l´Universitaire de Montreal, 1984
 Un mathématicien aux prises avec le siècle. Paris 1997, Autobiography, English translation: A mathematician grappling with his century. Birkhäuser, 2001, ISBN 3764360526
 Analyse. Hermann, 1998
See also
 Schwartz distribution
 Schwartz kernel theorem
 Schwartz space
 Schwartz–Bruhat function
 Nicolas Bourbaki
Notes
 ^ A Guerraggio, Laurent Schwartz: political commitment and mathematical rigour, in Mathematical lives (Springer, Berlin, 2011), 157164.
 ^ Schwartz, Laurent (1950). "Théorie des noyaux" (PDF). In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30–September 6, 1950. vol. 1. pp. 220–230.
 ^ "Site de D. MichelAmadry" Archived 20120712 at Archive.is

^ Laurent Schwartz (2001). A Mathematician Grappling With His Century. Springer. p. 193. ISBN 9783764360528.
My parents were atheists, I was an atheist, I never really felt Jewish.
 ^ Szász, Otto (1946). "Review Étude des sommes d'exponentielles réelles, by L. Schwartz". Bull. Amer. Math. Soc. 52 (11, Part 1): 976. doi:10.1090/s000299041946086747.
 ^ Bochner, S. (1952). "Review: Théorie des distributions, by L. Schwartz". Bull. Amer. Math. Soc. 58 (1): 78–85. doi:10.1090/s000299041952095550.
References
 Schwartz, Laurent (2001). "A Mathematician Grappling with His Century." Birkhauser. ISBN 3764360526. (An English translation of Laurent Schwartz's autobiography, "Un mathématicien aux prises avec le siècle," originally published in 1997.)
External links
 O'Connor, John J.; Robertson, Edmund F., "Laurent Schwartz", MacTutor History of Mathematics archive, University of St Andrews.
 Biography of Laurent Schwartz from the American Mathematical Society
 Review of Schwartz's autobiography, same source
 S.S. Kutateladze Sobolev and Schwartz: Two Fates and Two Fames
 20thcentury mathematicians
 21stcentury mathematicians
 French mathematicians
 Nicolas Bourbaki
 École Normale Supérieure alumni
 Fields Medalists
 French atheists
 French entomologists
 French Jews
 Alsatian Jews
 Jewish atheists
 People from Paris
 1915 births
 2002 deaths
 University of Grenoble faculty
 University of Paris faculty
 University of Lorraine faculty
 Members of the French Academy of Sciences