Laurent Schwartz | |
|---|---|
 | |
| Born | (1915-03-05)5 March 1915 Paris, France |
| Died | 4 July 2002(2002-07-04) (aged 87) Paris, France |
| 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 Jacques-Louis Lions Bernard Malgrange André Martineau Bernard Maurey Leopoldo Nachbin Henri Hogbe Nlend Gilles Pisier François Treves |
Laurent-Moïse Schwartz (French:[lɔʁɑ̃mɔizʃvaʁts]; 5 March 1915 – 4 July 2002) was a Frenchmathematician who received theFields Medal in 1950 for pioneering the theory ofdistributions or generalized functions, giving a well-defined meaning to objects such as theDirac delta function. For several years he taught at theÉcole polytechnique.
Laurent Schwartz came from aJewish family ofAlsatian origin, with a strong scientific background: his father was a well-knownsurgeon, his uncleRobert Debré (who contributed to the creation ofUNICEF) was a famouspediatrician, and his great-uncle-in-law,Jacques Hadamard, was a famous mathematician.
During his training atLycée Louis-le-Grand to enter theÉcole Normale Supérieure, he fell in love withMarie-Hélène Lévy, daughter of the probabilistPaul Lévy who was then teaching at theÉcole polytechnique. They married in 1938. Later they had two children, Marc-André and Claudine. Marie-Hélène was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at theUniversity of Lille.
Angelo Guerraggio describes "Mathematics, politics and butterflies" as Schwartz's "three great loves".[1]
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 theagrégation (with rank 2).
As a man ofTrotskyist affinities andJewish descent, life was difficult for Schwartz duringWorld War II. He had to hide and change his identity to avoid beingdeported after Nazi Germany overran France. He worked for theUniversity of Strasbourg (which had been relocated toClermont-Ferrand because of the war) under the name of Laurent-Marie Sélimartin (his thesis "Étude des sommes d'exponentielles réelles" being however published in 1943 under his real name in the Publications de l'Institut de Mathématique de l'Université de Clermont-Ferrand, volume 959 of Hermann's Actualités scientifiques et industrielles), while Marie-Hélène used the name Lengé instead of Lévy. Unlike other mathematicians at Clermont-Ferrand such asFeldbau, the couple managed to escape the Nazis.
Schwartz taught mainly atÉcole Polytechnique, from 1958 to 1980. At the end of the war, he spent one year inGrenoble (1944), then in 1945 joined the University ofNancy on the advice ofJean Delsarte andJean Dieudonné, where he spent seven years. He was both an influential researcher and teacher, with students such asBernard Malgrange,Jacques-Louis Lions,François Bruhat andAlexander Grothendieck. He joined the science faculty of theUniversity of Paris in 1952. In 1958 he became a teacher at theÉcole 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 theManifesto of the 121 about theAlgerian 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 1965 he established theCentre de mathématiques Laurent-Schwartz (CMLS) as its first director.
In 1973 he was elected corresponding member of theFrench Academy of Sciences, and was promoted to full membership in 1975.
At the 1950International Congress of Mathematicians in Cambridge (Massachusett), Schwartz was a plenary speaker[2] and was awarded theFields Medal for his work ondistributions. He was the first French mathematician to receive the Fields medal. Because of his sympathy forTrotskyism, Schwartz encountered serious problems trying to enter theUnited States to receive the medal; however, he was ultimately successful.
The theory of distributions clarified the (then) mysteries of theDirac delta function andHeaviside step function. It helps to extend the theory ofFourier transforms and is now of critical importance to the theory ofpartial differential equations.
Throughout his life, Schwartz actively worked to promote science and bring it closer to the general audience. Schwartz said: "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]
His mother, who was passionate about natural science, passed on her taste forentomology to Laurent. His personal collection of 20,000Lepidoptera specimens, collected during his various travels, was bequeathed to theMuséum national d'histoire naturelle, theScience Museum of Lyon, theMuseum of Toulouse and the Museo de Historia Natural Alcide d'Orbigny inCochabamba (Bolivia). Several species discovered by Schwartz bear his name.
Apart from his scientific work, Schwartz was a well-known outspokenintellectual. As a youngsocialist influenced byLeon Trotsky, Schwartz opposed thetotalitarianism of theSoviet Union, particularly underJoseph Stalin. Schwartz broke with Trotskyism in 1947 and wrote that his "political culture comes almost entirely from that Trotskyist period".[4]
On his religious views, Schwartz called himself anatheist.[5]
Research articles
Technical books
Seminar notes
Popular books
My parents were atheists, I was an atheist, I never really felt Jewish.
Media from Commons
Quotations from Wikiquote
