Laurent Schwartz
Laurent Schwartz | |
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François Treves |
Laurent-Moïse Schwartz (French: [ʃvaʁts]; 5 March 1915 – 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 École polytechnique.
Biography
Family
Laurent Schwartz came from a
During his training at
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
Later career
Schwartz taught mainly at
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 clarified the (then) mysteries of the Dirac delta function and Heaviside step function. It helps to extend the theory of Fourier transforms and is now of critical importance to the theory of partial differential equations.
Popular science
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]
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
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.[4]
Books
Research articles
- Œuvres scientifiques. I. With a general introduction to the works of Schwartz by Claude Viterbo and an appreciation of Schwartz by Bernard Malgrange. With 1 DVD. Documents Mathématiques (Paris), 9. Société Mathématique de France, Paris, 2011. x+523 pp. ISBN 978-2-85629-317-1
- the first half of his works in analysis and partial differential equations. After a preface by Claude Viterbo, which includes a few photos, one will find a note by Schwartz himself about his works, followed by a few original documents (letters, course notes), a presentation by Bernard Malgrange of the theory of distributions for which Schwartz received the Fields Medal in 1950, and a selection of articles covering the period 1944–1954.
- Œuvres scientifiques. II. With an appreciation of Schwartz by Alain Guichardet. With 1 DVD. Documents Mathématiques (Paris), 10. Société Mathématique de France, Paris, 2011. x+507 pp. ISBN 978-2-85629-318-8
- the second half of his works in analysis and partial differential equations. After a note by Alain Guichardet on Schwartz and his seminars, one will find a selection of articles covering the period 1954–1966.
- Œuvres scientifiques. III. With appreciations of Schwartz by Gilles Godefroy and Michel Émery. With 1 DVD. Documents Mathématiques (Paris), 11. Société Mathématique de France, Paris, 2011. x+619 pp. ISBN 978-2-85629-319-5
- his works on Banach space theory (1968–1987), introduced by Gilles Godefroy, and on probability theory (1970–1996), presented by Michel Émery, as well as some articles of a historical nature (1955–1994).
Technical books
- Analyse hilbertienne. Collection Méthodes. Hermann, Paris, 1979. ii+297 pp. ISBN 2-7056-5897-1
- Application of distributions to the theory of elementary particles in quantum mechanics. Gordon and Breach, New York, NY, 1968. 144pp. ISBN 978-0-677-30090-0
- Cours d'analyse. 1. Second edition. Hermann, Paris, 1981. xxix+830 pp. ISBN 2-7056-5764-9
- Cours d'analyse. 2. Second edition. Hermann, Paris, 1981. xxiii+475+21+75 pp. ISBN 2-7056-5765-7
- [5]Étude des sommes d'exponentielles. 2ième éd. Publications de l'Institut de Mathématique de l'Université de Strasbourg, V. Actualités Sci. Ind., Hermann, Paris 1959 151 pp.
- Geometry and probability in Banach spaces. Based on notes taken by Paul R. Chernoff. Lecture Notes in Mathematics, 852. Springer-Verlag, Berlin-New York, 1981. x+101 pp. ISBN 3-540-10691-X
- Lectures on complex analytic manifolds. With notes by M. S. Narasimhan. Reprint of the 1955 edition. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 4. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1986. iv+182 pp. ISBN 3-540-12877-8
- Mathematics for the physical sciences. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1966 358 pp.
- Radon measures on arbitrary topological spaces and cylindrical measures. Tata Institute of Fundamental Research Studies in Mathematics, No. 6. Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. xii+393 pp.
- Semimartingales and their stochastic calculus on manifolds. Edited and with a preface by Ian Iscoe. Collection de la Chaire Aisenstadt. Presses de l'Université de Montréal, Montreal, QC, 1984. 187 pp. ISBN 2-7606-0660-0
- Semi-martingales sur des variétés, et martingales conformes sur des variétés analytiques complexes. Lecture Notes in Mathematics, 780. Springer, Berlin, 1980. xv+132 pp. ISBN 3-540-09749-X
- Les tenseurs. Suivi de "Torseurs sur un espace affine by Y. Bamberger and J.-P. Bourguignon. Second edition. Hermann, Paris, 1981. i+203 pp. ISBN 2-7056-1376-5
- [6]Théorie des distributions. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée. Hermann, Paris 1966 xiii+420 pp.
Seminar notes
- Séminaire Schwartz in Paris 1953 bis 1961. Online edition: [1]
Popular books
- Pour sauver l'université. Editions du Seuil, 1983. 122 pp. ISBN 2-02-006587-8
- A mathematician grappling with his century. Translated from the 1997 French original by Leila Schneps. Birkhäuser Verlag, Basel, 2001. viii+490 pp. ISBN 3-7643-6052-6
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), 157-164.
- ^ 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. Michel-Amadry". Archived 2012-07-12 at archive.today.
- ISBN 978-3-7643-6052-8.
My parents were atheists, I was an atheist, I never really felt Jewish.
- .
- .
References
- Barany, Michael J.; Paumier, Anne-Sandrine; Lützen, Jesper (2017). "From Nancy to Copenhagen to the World: The internationalization of Laurent Schwartz and his theory of distributions". Historia Mathematica. 44 (4). Elsevier BV: 367–394. ISSN 0315-0860.
- Bohr, Harald (1997). "The Work of L. Schwartz". World Scientific Series in 20th Century Mathematics. Vol. 5. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS. pp. 25–29. ISSN 0219-9750.
- Connes, A. Hommage à Laurent Schwartz. Gaz. Math. No. 94 (2002), 7–8.
- Guerraggio, Angelo. Laurent Schwartz: political commitment and mathematical rigour. Mathematical lives, 157–164, Springer, Berlin, 2011. doi:10.1007/978-3-642-13606-1 22
- Guichardet, Alain. Présentation des archives de Laurent Schwartz. Gaz. Math. No. 100 (2004), 78–79.
- Kutateladze, S.S. Sobolev and L. Schwartz: two fates, two fames. Sib. Zh. Ind. Mat. 11 (2008), no. 3, 5–14. English translation in J. Appl. Ind. Math. 2 (2008), no. 3, 301–310. arXiv:0802.0533
- Paumier, A.-S. Laurent Schwartz (1915–2002) et le colloque d'analyse harmonique de Nancy, 15–22 juin 1947. Gaz. Math. No. 147 (2016), 39–51.
- Schwartz, Claudine. Autour des premiers travaux de Laurent Schwartz sur les distributions. Gaz. Math. No. 113 (2007), 113–118.
- Treves, François; Pisier, Gilles; Yor, Marc. Laurent Schwartz (1915–2002). Notices Amer. Math. Soc. 50 (2003), no. 9, 1072–1084.
External links
Media from Commons
Quotations from Wikiquote
- O'Connor, John J.; Robertson, Edmund F., "Laurent Schwartz", MacTutor History of Mathematics Archive, University of St Andrews
- "Laurent Schwartz (1915–2002)" (PDF). Notices of the American Mathematical Society. 50 (9): 1072–1084. October 2003.
- Review of Schwartz's autobiography, same source
- Sobolev and Schwartz: Two Fates and Two Fames by S. S. Kutateladze,
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