Henri Paul Cartan (born July 8, 1904 in Nancy , † August 13, 2008 in Paris ) was an important French mathematician . He was a founding member of N. Bourbaki .
Henri Cartan was the son of Élie Cartan , who was also a mathematician. He studied from 1923 at the École normal supérieure and befriended André Weil there. In 1928 he received his doctorate in function theory with Paul Montel ( Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications ). In 1935 he was a founding member of the Bourbaki group . From 1931 to 1939 he taught at the University of Strasbourg . In 1940 he was appointed professor at the Sorbonne , where he taught until 1969, interrupted by many stays abroad in Germany and the USA. Immediately after the war he ensured that relations with German mathematicians were resumed, especially with Heinrich Behnke's function theory school in Münster , with whom he had close contacts even before the war. Until 1975 he was at the Université de Paris-Sud in Orsay, after which he went into retirement. His seminar in Paris was a famous center for the development of algebraic geometry and complex analysis in the 1950s.
In 1958 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Edinburgh (Sur les fonctions de plusieurs variables complexes: les espaces analytiques) and also in 1950 at the ICM in Cambridge (Massachusetts) (Problèmes globaux dans la théorie des fonctions analytiques de plusieurs variables complexes). In 1950 he was President of the Société Mathématique de France . Also in 1950 he was elected to the American Academy of Arts and Sciences and in 1972 to the National Academy of Sciences . Since 1965 he was a corresponding and from 1974 a full member of the Académie des sciences .
His doctoral students include Jean-Pierre Serre , Max Karoubi , Pierre Dolbeault , Adrien Douady , Jacques Deny , Pierre Cartier , Jean-Louis Koszul , Jean Cerf , Roger Godement , René Thom .
Cartan made significant contributions to homological algebra , algebraic topology, and the complex analysis of several variables. (“Theorems A and B” about the coherence of coherent sheaves on Steinian spaces , together with Jean-Pierre Serre ).
In 1980 he was awarded the Wolf Prize for his scientific success . He was a member of numerous scientific academies and received numerous honorary doctorates . In 1994 he became an honorary member of the DMV .
- Reinhold Remmert , Jean-Pierre Serre (editor) Henri Cartan: Oeuvres , 3 volumes, Springer Verlag 1979
- Sur les groupes de transformations analytiques, Paris, Hermann 1935
- Sur les classes de fonctions définies par des inégalités portant sur leurs dérivées successives, Paris, Hermann 1940
- Cours de calcul différentiel, Paris, Hermann 1967, 1977
- German edition: Differentialrechnung, Mannheim, Bibliographisches Institut 1974
- Elementary theory of analytic functions of one or several complex variables, Dover 1995
- French edition Hermann 1961
- German edition: Elementary theory of the analytical functions of one or more complex variables, Mannheim, Bibliographisches Institut, BI university paperback 1966
- Formes différentielles, Paris, Hermann 1970,
- English edition: Differential Forms, Dover 2006
- German edition: Differentialformen, Mannheim, Bibliographisches Institut 1974
- with Samuel Eilenberg Homological Algebra , Princeton University Press 1956
- Nicolas Bourbaki and today's mathematics, Cologne, Westdeutscher Verlag 1959
- Michèle Audin (editor) Correspondance entre Henri Cartan et André Weil (1928–1991) , Documents Mathématiques 6, Société Mathématique de France, 2011.
- Seminaire Henri Cartan 1948–1964, with numdam
- Klaus Hulek , Thomas Peternell : Henri Cartan, a French friend, Annual Reports DMV, Volume 111, 2009, pp. 95–94
- Günter Ziegler : The French friend. ZEIT ONLINE, August 20, 2008
- Luc Illusie , Pierre Cartier (Editor): A Tribute to Henri Cartan , Notices AMS, September 2010
- Literature by and about Henri Cartan in the catalog of the German National Library
- John J. O'Connor, Edmund F. Robertson : Henri Cartan. In: MacTutor History of Mathematics archive .
- Some of his work, especially the lectures of the Cartan Seminar, are online here: 
- Files of Henri Cartan as a member of the l'Association européenne des enseignants' (AEDE) and the 'Mouvement fédéraliste européen' (MFE) are deposited in the Historical Archives of the EU in Florence .
- Henri Cartan in the Mathematics Genealogy Project (English)
- Page of the SMF on Henri Cartan
|ALTERNATIVE NAMES||Cartan, Henri Paul|
|BRIEF DESCRIPTION||French mathematician|
|DATE OF BIRTH||July 8, 1904|
|PLACE OF BIRTH||Nancy|
|DATE OF DEATH||August 13, 2008|
|Place of death||Paris|