July 8, 1904|
|Died||August 13, 2008
|Institutions||University of Paris|
|Alma mater||École Normale Supérieure|
|Doctoral advisor||Paul Montel|
|Doctoral students||Jean-Paul Benzécri
|Known for||Cartan's theorems A and B|
|Notable awards||Wolf Prize (1980)|
Henri Paul Cartan (French: [kaʁtɑ̃]; July 8, 1904 – August 13, 2008) was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan and the brother of composer Jean Cartan.
Cartan studied at the Lycée Hoche in Versailles, then at the École Normale Supérieure in Paris, receiving his doctorate in mathematics. He taught at the University of Strasbourg from November 1931 until the outbreak of the Second World War, after which he held academic positions at a number of other French universities, spending the bulk of his working life in Paris.
Cartan is known for work in algebraic topology, in particular on cohomology operations, the method of "killing homotopy groups", and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan also was a founding member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra  was an important text, treating the subject with a moderate level of abstraction with the help of category theory.
Cartan used his influence to help obtain the release of some dissident mathematicians, including Leonid Plyushch and Jose Luis Massera. For his humanitarian efforts, he received the Pagels Award from the New York Academy of Sciences.
The Cartan model in algebra is named after Cartan.
Honours and awards
Cartan received numerous honours and awards including the Wolf Prize in 1980. From 1974 until his death he had been a member of the French Academy of Sciences. He was a foreign member of the Finnish Academy of Science and Letters, Royal Danish Academy of Sciences and Letters, Royal Society of London, Russian Academy of Sciences, Royal Swedish Academy of Sciences, United States National Academy of Sciences, Polish Academy of Sciences and other academies and societies.
- O'Connor, John J.; Robertson, Edmund F., "Henri Cartan", MacTutor History of Mathematics archive, University of St Andrews.
- Décès du mathématicien français Henri Cartan, Agence France-Presse, 2008-08-18 (French)
- Chang, Kenneth (2008-08-25), Henri Cartan, French Mathematician, Is Dead at 104, The New York Times: A17, retrieved 2008-08-25
- Cartan, Henri; Eilenberg, Samuel (1956). Homological Algebra. Princeton Mathematical Series (PMS) 19. Princeton University Press. ISBN 978-0-691-04991-5.
- Rehmeyer, Julie (2008-08-29), Founder of the Secret Society of Mathematicians, Science News
- Henri Cartan at the Internet Movie Database
- Jackson, Allyn (July 1999), Interview with Henri Cartan (PDF), Notices of the American Mathematical Society 46 (7): 782–8
- Illusie, Luc; Cartier, Pierre (ed.), Dossier. Notices of the American Mathematical Society, Sept. 2010, vol. 57, issue 8
- Henri Cartan at l'Académie des Sciences (French)
- Henri Cartan at the Mathematics Genealogy Project
- Biographical sketch and bibliography by the Société Mathématique de France on the occasion of Cartan's 100th birthday. (French)
- Cerf, Jean (April 2004), Trois quarts de siècle avec Henri Cartan, Gazette des Mathématiciens (100): 7–8 (French)
- Samuel, Pierre (April 2004), Souvenirs personnels sur H. Cartan, Gazette des Mathématiciens (100): 13–15 (French)
- 100th Birthday of Henri Cartan, European Mathematical Society Newsletter (53), September 2004: 20–21 (translations of above two articles from the SMF Gazette)
- Papers by Henri Cartan as member of the 'Association européenne des enseignants' (AEDE) and the 'Mouvement fédéraliste européen' (MFE) are at the Historical Archives of the EU in Florence