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Élie Cartan
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Professor Élie Joseph Cartan
Born (1869-04-09)9 April 1869
Dolomieu, Isère, France
Died 6 May 1951(1951-05-06) (aged 82)
Paris, France
Nationality France
Alma mater University of Paris
Known for Lie groups (Cartan's theorem)
Vector spaces and exterior algebra
Differential geometry
Special and general relativity
Differential forms
Quantum mechanics (spinor, rotating vectors)
Awards Leconte Prize (1930)
Lobachevsky Prize (1937)
President of the French Academy of Sciences (1946)
Fellow of the Royal Society (1947)
Scientific career
Fields Mathematics and physics
Institutions University of Paris
École Normale Supérieure
Thesis Sur la structure des groupes de transformations finis et continus (1894)
Doctoral advisor Gaston Darboux
Sophus Lie
Doctoral students Charles Ehresmann
Mohsen Hashtroodi
Kentaro Yano

Élie Joseph Cartan, ForMemRS (French: [kaʁtɑ̃]; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He also made significant contributions to general relativity and indirectly to quantum mechanics. He is widely regarded as one of the greatest mathematicians of the twentieth century.

Cartan's recognition as a first–rate mathematician came to him only in his old age; before 1930 Henri Poincaré and Hermann Weyl were probably the only prominent mathematicians who correctly assessed his uncommon powers and depth. This was due partly to his extreme modesty and partly to the fact that in France the main trend of mathematical research after 1900 was in the field of function theory, but chiefly to his extraordinary originality. It was only after 1930 that a younger generation started to explore the rich treasure of ideas and results that lay buried in his papers. Since then his influence has been steadily increasing, and with the exception of Poincaré and Hilbert, probably no one else has done so much to give the mathematics of 20th century its shape and viewpoints.

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