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Élie Cartan

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.[1][2][3] He is widely regarded as one of the greatest mathematicians of the twentieth century.[3]

Élie Cartan

(1869-04-09)9 April 1869

Dolomieu, Isère, France

6 May 1951(1951-05-06) (aged 82)

Paris, France

University of Paris

Lie groups (Cartan's theorem)
Vector spaces and exterior algebra
Differential geometry
Special and general relativity
Differential forms
Quantum mechanics (spinors, rotating vectors)
List of things named after Élie Cartan

Henri Cartan

Anna Cartan (sister)

Leconte Prize (1930)
Lobachevsky Prize (1937)
President of the French Academy of Sciences (1946)
Fellow of the Royal Society (1947)

Mathematics and physics

University of Paris
École Normale Supérieure

Sur la structure des groupes de transformations finis et continus  (1894)

Gaston Darboux
Sophus Lie

Charles Ehresmann
Mohsen Hashtroodi
Kentaro Yano

Shiing-Shen Chern

His son Henri Cartan was an influential mathematician working in algebraic topology.

Exterior derivative

Integrability conditions for differential systems

Isotropic line

CAT(k) space

Einstein – Cartan theory

Hermitian symmetric space

Moving frame

Pseudogroup

Pure spinor

Media related to Élie Cartan at Wikimedia Commons

Shiing-Shen Chern

Chern, Shiing-Shen; (1952). "Élie Cartan and his mathematical work". Bulletin of the American Mathematical Society. 58 (2): 217–250. doi:10.1090/s0002-9904-1952-09588-4.

Chevalley, Claude

English translations of some of his books and articles: