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Élie Cartan



Professor Élie Joseph Cartan


Born  Dolomieu, Isère, France

9 April 1869
Died  6 May 1951 Paris, France

(aged 82)
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 (coordinatefree 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.