Cartan Élie Joseph

Born Apr. 9, 1869, in Dolomieu; died May 6, 1951, in Paris. French mathematician. Member of the Paris Academy of Sciences (1931).

Cartan graduated from the École Normale Supérieure in 1891. In 1912 he became a professor at the University of Paris. His principal works were on the theory of continuous groups, the theory of differential equations, and differential geometry. In 1894 he laid the foundations of the algebraic theory of Lie groups, and in 1913 he constructed the theory of representations of semisimple Lie groups. Furthermore, he connected Lie groups with differential geometry and topology. In 1899–1902 he created the method of exterior differential forms, which enabled him to solve the problem of the compatibility of the Pfaff equations. In differential geometry of multidimensional spaces he constructed generalized spaces of affine, projective, and conformai connectedness; he also proposed the general method of moving frames, which, in conjunction with the method of exterior differential forms, is an efficient means of solving geometric problems. The Kazan Physics and Mathematics Society in 1937 awarded the N. I. Lobachevskii Prize to Cartan for his studies in geometry and group theory.