Cartan , Elie Joseph

(1869–1951) French mathematician

Cartan is now recognized as one of the most powerful and original mathematicians of the 20th century, but his work only became widely known toward the end of his life. Cartan, who was born in Dolomieu, France, studied at the Ecole Normale Supérieure in Paris and held teaching posts at the universities of Montpellier, Lyons, Nancy, and, from 1912 to 1940, Paris.

Cartan's most significant work was in developing the concept of analysis on differentiable manifolds, which now occupies a central place in mathematics. He began his research career with a dissertation on Lie groups – a topic that led him on to his pioneering work on differential systems. The most important innovation in his work on Lie groups was his creation of methods for studying their global properties. Similarly his work on differential systems was distinguished by its global approach. One of his most useful inventions was the ‘calculus of exterior differential forms,’ which he applied to problems in many fields including differential geometry, Lie groups, analytical dynamics, and general relativity. Cartan's son Henri is also an eminent mathematician.