Élie Joseph Cartan (9 April 1869 - 6 May 1951) was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications. He also made significant contributions to mathematical physics, differential geometry, and group theory.He was the father of another influential mathematician, Henri Cartan. Joseph Cartan (9 April 1869 - 6 May 1951) was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications. He also made significant contributions to mathematical physics, differential geometry, and group theory. He was the father of another influential mathematician, Henri Cartan.