Jordan, Camille

in full MARIE-ENNEMOND-CAMILLE JORDAN, French mathematician whose work on substitution groups (groups of permutations) and the theory of equations first brought full understanding of the importance of the theories of the eminent mathematician Évariste Galois, who had died in 1832.

Jordan's early research was in geometry. His Traité des substitutions et des équations algebriques (1870; "Treatise on Substitutions and Algebraic Equations"), which brought him the Poncelet Prize of the Academy of Sciences, gave a comprehensive account of Galois's theory of substitution groups and applied them to algebraic equations. He also solved the problem proposed by Niels Henrik Abel of ascertaining the solvability of any given algebraic equation by radicals. Jordan published his lectures and researches on analysis in Cours d'analyse de l'École Polytechnique, 3 vol. (1882; "A Course of Analysis of the Polytechnic School"). In the third edition (1909-15) of this notable work, which contained a good deal more of Jordan's own work than did the first, he treated the theory of functions from the modern viewpoint, dealing with the function of bounded variation, which he applied to the curve known as Jordan's curve. The Jordan algebras are named in his honour.

In topology Jordan proved (1887) that a simple arc does not divide the plane and that a simple closed curve divides the plane into exactly two parts. Although intuitively obvious, these theorems require sophisticated proofs.

Jordan was professor of mathematics at the École Polytechnique, Paris, from 1876 to 1912. He also edited the Journal de mathématiques pures et appliquées (1885-1922).