Darboux, Jean Gaston (1842-1917)

French mathematician who contributed immensely to the differential geometry of his time, and to the theory of surfaces. In defining the Riemann integral 1879, he derived the Darboux sums and used the Darboux integrals. Darboux was born in Nîmes and educated at the Ecole Normale Supérieure and at the Sorbonne in Paris, where he became a professor 1873 and assistant to mathematician Joseph Liouville. Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal 1887-96 described all his work to date, but dealt mainly with the application of analysis to curves and surfaces, and the study of minimal surfaces and geodesics. In Leçons sur les systèmes orthogonaux et les coordonnées curvilignes 1898, Darboux applied the theorem on algebraic integrals to orthogonal systems in n dimensions. Important among Darboux's other work were his papers on the theory of integrations, proof of the existence of integrals of continuous functions, and the theory of analytical functions.