DARBOUX, JEAN-GASTON

born Aug. 14, 1842, Nmes, France died Feb. 23, 1917, Paris French mathematician who made important contributions to geometry and analysis and after whom the Darboux integral is named. After acting as an assistant in mathematical physics (186667) at the Collge de France, Paris, Darboux taught at the Lyce Louis le Grand (186772), the cole Normale Suprieure (187273), and the Sorbonne (187390). Besides being an excellent teacher and a notable mathematician, he was a very capable administrator. Practically all Darboux's mathematical work was in geometry. His early papers (1864 and 1866) on orthogonal surfaces were followed by a memoir (1870) on partial-differential equations of the second order, which embodied a new method of integration. In his treatise Sur une classe remarquable de courbes et de surfaces algbriques et sur la thorie des imaginaires (1873; On a Class of Remarkable Curves and Algebraic Surfaces and on the Theory of Imaginary Numbers), he developed the theory of the class of surfaces called cyclides. Leons sur la thorie gnrale des surfaces et les applications gomtriques du calcul infinitsimal, 4 vol. (188796; Lessons on the General Theory of Surfaces and the Geometric Applications of Infinitesimal Calculus), one of his most important works, deals with infinitesimal geometry and embodies most of his previous research work. In 1898 the publication of Leons sur les systmes orthogonaux et les coordonnes curvilignes (Lessons on Orthogonal Systems and Curvilinear Coordinates) was begun. He was the author of a number of papers and memoirs on the approximation to functions of very large numbers, discontinuous functions, dynamics, and other mathematical subjects.