STURM, CHARLES-FRANOIS

born Sept. 29, 1803, Geneva, Switz. died Dec. 18, 1855, Paris, France in full Jacques-charles-franois Sturm French mathematician whose work resulted in Sturm's theorem, an important contribution to the theory of equations. As tutor of the de Broglie family in Paris (182324), Sturm met many of the leading French scientists and mathematicians. In 1826, with the Swiss engineer Daniel Colladon, he made the first accurate determination of the velocity of sound in water and a year later wrote a prizewinning essay on compressible fluids. Sturm's theorem first appeared in Mmoire sur la rsolution des quations numriques (1829; Treatise on Numerical Equations) and provided a complete solution to the problemone that had been wrestled with since the time of Ren Descartesof finding the number of roots (or solutions) of an algebraic equation within a given range of the variable. Published in 1834, Sturm's work on the theory of differential equations of the second order won him prestigious awards in France. He was elected to the Acadmie in 1836 and became professor of mathematics at the cole Polytechnique, Paris, in 1838. Two years later he succeeded Simon-Denis Poisson in the chair of mechanics in the Facult des Sciences, Paris. Although primarily an analyst, Sturm made significant contributions to projective geometry and to the differential geometry of curves and surfaces. He also did important work on geometrical optics. Published posthumously, his Cours d'analyse de l'cole Polytechnique, 2 vol. (185763; Course on Analysis from the cole Polytechnique) and Cours de mchanique de l'cole Polytechnique, 2 vol. (1861; Course on Mechanics from the cole Polytechnique) were widely used, even in the early 20th century.