LIOUVILLE, JOSEPH

born March 24, 1809, Saint-Omer, Fr. died Sept. 8, 1882, Paris French mathematician known for his work in analysis, the theory of numbers, and differential geometry, and particularly for his discovery of transcendental numbersi.e., numbers that are not the roots of algebraic equations having rational coefficients. Liouville became professor at the cole Polytechnique, Paris, in 1833. In 1836 he founded and became editor of the Journal de Mathmatiques Pures et Appliques, sometimes known as Journal de Liouville, which did much to raise and maintain the standard of French mathematics throughout the 19th century. Most of the papers of the eminent French mathematician variste Galois were first published by Liouville in 1846. A boldly original mathematician, Liouville investigated (183233) criteria for the analytic character of integrals of algebraic functions. He was the first to prove (1844) the existence of transcendental numbers, and he constructed an infinite class of such numbers. He also worked in differential equations and boundary-value problems. His methods in the latter, now known as the StrmLiouville theory, became of major importance in 20th-century mathematical physics as well as in the theory of integral equations. In differential geometry, he contributed notably to the theories of applicability of surfaces and conformal transformations. The Liouville theorem concerning the measure-preserving property of the Hamiltonian dynamics is basic to statistical mechanics and measure theory. In number theory Liouville made contributions to numerical functions, quadratic representations, and general formulas in parity functions. Although nearly all this work was published without indication of the means by which he had obtained his striking results, proofs have since been provided. In analysis Liouville was the first to deduce the theory of doubly periodic functions from general theorems (including his own) in the theory of analytic functions of a complex variable. His works include about 400 items, more than 200 on the theory of numbers alone.