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Joseph Liouville (born March 24 1809, died September 8 1882) was a French mathematician. Liouville graduated from the École Polytechnique in 1827. After some years as assistant at various institutions he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at the Collège de France in 1850 and a chair in mechanics at the Faculté des Sciences in 1857.
Besides his academic achievements, he was very talented in organisatorial matters. Liouville founded the Journal de Mathématiques Pures et Appliquées which retains its high reputation up to today, in order to promote other mathematicians' work. He was the first to read, and to recognize the importance of, the unpublished work of Evariste Galois which appeared in his journal in 1846. Liouville was also involved in politics for some time, and he became member of the Constituting Assembly in 1848. However, after the defeat in the Assembly elections in 1849, he turned away from politics.
Liouville worked in a number of different fields in mathematics, including number theory, complex analysis, differential geometry and topology, but also mathematical physics and even astronomy. He is remembered particularly for Liouville's theoremComplex analysis Theorems Liouville's theorem in complex analysis states that every bounded (i. there exists a real number M such that f ''z | ≤ M for all z in C entire function (a holomorphic function f ''z defined on the whole complex plane C must be, a nowadays rather basic result in complex analysis. In number theory, he was the first to prove the existence of transcendental numberIn mathematics, a transcendental number is any irrational number that is not an algebraic number, i. it is not the solution of any polynomial equation of the form : where n ≥ 1 and the coefficients a are integers (or, equivalently, rationals), not alls by a construction using continued fractionIn mathematics, a continued fraction is an expression such as : where a is some integer and all the other numbers a are positive integers. Longer expressions are defined analogously. If the numerators are allowed to differ from unity, the resulting express ( Liouville numberIn number theory, a Liouville number is a real number x with the property that, for any positive integer n there exist integers p and q with q > 1 and such that :0 n''. A Liouville number can then be approximated "quite closely" by a sequence of rationals). In mathematical physics, the Sturm-Liouville theoryIn mathematics and its applications, a Sturm-Liouville problem named after Charles Francois Sturm (1803-1855) and Joseph Liouville (1809-1882), is a second-order linear differential equation of the form : (1) often together with specified boundary values which was joint work with Charles François Sturm is now a standard procedure to solve certain types of integral equationIn mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. Integral equations ars. Moreover, there is a second " Liouville's theoremLiouville's theorem (also sometimes known as the Liouville equation) is a key theorem in statistical mechanics of classical systems, studied in the physical sciences. It is also important in the mathematical study of Hamiltonian mechanics and symplectic t" in Hamiltonian dynamics.
Liouville, Joseph
Liouville, Joseph
Liouville, Joseph
