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 He was the first to read, and to recognize the importance of, the unpublished work of Evariste Galois which appeared in his journal in 1846.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 theorem, a nowadays rather basic result in complex analysis. In number theory, he was the first to prove the existence of transcendental numbers by a construction using continued fractions (Liouville numbers). In mathematical physics, the Sturm-Liouville theory which was joint work with Charles François Sturm is now a standard procedure to solve certain types of integral equations. Moreover, there is a second "Liouville's theorem" in Hamiltonian dynamics.