Joseph Liouville (March 24, 1809 - September 8, 1882) was a French mathematician. He 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. 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, Liouville made two fundamental contributions: the Sturm-Liouville theory, a procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system. In Hamiltonian dynamics, he also introduced the notion of action-angle variables as a description of completely integrable systems. He founded the Journal de Math矇matiques Pures et Appliqu矇es which retains its high reputation up to today, in order to promote other mathematicians' work. He died in 1882 at the age of 73.