Joseph Liouville | |
|---|---|
 | |
| Born | (1809-03-24)24 March 1809 |
| Died | 8 September 1882(1882-09-08) (aged 73) |
| Alma mater | École Polytechnique |
| Known for | Sturm–Liouville theory Liouville's equation Liouville's theorem (complex analysis) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | École Centrale Paris École Polytechnique |
| Doctoral advisor | Siméon Poisson Louis Jacques Thénard |
| Doctoral students | Eugène Charles Catalan Nikolai Bugaev |
Joseph LiouvilleFRS FRSEFAS (/ˌliːuˈvɪl/LEE-oo-VIL;French:[ʒozɛfljuvil]; 24 March 1809 – 8 September 1882)[1][2] was a French mathematician and engineer.
He was born inSaint-Omer in France on 24 March 1809.[3][4] His parents were Claude-Joseph Liouville (an army officer) and Thérèse Liouville (née Balland).
Liouville gained admission to theÉcole Polytechnique in 1825 and graduated in 1827. Just likeAugustin-Louis Cauchy before him, Liouville studied engineering atÉcole des Ponts et Chaussées after graduating from the Polytechnique, but opted instead for a career in mathematics. After some years as an assistant at various institutions including theÉcole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at theCollège 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 organisational matters. Liouville founded theJournal 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 He was the first to read, and to recognize the importance of, the unpublished work ofÉvariste Galois which appeared in his journal in 1846. Liouville was also involved in politics for some time, and he became a member of theConstituting Assembly in 1848. However, after his defeat in the legislative elections in 1849, he turned away from politics.
Liouville worked in a number of different fields in mathematics, includingnumber theory,complex analysis,differential geometry and topology, but alsomathematical physics and evenastronomy. He is remembered particularly forLiouville's theorem in complex analysis. In number theory, he was the first to prove the existence oftranscendental numbers by a construction usingcontinued fractions (Liouville numbers).[5] In mathematical physics, Liouville made two fundamental contributions: theSturm–Liouville theory, which was joint work withCharles François Sturm, and is now a standard procedure to solve certain types ofintegral equations by developing into eigenfunctions, and the fact (also known asLiouville's theorem) that time evolution is measure preserving for aHamiltonian system. In Hamiltonian dynamics, Liouville also introduced the notion ofaction-angle variables as a description of completelyintegrable systems. The modern formulation of this is sometimes called theLiouville–Arnold theorem, and the underlying concept of integrability is referred to asLiouville integrability. Additionally, Liouville developed theRiemann-Liouville integral to consider differentiation and integration of afractional order.
In 1851, he was elected a foreign member of theRoyal Swedish Academy of Sciences. In 1853, he was elected as a member of theAmerican Philosophical Society.[6]
The craterLiouville on theMoon is named after him. So is theLiouville function, an important function in number theory.
