# Joseph Liouville

Joseph Liouville ( born March 24, 1809 in Saint- Omer, † September 8, 1882 in Paris) was a French mathematician.

He studied in Toul, and in 1825 in Paris at the École Polytechnique, where he spent two years on, inter alia, Poisson, took his exams. After several years as an assistant at various universities, he was appointed in 1838 as professor at the École Polytechnique. In 1850, he sat down when applying for a mathematics chair at the Collège de France narrowly defeated by Cauchy, which developed a dispute between the two, and in 1857 he was also appointed to a Chair mechanics.

In addition to his outstanding research Liouville was also a very good organizer. In 1836 he founded the still very prestigious Journal de Mathématiques Pures et Appliquées to spread the work of other mathematicians and directed this journal from 1836 and 1874. He was the first of the importance of the writings of Évariste Galois fully recognized and published them in 1846 in his journal. Liouville was also partly politically active and in 1848 elected to the National Assembly. After a defeat in the following year he retired but retired from politics.

Liouville worked in numerous mathematical sciences, including number theory, function theory and differential geometry, but also in mathematical physics and even astronomy. A well-known result is the set of Liouville, walks past the now not an introduction to the theory of functions. In the theory of quasiconformal and quasiregular maps is called the set of Liouville be concluded that for the single conformal mapping of an area are restrictions of Möbius transformations. Liouville was also the first, the proof of the existence of transcendental numbers achieved by constructing an infinite class of such numbers as continued fractions ( Liouville numbers). He also introduced a number-theoretic function, the Liouville function. Next Liouville showed that the antiderivative of elementary functions need not be elementary. ( His question of an algorithm that can determine when this is the case, was answered by Robert Risch 1969. ) In mathematical physics, the Sturm- Liouville theory, which he developed in collaboration with Charles -François Sturm, a of the main entrances to the solution of integral equations dar. After the Liouville theorem for conservative physical systems that are described in the Hamiltonian formalism, the area enclosed by neighboring trajectories in phase space ( multi-dimensional ) volume is constant.

The lunar crater Liouville is named after him.

## Bibliography

- Jesper Lützen, Joseph Liouville 1809-1882: Master of Pure and Applied Mathematics, Springer Verlag, 1990.
- Norbert Verdier, Le Journal de Liouville et la presse de son temps: une entreprise d' édition et de circulation of Mathématiques XIXeme au siècle (1824-1885), Thèse de doctorat, Université Paris -Sud 11, 2009.
- Norbert Verdier, Alexandre Moatti Joseph Liouville (1809-1882, X 1825) Le bicentenaire, Bulletin de la SABIX, n ° 45, 2010