Joseph Liouville

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Joseph Liouville

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

Life

Liouville studied in Toul and from 1825 in Paris at the École polytechnique , where he passed his exams two years later, including with Poisson . After a few years as an assistant at various universities, he was appointed professor at the École Polytechnique in 1838. In 1850 he narrowly prevailed against Cauchy when applying for a mathematics chair at the Collège de France , which led to a dispute between the two, and in 1857 he was also appointed to a mechanics chair.

Besides his excellent research, Liouville was also a very good organizer. In 1836 he founded the still very respected Journal de Mathématiques Pures et Appliquées to disseminate the work of other mathematicians and directed this journal from 1836 and 1874. He was the first to fully understand the meaning of the writings of Évariste Galois and published them in 1846 in his magazine. Liouville was also politically active at times and was elected to the National Assembly in 1848 . After an election defeat the following year, however, he withdrew from politics. In 1839 he became a member of the Académie des Sciences , in 1840 a corresponding member of the Russian Academy of Sciences in St. Petersburg and in 1850 a foreign member of the Royal Society . In 1856 he was elected a foreign member of the Göttingen Academy of Sciences . In 1859 he was elected to the American Academy of Arts and Sciences . In 1875 he became an Honorary Fellow of the Royal Society of Edinburgh .

Liouville worked in numerous mathematical sub-areas, including number theory , function theory and differential geometry , but also in mathematical physics and even in astronomy . A well-known result is Liouville's theorem , which no introduction to function theory can ignore today. In the theory of quasi- conformal and quasi- regular mappings, Liouville's theorem denotes his result that the only conformal mappings of a region are in constraints of Möbius transformations . Liouville was also the first to prove the existence of transcendent numbers by constructing an infinite class of such numbers as continued fractions ( Liouville numbers ). He also introduced a number theoretic function, the Liouville function . Liouville also showed that the antiderivative of elementary functions need not be elementary. (His question about an algorithm that can be used to decide when this is the case was answered by Robert Risch in 1969. ) In mathematical physics, the Sturm-Liouville theory , which he developed together with Charles-François Sturm , provides one of the most important approaches to the solution of integral equations . According to Liouville's theorem for conservative physical systems, which are described in the Hamilton formalism , the (multidimensional) volume enclosed by neighboring trajectories in phase space 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 des mathématiques au XIXeme 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
  • Bruno Belhoste : Joseph Liouville et le Collège de France, Revue d'histoire des sciences, Volume 37, 1984, pp. 255-304, online

Web links

Commons : Joseph Liouville  - Collection of Images

Individual evidence

  1. ^ Entry on Liouville, Joseph (1809 - 1882) in the archives of the Royal Society , London
  2. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 153.
  3. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. (PDF file) Royal Society of Edinburgh, accessed January 1, 2020 .
personal data
SURNAME Liouville, Joseph
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH March 24, 1809
PLACE OF BIRTH Saint-Omer
DATE OF DEATH September 8, 1882
Place of death Paris