Liouville

Joseph Liouville

Born: 24 March 1809 in Saint-Omer, France
Died: 8 Sept 1882 in Paris, France

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Liouville is best known for his work on the existence of transcendental numbers.

Liouville became professor at the École Polytechnique in Paris in 1833. In 1836 he founded a mathematics journal Journal de Mathématiques Pures et Appliquées . This journal, sometimes known as Journal de Liouville , did much for mathematics in France throughout the 19th century.

Liouville investigated criteria for integrals of algebraic functions to be analytic during the period 1832-33. This led on to his proof of the existence of a transcendental number in 1844 when he constructed an infinite class of such numbers.

His work on boundary value problems on differential equations is remembered because of what is called today Stürm-Liouville theory which is used in solving integral equations. It has major importance in mathematical physics.

Liouville contributed to differential geometry studying conformal transformations. He proved a major theorem concerning the measure preserving property of Hamiltonian dynamics. The result is of fundamental importance in statistical mechanics and measure theory.

In number theory he wrote around 200 papers, working on quadratic reciprocity and many other topics.

He wrote over 400 papers in total and was a major influence in bringing Galois' work to general notice when he published this work in 1846 in his Journal.

References elsewhere in this archive:

Tell me about Liouville's work on Fermat's last theorem

Tell me about his part in the life of Évariste Galois and in the development of group theory

Tell me about Liouville's work on orbits and gravitation

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. G Chrystal, Joseph Liouville, Proc. Royal Soc. Edinburgh 14 (1888), 83-91.
  4. J Lützen, Joseph Liouville 1809-1882: Master of Pure and Applied Mathematics (New York- Berlin- ,1990).
  5. J Peiffer, Joseph Liouville (1809-1882) : ses contributions à la théorie des fonctions d'une variable complexe, Rev. Hist. Sci. 36 (1983), 209-248.
  6. J Lützen, Joseph Liouville's Contribution to the Theory of Integral Equations, Historia Mathematica 9 (1982), 371-391.
  7. J Lützen, Joseph Liouville's Work on the Figures of Equilibrium of a Rotating Mass of fluid, Rev. Hist. Sci. 30 (1984), 113-166. 
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