Background
Liouville was born on March 24, 1809, in Saint-Omer, France, the second son of Claude-Joseph Liouville, an army captain, and Thérèse Balland, both originally from Lorraine.
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Liouville studied in Commerey and then in Tout. Admitted to the École Polytechnique in November 1825, he graduated in 1827.
(Volume 1, French Edition)
Volume 1, French Edition
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1836
Liouville was born on March 24, 1809, in Saint-Omer, France, the second son of Claude-Joseph Liouville, an army captain, and Thérèse Balland, both originally from Lorraine.
Liouville studied in Commerey and then in Tout. Admitted to the École Polytechnique in November 1825, he graduated in 1827.
While preparing for a career in engineering, Liouville began original research in mathematics and mathematical physics. Between June 1828 and November 1830, he presented before the Académie des Sciences seven memoirs, two of which dealt with the theory of electricity, three with the analytic theory of heat, and two with mathematical analysis. In order to secure as much freedom as possible to pursue his research, Liouville soon thought of changing professions. In 1830, he refused the position of engineer that he was offered, hoping that his reputation would permit him to obtain a teaching post fairly soon.
In November 1831, Liouville was selected by the Council on Instruction of the École Polytechnique to replace P. Binet as répétiteur in L. Mathieu’s course in analysis and mechanics. This was the beginning of a brilliant career of some fifty years, in the course of which Liouville taught pure and applied mathematics in the leading Paris institutions of higher education.
In 1838 Liouville succeeded Mathieu as a holder of one of the two chairs of analysis and mechanics at the École Polytechnique, a position that he resigned in 1851, immediately after his election to the Collège de France. From 1833 to 1838 Liouville also taught mathematics and mechanics, but at a more elementary level, at the recently founded École Centrale des Arts et Manufactures. In March 1837 he was chosen to teach mathematical physics at the Collège de France as suppléant for J. B. Biot. He resigned in March 1843 to protest the election of Count Libri-Carrucci to the chair of mathematics at that institution.
Liouville did not return to the Collège de France until the beginning of 1851 when he succeeded Libri-Carrucci, who had left France. This chair had no fixed program, and so for the first time, Liouville could present his own research and discuss current topics. He took advantage of this to present unpublished works, some of which were developed by his students before he himself published them. Appreciating the interest and flexibility of such teaching, he remained in the post until 1879, when he arranged for O. Bonnet to take over his duties.
Liouville also wished to teach on the university level. Toward this end, he had earned his doctorate with a dissertation on certain developments in Fourier series and their applications in mathematical physics (1836). He was therefore eligible for election, in 1857, to the chair of rational mechanics at the Paris Faculty of Sciences, a position vacant since the death of Charles Sturm. In 1874, he stopped teaching there and arranged for his replacement by Darboux.
Parallel with this very full academic career, Liouville was elected a member of the astronomy section of the Académie des Sciences in June 1839, succeeding M. Lefrançois de Lalande; and in 1840 he succeeded Poisson as a member of the Bureau des Longitudes. From this time on, he participated regularly in the work of these two groups. For forty years he also passionately devoted himself to another particularly burdensome task, heading an important mathematical journal. The almost simultaneous demise, in 1831, of the only French mathematical review, Gergonne’s Annales de mathématiques pures et appliquées, together with one of the principal science reviews, Férussac’s Bulletin des sciences mathématiques, astronomiques, physiques et chimiques, deprived French-language mathematicians of two of their favorite forums. Liouville understood that the vigor of French mathematical writings demanded the creation of new organs of communication. Despite his youth and inexperience in the problems of editing and publishing, he launched the Journal de mathématiques pures et appliquées in January 1836.
During the first thirty years of his career Liouville, while maintaining a very special interest in mathematical analysis, also did research in mathematical physics, algebra, number theory, and geometry. Starting in 1857, however, he considerably altered the orientation of his studies, concentrating more and more on particular problems of number theory, Departing in this way from the most fruitful paths of mathematical research, Liouville saw his influence decline rapidly. Yet it was the abandonment of the editorship of his Journal in 1874 that signaled the real end of his activity. His publications, which had been appearing with decreasing frequency since 1867, stopped with decreasing frequency since 1867, stopped altogether at this time. Simultaneously he gave up his courses at the Sorbonne, where his suppléants were Darboux and then Tisserand. He still attended the sessions of the Académic des Sciences and of the Bureau des Longitudes and still lectured at the Collège de France; but he no longer really participated in French mathematical life.
(Volume 1, French Edition)
1836Already known for his democratic convictions, Liouville was elected on 23 April 1848 to the Constituent Assembly as one of the representatives from the department of the Meurthe. He voted with the moderate democratic party. His defeat in the elections for the Legislative Assembly in May 1849 marked the end of his political ambitions.
It was in mathematical analysis that Liouville published the greatest number and the most varied of his works. Certain of his earliest investigations in the mathematical analysis should be viewed as a continuation of the then most recent works of Abel and Jacobi. The most important are concerned with attempts to classify all algebraic functions and the simplest types of transcendental functions, with the theory of elliptic functions, and with certain types of integrals that can be expressed by an algebraic function.
In 1831 Liouville married a maternal cousin, Marie-Louise Balland (1812-1880); they had three daughters and one son.