This work was published in the' ' Journal de Mathématiques Pures et the Appliqueés' ' (Gauthier-Villars/Elsevier), oldest of the specialized magazines in France, founded in 1836 by Joseph Liouville.
He was the first to read, and to recognize, the importance of the unpublished work of Évariste Galois which appeared in his journal in 1846.
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He is remembered particularly for Liouville's theorem, a nowadays rather basic result in complex analysis.
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In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint work with Charles François Sturm, and is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system.
Poisson, Liouville, Fourier and others studied partial differential equations and harmonic analysis.
Euler's assertion was not proved until the twentieth century, but almost a hundred years after his claim Joseph Liouville did manage to prove the existence of numbers that are not algebraic, something that until then had not been known for sure.
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