Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841.

Transcendental numbers were first constructed by Joseph Liouville in 1844.

* 1809 – Joseph Liouville, French mathematician ( d. 1882 )

Joseph Liouville first proved the existence of transcendental numbers in 1844, and in 1851 gave the first decimal examples such as the Liouville constant

* March 24 – Joseph Liouville, French mathematician ( d. 1882 )

* September 8 – Joseph Liouville, French mathematician ( b. 1809 )

A classical theorem of Joseph Liouville called Liouville's theorem shows the higher-dimensions have less varied conformal maps:

Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville:

* Mathematicians Joseph Liouville, Émile Picard, Paul Appell and Jacques Hadamard

The Liouville function, denoted by λ ( n ) and named after Joseph Liouville, is an important function in number theory.

Not all closed-form expressions have closed-form antiderivatives ; this study forms the subject of differential Galois theory, which was initially developed by Joseph Liouville in the 1830s and 1840s, leading to Liouville's theorem which classifies which expressions have closed form antiderivatives.

In 1839, during a visit to Paris, Dirichlet met Joseph Liouville, the two mathematicians becoming friends, keeping in contact and even visiting each other with the families a few years later.

In complex analysis, Liouville's theorem, named after Joseph Liouville, states that every bounded entire function must be constant.

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.

Joseph Liouville (, ; 24 March 1809 – 8 September 1882 ) was a French mathematician.

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