Joseph Liouville

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Joseph Liouville

Joseph Liouville (March 24 1809 – September 8 1882) was a French

France

France , officially the French Republic , is a country whose Metropolitan France is located in Western Europe and that also comprises various Overseas departments and territories of France....
mathematician

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
.

Life and work
Liouville graduated from the École Polytechnique

École Polytechnique

The ?cole Polytechnique , often referred to by the nickname X, is the foremost France grande ?cole of engineering . Founded in 1794 and initially located in the Quartier Latin in central Paris, it was moved to Palaiseau in 1976....
in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris

École Centrale Paris

?cole Centrale Paris is a renowned French university-level institution in the field of engineering. It is also known by its original name ?cole centrale des arts et manufactures, or ECP....
, he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at the Collège de France

Collège de France

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Joseph Liouville (March 24 1809 – September 8 1882) was a French

France

Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
.

Life and work

Liouville graduated from the École Polytechnique

École Polytechnique

École Centrale Paris

Collège de France

The Coll?ge de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Ecoles....
in 1850 and a chair in mechanics at the Faculté des Sciences in 1857.

Besides his academic achievements, he was very talented in organisatorial matters. Liouville founded the Journal de Mathématiques Pures et Appliquées which retains its high reputation up to today, in order to promote other mathematicians' work. He was the first to read, and to recognize the importance of the unpublished work of Évariste Galois

Évariste Galois

?variste Galois was a France mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a Necessary and sufficient conditions for apolynomial to be solvable by Nth root, thereby solving a long-standing problem....
which appeared in his journal in 1846. Liouville was also involved in politics for some time, and he became member of the Constituting Assembly

National Assembly

The National Assembly is either a legislature, or the lower house of a bicameral legislature in some countries. The best known National Assembly, and the first legislature to be known by this title, was that established during the French Revolution in 1789, known as the National Assembly ....
in 1848. However, after the defeat in the Assembly elections in 1849, he turned away from politics.

Liouville worked in a number of different fields in mathematics, including number theory

Number theory

Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study....
, complex analysis

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics investigating Function of complex numbers....
, differential geometry and topology

Differential geometry and topology

Differential geometry is a Mathematics discipline that uses the methods of differential calculus to study problems in geometry. The theory of plane and space Differential geometry of curves and of Differential geometry of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and ninet...
, but also mathematical physics

Mathematical physics

Mathematical physics is the scientific discipline concerned with the interface of mathematics and physics. There is no real consensus about what does or does not constitute mathematical physics....
and even astronomy

Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
. He is remembered particularly for Liouville's theorem

Liouville's theorem (complex analysis)

In complex analysis, Liouville's theorem, named after Joseph Liouville, states that every bounded function entire function must be constant. That is, every holomorphic function f for which there exists a positive number M such that |f| = M for all z in C is constant....
, a nowadays rather basic result in complex analysis. In number theory, he was the first to prove the existence of transcendental number

Transcendental number

In mathematics, a transcendental number is a number that is not algebraic number, that is, not a solution of a non-zero polynomial equation with rational number coefficients....
s by a construction using continued fraction

Continued fraction

In mathematics, a continued fraction is an expression such aswhere a0 is an integer and all the other numbers ai are positive integers....
s (Liouville number

Liouville number

In number theory, a Liouville number is a real number x with the property that, for any positive integer n, there exist integers p and q with q > 1 and such that...
s). 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 equation

Integral equation

In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential equation and integral equations, and some problems may be formulated either way....
s by developing into eigenfunctions, and the fact (also known as Liouville's theorem

Liouville's theorem (Hamiltonian)

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical mechanics and Hamiltonian mechanics....
) that time evolution is measure preserving for a Hamiltonian

Hamiltonian mechanics

Hamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without recourse to Lagrangian mechanics using sym...
system. In Hamiltonian dynamics, Liouville also introduced the notion of action-angle variables as a description of completely integrable systems. The modern formulation of this is sometimes called the Liouville-Arnold theorem, and the underlying concept of integrability is referred to as Liouville integrability.

The crater Liouville

Liouville (crater)

Liouville is a small moon impact crater that is located near the eastern limb of the Moon. It lies to the southeast of the larger crater Dubyago , and was previously designated Dubyago S before being given a name by the International Astronomical Union....
on the Moon

Moon

The Moon is Earth's only natural satellite and the List of natural satellites by diameter satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is km, about thirty times the diameter of the Earth....
is named after him.

Joseph Liouville

Life and work

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