* 1832 – Évariste Galois is released from prison.

Évariste Galois () ( 25 October 1811 – 31 May 1832 ) was a French mathematician born in Bourg-la-Reine.

On 2 June, Évariste Galois was buried in a common grave of the Montparnasse cemetery whose exact location is unknown.

* La vie d ' Évariste Galois by Paul Dupuy The first and still one of the most extensive biographies, referred to by every other serious biographer of Galois

* Évariste Galois at Mathematics Genealogy Project.

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Lie's idée fixe was to develop a theory of symmetries of differential equations that would accomplish for them what Évariste Galois had done for algebraic equations: namely, to classify them in terms of group theory.

Évariste Galois was the first to realize the importance of the existence of normal subgroups.

Simple groups have been studied at least since early Galois theory, where Évariste Galois realized that the fact that the alternating groups on five or more points was simple ( and hence not solvable ), which he proved in 1831, was the reason that one could not solve the quintic in radicals.

While Ruffini and Abel established that the general quintic could not be solved, some particular quintics can be solved, such as ( x − 1 )< sup > 5 </ sup >= 0, and the precise criterion by which a given quintic or higher polynomial could be determined to be solvable or not was given by Évariste Galois, who showed that whether a polynomial was solvable or not was equivalent to whether or not the permutation group of its roots – in modern terms, its Galois group – had a certain structure – in modern terms, whether or not it was a solvable group.

The general linear group over a prime field, GL ( ν, p ), was constructed and its order computed by Évariste Galois in 1832, in his last letter ( to Chevalier ) and second ( of three ) attached manuscripts, which he used in the context of studying the Galois group of the general equation of order p < sup > ν </ sup >.

The precise criterion that distinguishes between those equations that can be solved by radicals and those that cannot was given by Évariste Galois and is now part of Galois theory: a polynomial equation can be solved by radicals if and only if its Galois group ( over the rational numbers, or more generally over the base field of admitted constants ) is a solvable group.

Terquem was among the first who recognized the importance of the work of Évariste Galois.

The concept of field was used implicitly by Niels Henrik Abel and Évariste Galois in their work on the solvability of equations.

The notes left by Évariste Galois prior to dying in a duel in 1832 later led to an elegant complete theory of the roots of polynomials, of which this theorem was one result.

Évariste Régis Huc, or Abbé Huc, ( 1813 – 1860 ) was a French missionary traveller, famous for his accounts of China, Tartary and Tibet.

When Évariste was twenty-four, he entered the congregation of the Lazarists ( also known as Vincentians ) at Paris.

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.

Évariste Desiré de Forges, vicomte de Parny ( February 6, 1753 on the Isle of Bourbon ( Reunion ) – December 5, 1814, Paris, France ) was a French poet.

This was the original point of view of Évariste Galois.

He was influenced by reading Évariste Régis Huc's Recollections of a Journey Through Tartary, Thibet, and China in 1852, which extolled the camel's virtues.

In abstract algebra, a finite field or Galois field ( so named in honor of Évariste Galois ) is a field that contains a finite number of elements.

The study of field extensions ( and polynomials which give rise to them ) via Galois groups is called Galois theory, so named in honor of Évariste Galois who first discovered them.

In 1830, Évariste Galois, studying the permutations of the roots of a polynomial, extended Abel-Ruffini theorem by showing that, given a polynomial equation, one may decide if it is solvable by radicals, and, if it is, solve it.

Niels Henrik Abel ( 1802 – 1829 ), a Norwegian, and Évariste Galois, ( 1811 – 1832 ) a Frenchman, investigated into the solutions of various polynomial equations, and proved that there is no general algebraic solution to equations of degree greater than four ( Abel – Ruffini theorem ).

Galois theory, named after Évariste Galois, were introduced to give criteria deciding if an equation is solvable using radicals.

The finite field with p < sup > n </ sup > elements is denoted GF ( p < sup > n </ sup >) and is also called the Galois Field, in honor of the founder of finite field theory, Évariste Galois.

He considers that Rolle's theorem for example, though it is of some importance for calculus, cannot be compared to the elegance and preeminence of the mathematics produced by Leonhard Euler or Évariste Galois and other pure mathematicians.

Nomos Alpha is a piece for solo cello composed by Iannis Xenakis in 1965, commissioned by Radio Bremen for cellist Siegfried Palm, and dedicated to mathematicians Aristoxenus of Tarentum, Évariste Galois, and Felix Klein.

* The resolvent ( Galois theory ) for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has a rational root if and only if the Galois group of p is included in G. Resolvents were introduced by Joseph Louis Lagrange and systematically used by Évariste Galois.

This terminology has been introduced in his last letter by Évariste Galois who called ( in French ) equation primitive an equation whose Galois group is primitive.