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"Since my mathematical youth, I have been under the spell of the classical theory of Galois. This charm has forced me to return to it again and again."
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Évariste Galois[In the first case, the problem is solving equations, including solvin — Évariste Galois
"[In the first case, the problem is solving equations, including solving an algebraic equation with an unknown variable. In the second case, the problem is integrating differential equations. Galois was the first to recognize with absolute clarity how extraordinarily important the concepts of substitution group and invariant of a discontinuous group are for dealing with problems of the first kind.] Im ersten Falle hat man das Problem der Auflösung der Gleichungen, unter Anderm der Auflösung einer algebraischen Gleichung mit einer Unbekanuten. Im zweiten Falle hat man das Problem der Integration von Differentialgleichungen. Galois war der erste, der vollkommen klar erkannte, wie ausserordentlich wichtig die Begriffe Substiutionengruppe und Invariante einer discontinuirlichen Gruppe für die Behandlung von Problemen jener ersten Art sind."
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Évariste Galois
Évariste Galois
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Évariste Galois was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra.
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"[This] science is the work of the human mind, which is destined rather to study than to know, to seek the truth rather than to find it."
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Évariste GaloisQuote
"He was still a mere boy, yet within these short years he had accomplished enough to prove indubitably that he was one of the greatest mathematicians of all times."
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Évariste GaloisQuote
"Preserve my memory, since fate has not given me life enough for the country to know my name."
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Évariste GaloisQuote
"He had read... books of geometry as easily as a novel... No sooner had he begun to study algebra than he read Lagranges original memoirs. This extraordinary facility had been at first a revelation... but... it became more difficult for him to curb his own domineering thought and to sacrifice it to the routine of class work. ...By 1827 it had reached a critical point. This might be called the second crisis of his childhood: his scientific initiation. His change of mood was observed by the family. Juvenile gaiety was suddenly replaced by concentration; his manners became stranger every day. A mad desire to march forward along the solitary path... possessed him."
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Évariste GaloisQuote
"[We will not dwell further on the theory of transformation groups of a linear equation. We believe we have sufficiently demonstrated... the value of this theory, which is simply the natural extension to a question of analysis of the fruitful ideas introduced into algebra by Galois] Nous ninsisterons pas davantage sur la théorie des groupes de transformations dune équation linéaire. Nous pensons avoir suffisamment montré... lintérèt de cette théorie, qui nest que lextension bien naturelle à une question dAnalyse des idées si fécondes introduites en Algèbre par Galois."
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Évariste Galois