Évariste Galois - Collected Quotes

"It is clear that such elegance, so vaunted and so aptly named, has no other goal. From the well established fact that the efforts of the most advanced mathematicians have elegance as their object, one may therefore conclude with certainty that it becomes more and more necessary to embrace several operations at once because the mind does not have the time any more to stop at details." (Évariste Galois, "Two memoirs in pure analysis", 1831)

"Long algebraic calculations were at first hardly necessary for progress in Mathematics; the very simple theorems hardly gained from being translated into the language of analysis. It is only since Euler that this briefer language has become indispensable to the new extensions which this great mathematician has given to science. Since Euler calculations have become more and more necessary but more and more difficult, at least insofar as they are applied to the most advanced objects of science. Since the beginning of this century computational procedures have attained such a degree of complication that any progress had become impossible by these means, except with the elegance with which new modern mathematicians have believed they should bring to their research, and by means of which the mind promptly and with a single glance comprehends a large number of operations." (Évariste Galois, "Two memoirs in pure analysis", 1831)

"Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author never does more damage to his readers than when he hides a difficulty." (Évariste Galois, "Deux mémoires d'Analyse pure", 1831)

"Concerning the theory of equations, I have tried to find out under what circumstances equations are solvable by radicals, which gave me the opportunity of investigating thoroughly, and describing, all transformations possible on an equation, even if it is the case that it is not solvable by radicals." (Évariste Galois, [letter to Auguste Chevalier] 1832)

"From the beginning of this century, computational procedures have become so complicated that any progress by those means has become impossible." (Évariste Galois)

"Go to the roots of these calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe, is the mission of future mathematicians. This is the road on which I am embarking in this work." (Évariste Galois)

"It seems there is no fruit to be drawn from the solution we offer." (Évariste Galois)

"[Mathematics] 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." (Évariste Galois)

"Science progresses by a series of combinations in which chance plays not the least role. Its life is rough and resembles that of minerals which grow by juxtaposition [accretion]. This applies not only to science such as it emerges [results] from the work of a series of scientists, but also to the particular research of each one of them. In vain would analysts dissimulate: (however abstract it may be, analysis is no more our power than that of others); they do not deduce, they combine, they compare: (it must be sought out, sounded out, solicited.) When they arrive at the truth it is by cannoning from one side to another that they come across it." (Évariste Galois)

"The analysts try in vain to conceal the fact that they do not deduce: they combine, they compose [...] when they do arrive at the truth they stumble over it after groping their way along." (Évariste Galois)