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Home > Dictionary of Science Quotations > Scientist Names Index G > Évariste Galois Quotes

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Évariste Galois
(25 Oct 1811 - 31 May 1832)

French mathematician famous for his contributions to group theory. He solved various long-unanswered questions, including the impossibility of trisecting the angle and squaring the circle. Galois died at age 20, fatally wounded in a duel.

Science Quotes by Évariste Galois (4 quotes)

If you now give me an equation that you have chosen at will, and you wish to know whether or not it is soluble by radicals, I will have nothing to do other than to indicate to you the way to respond to your question, without wishing to charge myself or anyone else with doing it. In a word, calculations are impracticable.
— Évariste Galois
As translated in Évariste Galois and Peter M. Neumann (ed. and trans.), The Mathematical Writings of Évariste Galois (2011), 227, with a new transcription of the original Galois manuscript. Earlier French publications are Oevres Mathématiques (1897), or Évariste Galois and Jules Tannery (ed.) Manuscrits de Évariste Galois (1908), 22. From the original French given in Neumann, “Si maintenant vous me donnez une équation que vous aurez choisie à votre gré, et que vous desiriez connaître si elle est ou non résoluble par radicaux, je n’aurai rien à y faire que de vous indiquer le moyen de répondre à votre question, sans vouloir charger ni moi ni personne de la faire. En un mot les calculs sont impraticables.”

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
English translation from manuscript, in Évariste Galois and Peter M. Neumann, 'Dossier 12: On the progress of pure analysis', The Mathematical Writings of Évariste Galois (2011), 263. A transcription of the original French is on page 262. In the following quote from that page, indicated deletions are omitted, and Webmaster uses parentheses to enclose indications of insertions above the original written line. “La science progresse par une série de combinaisons où le hazard ne joue pas le moindre rôle; sa vie est brute et ressemble à celle des minéraux qui croissent par juxtà position. Cela s’applique non seulement à la science telle qu’elle résulte des travaux d’une série de savants, mais aussi aux recherches particulières à chacun d’eux. En vain les analystes voudraient-ils se le dissimuler: (toute immatérielle qu’elle wst analyse n’est pas pas plus en notre pouvoir que des autres); ils ne déduisent pas, ils combinent, ils comparent: (il faut l’epier, la sonder, la solliciter) quand ils arrivent à la vérité, c’est en heurtant de côté et d’autre qu’il y sont tombés.” Webmaster corrected from typo “put” to “but” in the English text.
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Since the beginning of the century, computational procedures have become so complicated that any progress by those means has become impossible, without the elegance which modern mathematicians have brought to bear on their research, and by means of which the spirit comprehends quickly and in one step a great many computations.
It is clear that elegance, so vaunted and so aptly named, can have no other purpose. …
[But, the simplifications produced by this elegance will soon outrun the problems supplied by analysis. What happens then?]
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
From the preface to his final manuscript, 'Two Memoirs in Pure Analysis', written (Dec 1831) while he was in Sainte Pélagie prison. Translation as quoted by B. Melvin Kiernan, 'The Development of Galois Theory from Lagrange to Artin', Archive for History of Exact Sciences (30 Dec 1971), 8, No. 1/2, 92. [The sentence in brackets above, is how Kiernan summarizes Galois, at the ellipsis. Kiernan introduces the conclusion with his own question.] Kiernan cites in a footnote Ecrits et Mémoires, 9. The French 'Preface' was published for the first time in René Taton, 'Les relations d’Evariste Galois Avec Les Mathématiciens de Son Temps', Revue d’Histoire des Sciences (1949), 1, No. 1-2, 114-130. [Six months after writing his manuscript, Galois died in a duel (31 May 1832), at just 20 years old. In the papers he left after his death, he had established the foundation of the powerful Permutational Group Theory, hence “Group the Operations.” —Webmaster] The full Preface, in translation, is on the MacTutor website, titled, 'Évariste Galois’ Preface written in Sainte Pélagie'.
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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 most hurts his readers by concealing difficulties.
— Évariste Galois
English version as given in Nicholas J. Rose, Mathematical Maxims and Minims (1988). Also seen (without citation) as an epigraph in Morris Kline, Mathematical Thought From Ancient to Modern Times (1990), Vol. 2, 752. From the original French, “C’est que, malheureusement, on ne se doute pas que le livre le plus précieux du plus savant serait celui où il dirait tout ce qu’il ne sait pas, c’est qu’on ne se doute pas qu’un auteur ne nuit* jamais tant à ses lecteurs que quand il dissimule une difficulté.” In 'Deux Mémoires d’Analyse Pure par E. Galois: Préface' (8 Oct 1831), collected in Jules Tannery (ed.), Manuscrits de Évariste Galois (1908), 27. A footnote indicates that the word “nuit” comes from an indistinct original. Since “nuit” (night) is an obvious error, Webmaster suggests the word “bruit” might make better sense, but is open to a better suggestion.
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Quotes by others about Évariste Galois (2)

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
In A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.
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[As a young teenager] Galois read [Legendre's] geometry from cover to cover as easily as other boys read a pirate yarn.
Men of Mathematics (1937, 1986), 364.
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See also:
  • 25 Oct - short biography, births, deaths and events on date of Galois's birth.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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