(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 Ă‰variste 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.
— Ă‰variste Galois
As translated in Ă‰variste Galois and Peter M. Neumann (ed. and trans.), The Mathematical Writings of Ă‰variste Galois (2011), 227, with a new transcription of the original Galois manuscript.
Earlier French publications are Oevres MathĂ©matiques (1897), or Ă‰variste Galois and Jules Tannery (ed.) Manuscrits de Ă‰variste Galois (1908), 22. From the original French given in Neumann, â€śSi maintenant vous me donnez une Ă©quation que vous aurez choisie Ă votre grĂ©, et que vous desiriez connaĂ®tre si elle est ou non rĂ©soluble par radicaux, je nâ€™aurai rien Ă y faire que de vous indiquer le moyen de rĂ©pondre Ă votre question, sans vouloir charger ni moi ni personne de la faire. En un mot les calculs sont impraticables.â€ť
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.
— Ă‰variste Galois
English translation from manuscript, in Ă‰variste Galois and Peter M. Neumann, 'Dossier 12: On the progress of pure analysis', The Mathematical Writings of Ă‰variste 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. â€śLa science progresse par une sĂ©rie de combinaisons oĂą le hazard ne joue pas le moindre rĂ´le; sa vie est brute et ressemble Ă celle des minĂ©raux qui croissent par juxtĂ position. Cela sâ€™applique non seulement Ă la science telle quâ€™elle rĂ©sulte des travaux dâ€™une sĂ©rie de savants, mais aussi aux recherches particuliĂ¨res Ă chacun dâ€™eux. En vain les analystes voudraient-ils se le dissimuler: (toute immatĂ©rielle quâ€™elle wst analyse nâ€™est pas pas plus en notre pouvoir que des autres); ils ne dĂ©duisent pas, ils combinent, ils comparent: (il faut lâ€™epier, la sonder, la solliciter) quand ils arrivent Ă la vĂ©ritĂ©, câ€™est en heurtant de cĂ´tĂ© et dâ€™autre quâ€™il y sont tombĂ©s.â€ť Webmaster corrected from typo â€śputâ€ť to â€śbutâ€ť in the English text.
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. â€¦
[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.
— Ă‰variste Galois
From the preface to his final manuscript, 'Two Memoirs in Pure Analysis', written (Dec 1831) while he was in Sainte PĂ©lagie 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 MĂ©moires, 9. The French 'Preface' was published for the first time in RenĂ© Taton, 'Les relations dâ€™Evariste Galois Avec Les MathĂ©maticiens de Son Temps', Revue dâ€™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 â€śGroup the Operations.â€ť â€”Webmaster] The full Preface, in translation, is on the MacTutor website, titled, 'Ă‰variste Galoisâ€™ Preface written in Sainte PĂ©lagie'.
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.
— Ă‰variste 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, â€śCâ€™est que, malheureusement, on ne se doute pas que le livre le plus prĂ©cieux du plus savant serait celui oĂą il dirait tout ce quâ€™il ne sait pas, câ€™est quâ€™on ne se doute pas quâ€™un auteur ne nuit* jamais tant Ă ses lecteurs que quand il dissimule une difficultĂ©.â€ť In 'Deux MĂ©moires dâ€™Analyse Pure par E. Galois: PrĂ©face' (8 Oct 1831), collected in Jules Tannery (ed.), Manuscrits de Ă‰variste Galois (1908), 27. A footnote indicates that the word â€śnuitâ€ť comes from an indistinct original. Since â€śnuitâ€ť (night) is an obvious error, Webmaster suggests the word â€śbruitâ€ť might make better sense, but is open to a better suggestion.
Quotes by others about Ă‰variste 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. â€¦ 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; â€¦ [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. â€¦ 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.
[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.
- - short biography, births, deaths and events on date of Galois's birth. 25 Oct