TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index G > Évariste Galois Quotes

Thumbnail of Évariste Galois (source)
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.
Science quotes on:  |  Abstract (141)  |  Abstract Mathematics (9)  |  Accretion (5)  |  Across (32)  |  Analysis (244)  |  Analyst (8)  |  Apply (170)  |  Arrive (40)  |  Chance (244)  |  Combination (150)  |  Combine (58)  |  Compare (76)  |  Deduce (27)  |  Do (1905)  |  Emerge (24)  |  Grow (247)  |  In Vain (12)  |  Juxtaposition (3)  |  Least (75)  |  Life (1870)  |  Mineral (66)  |  More (2558)  |  Must (1525)  |  Other (2233)  |  Particular (80)  |  Play (116)  |  Power (771)  |  Progress (492)  |  Research (753)  |  Resemble (65)  |  Result (700)  |  Role (86)  |  Rough (5)  |  Scientist (881)  |  Seek (218)  |  Series (153)  |  Side (236)  |  Solicit (2)  |  Sound (187)  |  Truth (1109)  |  Vain (86)  |  Work (1402)

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'.
Science quotes on:  |  19th Century (41)  |  Appearance (145)  |  Calculation (134)  |  Complexity (121)  |  Complicated (117)  |  Computation (28)  |  Elegance (40)  |  Future (467)  |  Group (83)  |  Impossible (263)  |  Mathematician (407)  |  Mission (23)  |  Modern (402)  |  Operation (221)  |  Procedure (48)  |  Progress (492)  |  Purpose (336)  |  Research (753)  |  Spirit (278)

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.
Science quotes on:  |  Author (175)  |  Book (413)  |  Concealment (10)  |  Difficulty (201)  |  Hurt (14)  |  Indicate (62)  |  Know (1538)  |  Knowledge (1647)  |  Little (717)  |  Most (1728)  |  Reader (42)  |  Recognition (93)  |  Scientific (955)  |  Unfortunately (40)  |  Worthwhile (18)



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.
Science quotes on:  |  Niels Henrik Abel (15)  |  Advance (298)  |  Age (509)  |  Art (680)  |  Do (1905)  |  Enough (341)  |  Expect (203)  |  Forget (125)  |  Game (104)  |  Great (1610)  |  Idea (881)  |  Know (1538)  |  Major (88)  |  Man (2252)  |  Mathematician (407)  |  Mathematics (1395)  |  More (2558)  |  Other (2233)  |  Past (355)  |  Srinivasa Ramanujan (17)  |  Single (365)  |  Still (614)  |  Work (1402)  |  Young (253)  |  Youth (109)

[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.
Science quotes on:  |  Book (413)  |  Boy (100)  |  Geometry (271)  |  Adrien-Marie Legendre (3)  |  Other (2233)  |  Pirate (2)  |  Read (308)  |  Yarn (2)  |  Young (253)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.