Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “We are here to celebrate the completion of the first survey of the entire human genome. Without a doubt, this is the most important, most wondrous map ever produced by human kind.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index H > David Hilbert Quotes

Thumbnail of David Hilbert (source)
David Hilbert
(23 Jan 1862 - 14 Feb 1943)

German mathematician.


Science Quotes by David Hilbert (31 quotes)

>> Click for David Hilbert Quotes on | Mathematics |

(On Cantor’s set theory:) The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
— David Hilbert
…...
Science quotes on:  |  Achievement (128)  |  Activity (97)  |  Fine (24)  |  Genius (186)  |  Human (445)  |  Intellectual (79)  |  Mathematics (587)  |  Product (72)  |  Purely (15)  |  Set Theory (3)  |  Supreme (24)

Meine Herren, der Senat ist doch keine Badeanstalt.
The faculty is not a pool changing room.
Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.
— David Hilbert
Quoted in A L Mackay, Dictionary of Scientific Quotations (1994).
Science quotes on:  |  Discrimination (5)  |  Emmy Noether (6)

Wir mussen wissen. Wir werden wissen.
We must know. We will know.
Inscribed on his tomb in Gilttingen.
— David Hilbert
Lecture at Konigsberg, 1930. Gesammelte Abhandlungen, Vol. 3, 387, trans. Ivor Grattan-Guinness.
Science quotes on:  |  Epitaph (19)  |  Knowledge (1128)

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
— David Hilbert
…...
Science quotes on:  |  Clear (52)  |  Complete (43)  |  Consider (45)  |  Explain (61)  |  First (174)  |  Mathematics (587)  |  Meet (16)  |  Street (17)  |  Theory (582)

Before beginning I should put in three years of intensive study, and I haven’t that much time to squander on a probable failure.
— David Hilbert
Answering (1920) why he did not attempt a proof of Fermat's last theorem. As quoted, without citation, by Eric Temple Bell, Mathematics, Queen and Servant of Science (1951, 1961), 238. Collected in 'The Queen of Mathematics', The World of Mathematics (1956), Vol. 1, 510.
Science quotes on:  |  Beginning (114)  |  Failure (118)  |  Intensive (7)  |  Probable (14)  |  Study (331)  |  Time (439)  |  Year (214)

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
— David Hilbert
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 441.
Science quotes on:  |  Rigour (10)  |  Simplicity (126)

Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
— David Hilbert
Quoted in R Remmert, Theory of complex functions (New York, 1989).
Science quotes on:  |  Critical (34)  |  Development (228)  |  Discipline (38)  |  Formal (11)  |  Mathematics (587)  |  Naive (8)  |  Period (49)

From time immemorial, the infinite has stirred men's emotions more than any other question. Hardly any other idea has stimulated the mind so fruitfully. Yet, no other concept needs clarification more than it does.
— David Hilbert
In address (4 Jun 1925), at a congress of the Westphalian Mathematical Society in Munster, in honor of Karl Weierstrass. First published in Mathematische Annalen (1926), 95, 161-190. Translated by Erna Putnam and Gerald J. Massey as 'On the Infinite', collected in Paul Benacerraf (ed.) Philosophy of Mathematics: Selected Readings (1983), 185. Compare another translation elsewhere on this page, beginning, “The Infinite!…”.
Science quotes on:  |  Clarification (6)  |  Concept (102)  |  Emotion (62)  |  Fruitful (31)  |  Idea (440)  |  Immemorial (3)  |  Infinite (88)  |  Mind (544)  |  Need (211)  |  Question (315)  |  Stimulate (9)  |  Stirred (3)  |  Time (439)

Galileo was no idiot. Only an idiot could believe that science requires martyrdom—that may be necessary in religion, but in time a scientific result will establish itself.
— David Hilbert
As quoted, without citation, in Harold Eves, Mathematical Circles Squared (1971). Collected in Bill Swainson, The Encarta Book of Quotations (2000), 361.
Science quotes on:  |  Belief (400)  |  Establish (30)  |  Galileo Galilei (101)  |  Idiot (14)  |  Martyrdom (2)  |  Necessary (89)  |  Religion (210)  |  Requirement (45)  |  Result (250)  |  Science (1699)  |  Scientific (169)  |  Time (439)

Geometry is the most complete science.
— David Hilbert
Quotation noted by Ivor Grattan-Guinness from unpublished Hilbert lecture course on Geometry.
Science quotes on:  |  Geometry (99)

He who seeks for methods without having a definite problem in mind seeks for the most part in vain.
— David Hilbert
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 444.
Science quotes on:  |  Method (154)  |  Problem (362)

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
— David Hilbert
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479. As quoted and cited in Robert Ιdouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 94-95. It is reprinted in Jeremy Gray, The Hilbert Challenge (2000), 282.
Science quotes on:  |  Advance (123)  |  Complicated (38)  |  Development (228)  |  Ingrained (4)  |  Invention (283)  |  Mathematics (587)  |  Method (154)  |  Sharp (12)  |  Simpler (5)  |  Theory (582)  |  Thoroughly (7)  |  Tool (70)  |  Understanding (317)

I have tried to avoid long numerical computations, thereby following Riemann’s postulate that proofs should be given through ideas and not voluminous computations.
— David Hilbert
In Report on Number Theory (1897). As given in epigraph, without citation, in Eberhard Zeidler and Juergen Quandt (trans.), Nonlinear Functional Analysis and its Applications: IV: Applications to Mathematical Physics (2013), 448.
Science quotes on:  |  Avoid (34)  |  Computation (11)  |  Idea (440)  |  Long (95)  |  Number (179)  |  Postulate (23)  |  Proof (192)  |  Bernhard Riemann (2)  |  Try (103)

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
— David Hilbert
…...
Science quotes on:  |  Awaken (8)  |  First (174)  |  Hypothesis (227)  |  Prove (60)  |  Question (315)  |  Sleep (42)  |  Thousand (106)  |  Year (214)

If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.
— David Hilbert
Quoted in D MacHale, Comic Sections (Dublin 1993)
Science quotes on:  |  Ask (99)  |  Astrology (35)  |  Bring (53)  |  Discover (115)  |  Existence (254)  |  Stupid (15)  |  Together (48)  |  Wise (43)  |  World (667)

In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly
— David Hilbert
Geometry and the imagination (New York, 1952).
Science quotes on:  |  Abstraction (29)  |  Correlate (3)  |  Find (248)  |  Hand (103)  |  Inherent (27)  |  Logical (20)  |  Material (124)  |  Mathematics (587)  |  Maze (9)  |  Orderly (6)  |  Present (103)  |  Relation (96)  |  Seek (57)  |  Study (331)  |  Systematic (25)  |  Tendency (40)

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
— David Hilbert
…...
Science quotes on:  |  Condition (119)  |  Connection (86)  |  Indivisible (7)  |  Mathematics (587)  |  Opinion (146)  |  Organism (126)  |  Part (146)  |  Science (1699)  |  Vitality (10)  |  Whole (122)

Mathematics is a game played according to certain simple rules with meaningless marks on paper.
— David Hilbert
Given as narrative, without quotation marks, in Eric Temple Bell, Mathematics, Queen and Servant of Science (1951, 1961), 21.
Science quotes on:  |  Game (45)  |  Mark (28)  |  Mathematics (587)  |  Meaningless (15)  |  Paper (52)  |  Play (60)  |  Rule (135)  |  Simple (111)

Mathematics is that peculiar science in which the importance of a work can be measured by the number of earlier publications rendered superfluous by it.
— David Hilbert
As stated in narrative, without quotation marks, in Joong Fang, Bourbaki (1970), 18, citing “as Hilbert declared at the end of his famous paper on the twenty-three unsolved problems.” Webmaster has not identified this in that paper, however. Also quoted, without citation, in Harold Eves, Mathematical Circles Revisited (1971), as “One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.”
Science quotes on:  |  Importance (183)  |  Mathematics (587)  |  Measurement (148)  |  Number (179)  |  Peculiar (24)  |  Publication (83)  |  Science (1699)  |  Superfluous (8)  |  Work (457)

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
— David Hilbert
In H. Eves, Mathematical Circles Squared (1972). As cited in Anton Zettl, Sturm-Liouville Theory (2005), 171.
Science quotes on:  |  Boundary (27)  |  Country (121)  |  Cultural (16)  |  Geographic (2)  |  Knowledge (1128)  |  Mathematics (587)  |  Race (76)  |  World (667)

Meine Herren, I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bathhouse.
Objecting to sex discrimination being the reason for rejection of Emmy Noether's application to join the faculty at the University of Gottingen.
— David Hilbert
Quoted in C. Reid Hilbert: With an appreciation of Hilbert's Mathematical Work by Hermann Weyl (1970), 143.
Science quotes on:  |  Emmy Noether (6)

No one shall expel us from the paradise which Cantor has created for us.
Expressing the importance of Cantor's set theory in the development of mathematics.
— David Hilbert
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 33.
Science quotes on:  |  Georg Cantor (4)  |  Creation (211)  |  Mathematics (587)  |  Paradise (7)  |  Set Theory (3)

One hears a lot of talk about the hostility between scientists and engineers. I don't believe in any such thing. In fact I am quite certain it is untrue... There cannot possibly be anything in it because neither side has anything to do with the other.
— David Hilbert
Quoted in A. Rosenfeld, Langmuir: The Man and the Scientist (1962), 57.
Science quotes on:  |  Engineer (72)  |  Hostility (10)  |  Scientist (447)

Physics is becoming too difficult for the physicists.
— David Hilbert
Quoted in C Reid, Hilbert (London 1970)
Science quotes on:  |  Become (100)  |  Difficult (62)  |  Physicist (130)  |  Physics (301)

The art of doing mathematics consists in finding that special case which contains all the germs of generality.
— David Hilbert
Attributed, perhaps apocryphal. As given in Felix E. Browder, Norbert Wiener (1966), 65.
Science quotes on:  |  Art (205)  |  Case (64)  |  Contain (37)  |  Containing (4)  |  Find (248)  |  Finding (30)  |  Generality (22)  |  Germ (27)  |  Mathematics (587)  |  Special (51)

The art of doing mathematics consists in finding that special case which contains all the germs of generality.
— David Hilbert
Stated without quotation marks, as “attributed apocryphally perhaps”, in M. Kac, 'Wiener and Integration in Function Spaces', Bulletin of the American Mathematical Society (Jan 1966), 72, No. 1, Part 2, 65.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.
— David Hilbert
Attributed (apocryphally perhaps). As cited in Bulletin of the American Mathematical Society (1966), 72, 65.

The farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
— David Hilbert
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479.
Science quotes on:  |  Branch (61)  |  Construction (69)  |  Developed (8)  |  Harmonious (4)  |  Mathematics (587)  |  Proceed (25)  |  Relation (96)  |  Science (1699)  |  Separate (46)  |  Theory (582)  |  Uniform (14)  |  Unsuspected (5)

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
— David Hilbert
Address in memory of Karl Weierstrass. As quoted in Journal of the University of Bombay (1933), 2, 201. Also in Tobias Dantzig, Number: The Language of Science (1937), 237. Also partially quoted as epigraph in in James Roy Newman, The World of Mathematics (1956), Vol. 3, 1593. which dates the address as 1921. Another translation for perhaps the same address ('On the Infinite'), in honor of Weierstrass, dates it as 4 Jun 1925, in Paul Benacerraf (ed.) Philosophy of Mathematics (1983), 183. See this alternate version elsewhere on this page, beginning, “From time immemorial…”.
Science quotes on:  |  Clarification (6)  |  Concept (102)  |  Fruitful (31)  |  Greater (36)  |  Idea (440)  |  Infinite (88)  |  Intellect (157)  |  Move (58)  |  Need (211)  |  Profound (46)  |  Question (315)  |  Spirit (113)  |  Stand (60)  |  Stimulate (9)

The most suggestive and notable achievement of the last century is the discovery of Non-Euclidean geometry.
— David Hilbert
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
Science quotes on:  |  Achievement (128)  |  Century (94)  |  Discovery (591)  |  Geometry (99)  |  Non-Euclidean (2)  |  Notable (2)  |  Suggestive (3)

Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the lead
— David Hilbert
Opening of his speech to the 1900 Congress in Paris.
Science quotes on:  |  Advance (123)  |  Behind (25)  |  Cast (15)  |  Century (94)  |  Development (228)  |  Future (229)  |  Glad (4)  |  Glance (8)  |  Goal (81)  |  Hide (36)  |  Lead (101)  |  Lie (80)  |  Lift (17)  |  Next (23)  |  Particular (54)  |  Science (1699)  |  Secret (98)  |  Toward (29)  |  Veil (12)



Quotes by others about David Hilbert (4)

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.
In A History of Geometrical Methods (1940, reprint 2003), 423.
Science quotes on:  |  Arbitrary (16)  |  Consistent (10)  |  Influence (110)  |  Interesting (38)  |  Lead (101)  |  Postulate (23)  |  Unproven (3)

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
In Axiomatic Set Theory (1971), 9-15. In Thomas Tymoczko, New Directions in the Philosophy of Mathematics: an Anthology (), 11-12.
Science quotes on:  |  Appeal (30)  |  Average (31)  |  Choice (64)  |  Consistency (21)  |  Difficulty (113)  |  Enjoyment (27)  |  Formal (11)  |  Formalism (5)  |  Game (45)  |  Mathematician (177)  |  Security (27)  |  Set Theory (3)  |  Shelter (13)  |  Work (457)

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
Science quotes on:  |  Ability (75)  |  Assignment (10)  |  Discourse (13)  |  Eminence (11)  |  G. H. Hardy (69)  |  Informal (3)  |  John Edensor (J. E.) Littlewood (5)  |  Mathematician (177)  |  Mathematics (587)  |  Natural (128)  |  Srinivasa Ramanujan (15)  |  Scale (49)

Das ist nicht Mathematik, das ist Theologie!
This is not mathematics; this is theology.
[Remark about David Hilbert's first proof of his finite basis theorem.]
Attributed. It does not seem to appear in Gordan's written work. According to Colin McClarty, in 'Theology and its Discontents: the Origin of the Myth of Modern Mathematics' (2008), “The quote first appeared a quarter of a century after the event, as an unexplained side comment in a eulogy to Gordan by his long-time colleague Max Noether. Noether was a reliable witness ... but he says little about what Gordan meant.” See Noether's obituary of Gordan in Mathematische Annalen (1914), 75, 18. It is still debated if the quote is pejorative, complimentary or merely a joke.
Science quotes on:  |  Joke (39)  |  Mathematics (587)  |  Theology (35)


See also:

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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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 |

- 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



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