David Hilbert Quotes

Quotes about:

• Some people have got a mental horizon of radius zero and call it their point of view.

  David Hilbert

  Zero, Views, People

  68 Copy quote

• Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

  David Hilbert

  Country, Math, Race

  "Mathematical Circles Revisited". Book by Howard Whitley Eves, 1971.

  96 Copy quote

• Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

  David Hilbert

  Sad, Zero, Men

  "Hilbert - Courant". Book by Constance Reid, p. 104, 1984.

  80 Copy quote

• Mathematics is a game played according to certain simple rules with meaningless marks on paper.

  David Hilbert

  Math, Simple, Games

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• Begin with the simplest examples.

  David Hilbert

  Example, Simplest

  "Hilbert - Courant". Book by Constance Reid, p. 104, 1984.

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• 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

  Men, Ideas, Needs

  "Über das Unendliche" ["On the Infinite"] (1925) address to der Westfälischen Mathematischen Gesellschaft in honour to the memory of Karl Weierstrass, as quoted in "Number The Language of Science" by Tobias Dantzig, 1930.

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• Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.

  David Hilbert

  Maturity, Degrees, Kind

  "Axiomatic Thought (1918)". "From Kant to Hilbert: a source book in the foundations of mathematics". Book by William Bragg Ewald, 1996.

  17 Copy quote

• 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

  Years, Would Be, Awakening

  "Mathematical Mysteries: The Beauty and Magic of Numbers". Book by Calvin C. Clawson, p. 258, 1999.

  65 Copy quote

• The art of doing mathematics consists in finding that special case which contains all the germs of generality.

  David Hilbert

  Art, Math, Special

  "Hilbert". Book by Constance Reid, 1970.

  41 Copy quote

• He who seeks for methods without having a definite problem in mind seeks in the most part in vain.

  David Hilbert

  Science, Mind, Problem

  37 Copy quote

• One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it

  David Hilbert

  Work, Math, Science

  Quoted in Howard Eves, Mathematical Circles Revisited (1971)

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• A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

  David Hilbert

  Successful, Order, Effort

  "Mathematical Problems". Lecture delivered before the International Congress of Mathematicians at Paris, translated by Maby Winton Newson, mathcs.clarku.edu. 1900.

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• Physics is becoming too difficult for the physicists.

  David Hilbert

  Becoming, Physics, Difficult

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• For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We must know - we will know!"

  David Hilbert

  Knowledge, Science, Knows

  Address to the Society of German Scientists and Physicians, in Königsberg, September 08, 1930.

  45 Copy quote

• Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.

  David Hilbert

  Knowledge, Tombs, Knows

  7 Copy quote

• 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

  Stupid, Men, Astrology

  "Comic Sections". Book by Desmond MacHale, 1993.

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• One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs

  David Hilbert

  Beer, Lines, Tables

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• I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.

  David Hilbert

  School, Mathematics, Hard

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• 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

  Believe, Math, Errors

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• Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.

  David Hilbert

  Understanding, Consistency, Intuition

  "Grundlagen der Mathematik". Book by David Hilbert, 1927.

  32 Copy quote

• The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

  David Hilbert

  Practice, Bridges, Giving

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• Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.

  David Hilbert

  Discipline, Three, Development

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• 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 manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.

  David Hilbert

  Stress, Hands, Two

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• 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

  Time, Believe, Math

  "Mathematical Circles Squared : A Third Collection of Mathematical Stories and Anecdotes" by Howard Whitley Eves, (p. 125), 1972.

  31 Copy quote

• Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

  David Hilbert

  Simple, Small Numbers, Principles

  David Hilbert (1910). “The Foundations of Geometry”

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