David Hilbert quotes
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“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”
-- David HilbertSource : "Mathematical Circles Revisited". Book by Howard Whitley Eves, 1971.
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“Mathematics is a game played according to certain simple rules with meaningless marks on paper.”
-- David Hilbert -
“Begin with the simplest examples.”
-- David HilbertSource : "Hilbert - Courant". Book by Constance Reid, p. 104, 1984.
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“The further 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 -
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“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 HilbertSource : "Hilbert - Courant". Book by Constance Reid, p. 104, 1984.
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“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 -
“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 HilbertSource : "Mathematical Circles Squared : A Third Collection of Mathematical Stories and Anecdotes" by Howard Whitley Eves, (p. 125), 1972.
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“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?”
-- David HilbertSource : "Mathematical Mysteries: The Beauty and Magic of Numbers". Book by Calvin C. Clawson, p. 258, 1999.
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“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 -
“Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.”
-- David Hilbert -
“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 HilbertSource : "Comic Sections". Book by Desmond MacHale, 1993.
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“Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.”
-- David Hilbert -
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“The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.”
-- David Hilbert -
“The art of doing mathematics consists in finding that special case which contains all the germs of generality”
-- David HilbertSource : "Hilbert". Book by Constance Reid, 1970.
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“Physics is becoming too difficult for the physicists.”
-- David Hilbert -
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“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 -
“Some people have got a mental horizon of radius zero and call it their point of view.”
-- David Hilbert -
“An old French mathematician said: 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. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.”
-- David Hilbert -
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“One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it”
-- David HilbertSource : Quoted in Howard Eves, Mathematical Circles Revisited (1971)
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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 HilbertSource : "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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“One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs”
-- David Hilbert -
“The infinite! No other question has ever moved so profoundly the spirit of man.”
-- David Hilbert -
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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 -
“He who seeks for methods without having a definite problem in mind seeks in the most part in vain.”
-- David Hilbert -
“Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.”
-- David Hilbert -
“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 HilbertSource : Kurt Gödel, S. Feferman (1986). “Kurt Gödel: Collected Works: Volume I: Publications 1929-1936”, p.145, Oxford University Press
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“I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.”
-- David Hilbert -
“Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.”
-- David Hilbert -
“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 -
“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 -
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“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 -
“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 HilbertSource : "Grundlagen der Mathematik". Book by David Hilbert, 1927.
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“Keep computations to the lowest level of the multiplication table.”
-- David Hilbert -
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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 HilbertSource : "Axiomatic Thought (1918)". "From Kant to Hilbert: a source book in the foundations of mathematics". Book by William Bragg Ewald, 1996.
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“[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.”
-- David Hilbert
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