David Hilbert Quotes - Page 2

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• However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.

  David Hilbert

  Finite Number, Numbers, May

  27 Copy quote

• As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.

  David Hilbert

  Independent, Long, Development

  12 Copy quote

• Geometry is the most complete science.

  David Hilbert

  Science, Geometry

  14 Copy quote

• 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

  Time, Real, Math

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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.

  33 Copy quote

• Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

  David Hilbert

  Ontology, Vitality, Connections

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

  22 Copy quote

• 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

  Men, Perfect, Ease

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

  17 Copy quote

• 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

  Development, Paradise, Creation

  5 Copy quote

• 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

  Math, Science, Doe

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

  34 Copy quote

• 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 leading mathematical spirits of coming generations will strive? What new methods and new facts in the
  wide and rich field of mathematical thought will the new centuries disclose?

  David Hilbert

  Lying, Goal, Secret

  4 Copy quote

• Keep computations to the lowest level of the multiplication table.

  David Hilbert

  Levels, Tables, Multiplication

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

  9 Copy quote

• 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

  17 Copy quote

• 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

  Believe, Science, Facts

  32 Copy quote

• We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

  David Hilbert

  Theory, Masters, Mathematical

  4 Copy quote

• 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

  Confused, Mean, Games

  15 Copy quote

• 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

  Sex, Rejection, Discrimination

  4 Copy quote

• The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

  David Hilbert

  Math, Figures, Diagrams

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• 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

  Time, Math, Should Have

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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

  Math, Ideas, Long

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• Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.

  David Hilbert

  Fate, Champion, Suffering

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• We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know.

  David Hilbert

  Philosophical, Believe, Self

  8 Copy quote

• [On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

  David Hilbert

  Discovery, Achievement, Intellectual

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• 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

  Sex, Firsts, Discrimination

  6 Copy quote

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