David Hilbert Quotes About Mathematics

Quotes about: Mathematics

• 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.

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

  David Hilbert

  Math, Simple, Games

• 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

• 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

• 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.

• 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.

• 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.

• The infinite! No other question has ever moved so profoundly the spirit of man.

  David Hilbert

  Math, Men, Spirit

  "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.

• 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.

• 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.

• 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

• Physics is much too hard for physicists.

  David Hilbert

  Math, Physics, Physicist

• 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

• 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.

• 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)

• 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

• 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

• 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

• 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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