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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
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David Hilbert's Popular Quotes

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds th…

- David Hilbert

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

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 stan…

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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 understa…

- David Hilbert

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

- David Hilbert

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

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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

Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific resul…

- David Hilbert

Begin with the simplest examples.

- David Hilbert
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