mathematical-science-is-in-my-opinion-an-indivisible-whole-an-organism-whose-vitality-is-conditioned-upon-the-connection-of-its-parts

mathematics-is-a-game-played-according-to-certain-simple-rules-with-meaningless-marks-on-paper

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**

in-mathematics-we-find-two-tendencies-present-on-one-hand-tendency-towards-abstraction-seeks-to-crystallise-logical-relations-inherent-in-maze-david-hilbert

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keep-computations-to-lowest-level-multiplication-table-david-hilbert

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 ofour science and at the secrets of its development during future centuries? What particular goals will there be towardwhich the leading mathematical spirits of coming generations will strive? What new methods and new facts in thewide and rich field of mathematical thought will the new centuries disclose?

**David Hilbert**

who-us-would-not-be-glad-to-lift-veil-behind-which-future-lies-hidden-to-cast-glance-at-next-advances-ofour-science-at-secrets-its-development-david-hilbert

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if-i-were-to-awaken-after-having-slept-for-thousand-years-my-first-question-would-be-has-riemann-hypothesis-been-proven-david-hilbert

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**

we-ought-not-to-believe-those-who-today-adopting-philosophical-air-with-tone-superiority-prophesy-decline-culter-are-content-with-unknowable-david-hilbert

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physics-is-becoming-too-difficult-for-physicists-david-hilbert

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**

besides-it-is-error-to-believe-that-rigour-is-enemy-simplicity-on-contrary-we-find-it-confirmed-by-numerous-examples-that-rigorous-method-is-at-david-hilbert

on-cantors-work-the-finest-product-mathematical-genius-one-supreme-achievements-purely-intellectual-human-activity-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**

an-old-french-mathematician-said-a-mathematical-theory-is-not-to-be-considered-complete-until-you-have-made-it-clear-that-you-can-explain-it-to-david-hilbert

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one-must-be-able-to-say-at-all-timesinstead-points-straight-lines-planestables-chairs-beer-mugs-david-hilbert

the-art-doing-mathematics-consists-in-finding-that-special-case-which-contains-all-germs-generality-david-hilbert

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**

i-do-not-want-to-presuppose-anything-as-known-i-see-in-my-explanation-in-section-1-definition-concepts-point-straight-line-plane-if-one-adds-to-david-hilbert

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every-mathematical-discipline-goes-through-three-periods-development-naive-formal-critical-david-hilbert

he-who-seeks-for-methods-without-having-definite-problem-in-mind-seeks-in-most-part-in-vain-david-hilbert

mathematics-knows-no-races-geographic-boundaries-for-mathematics-cultural-world-is-one-country

no-one-shall-expel-us-from-paradise-that-cantor-has-created-for-us

one-can-measure-importance-scientific-work-by-number-earlier-publications-rendered-superfluous-by-it

the-infinite-no-other-question-has-ever-moved-profoundly-spirit-man

the-art-doing-mathematics-consists-in-finding-that-special-case-which-contains-all-germs-generality