David Hilbert Quotes
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Immer mit den einfachsten Beispielen anfangen.
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To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts.
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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.
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Keep computations to the lowest level of the multiplication table.
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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.
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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.
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Good, he did not have enough imagination to become a mathematician.
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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
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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.
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From the paradise, that Cantor created for us, no-one can expel us.
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Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
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No one shall expel us from the paradise that Cantor has created for us.
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Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
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The art of doing mathematics consists in finding that special case which contains all the germs of generality.
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Physics is becoming too difficult for the physicists.
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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?
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He who seeks for methods without having a definite problem in mind seeks in the most part in vain.
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This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.
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Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.
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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.
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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.
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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.
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The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!
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One of the supreme achievements of purely intellectual human activity.