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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
David Hilbert
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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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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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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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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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He who seeks for methods without having a definite problem in mind seeks in the most part in vain.
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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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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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