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Hilbert, David (1862-1943)
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
In H. Eves, Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971.
Hilbert, David (1862-1943)
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
Report on Number Theory, 1897.
Hilbert, David (1862-1943)
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.
In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Hilbert, David (1862-1943)
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Hilbert, David (1862-1943)
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.
Hilbert, David (1862-1943)
Physics is much too hard for physicists.
Constance Reid, Hilbert, London: Allen and Unwin, 1970.
Hilbert, David (1862-1943)
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Hilbert, David (1862-1943)
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.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1971.
Hilbert, David (1862-1943)
Wir mussen wissen.
Wir werden wissen.
[Engraved on his tombstone in Gottingen.]
Hilbert, David (1862-1943)
Before beginning I should put in three years of intensive study, and I haven't that much time to squander on a probable failure.
[On why he didn't try to solve Fermat's last theorem]
Quoted in E.T. Bell Mathematics, Queen and Servant of Science, New York: McGraw Hill Inc., 1951.

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