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.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Physics is becoming too difficult for the physicists.
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.
The infinite! No other question has ever moved so profoundly the spirit of man.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
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.
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.
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.
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
Every mathematical discipline goes through three periods of development the naive, the formal, and the critical.
Physics is much too hard for physicists.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
He who seeks for methods without having a definite problem in mind seeks in the most part in vain.
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.
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.
No one shall expel us from the paradise that Cantor has created for us.
Wir mssen wissen, wir werden wissen We must know, we will know.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
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.
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