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.
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
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.
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.
No one shall expel us from the paradise that Cantor has created for us.
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.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
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.
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
