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.
No one will expel us from the paradise that Cantor has created for us.
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
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.
The infinite! No other question has ever moved so profoundly the spirit of man.
The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
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.