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 stan….

Mathematics is a game played according to certain simple rules with meaningless marks on paper..

Begin with the simplest examples..

Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understa….

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?.

Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific resul….

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country..

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds th….

Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical..

Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And ….

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a ….

He who seeks for methods without having a definite problem in mind seeks in the most part in vain..

Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen..

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 ….

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous….

The art of doing mathematics consists in finding that special case which contains all the germs of generality..

One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs.

Physics is becoming too difficult for the physicists..

I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later..

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler meth….

In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inher….