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

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

Begin with the simplest examples..

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….

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….

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

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 ….

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

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….

Physics is becoming too difficult for the physicists..

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

For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We….

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

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics..

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

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

One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.