In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.

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

One hears a lot of talk about the hostility between scientists and engineers. I don't believe in any such thing. In fact I am quite certain it is untrue... There cannot possibly be anything in it because neither side has anything to do with the other.

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.

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 then that becomes his point of view.

Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.

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.