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

The infinite! No other question has ever moved so profoundly the spirit of man.

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 guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

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.

Some people have got a mental horizon of radius zero and call it their point of view.

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.

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