Physics is much too hard for physicists.

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

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

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.