Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers.

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.