In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.

I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

Bombs are probably more merciful than bayonets

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

The mathematician's patterns, like the painter's or the poet's, must be beautiful.

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

I wrote a great deal during the next ten [early] years,but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction.