No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game

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.

Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

The creative life was the only one for a serious man.

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.