Chess problems are the hymn-tunes of mathematics.

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.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

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.

There is always more in one of Ramanujan's formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface; but there is not one which is not curious and entertaining.

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

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