I do not know an instance of a major mathematical advance initiated by a man past fifty

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

I do not know an instance of a major mathematical advance initiated by a man past fifty

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

A mathematician, like a painter or a poet, is a maker of patterns.

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