Exposition, criticism, appreciation, is work for second-rate minds.

The case for my life... is this: that I have added something to knowledge, and helped others to add more

Mathematics is not a contemplative but a creative subject.

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

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

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

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