Beauty is the first test: there is no permanent place in the world for ugly mathematics.

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

Good work is not done by 'humble' men

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

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

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

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.