It is the business of future to be dangerous.... The major advances in civilization are processes that all but wreck the societies in which they occur.

Other nations of different habits are not enemies: they are godsends. Men require of their neighbours something sufficiently akin to be understood, something sufficiently different to provoke attention, and something great enough to command admiration. We must not expect, however, all the virtues.

Every epoch has its character determined by the way its population reacts to the material events which they encounter.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.

No Roman ever died in contemplation over a geometrical diagram.

It takes an extraordinary intelligence to contemplate the obvious.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise