Pick the assumptions to pieces till the stuff they are made of is exposed to plain view - this is the cardinal rule for understanding the basis of our beliefs.

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.

Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future...

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.

Time makes fools of us all. Our only comfort is that greater shall come after us.