If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

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

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

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.

Fashion as King is sometimes a very stupid ruler.

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.