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.

Science makes no pretension to eternal truth or absolute truth.

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

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

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.

The only royal road to elementary geometry is ingenuity.