The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting importance who has not also been an innovator.

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.

I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

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 full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.