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

Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.

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.

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.

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."

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