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

Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.

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

If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

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."

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.

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