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

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.

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

Science makes no pretension to eternal truth or absolute truth.

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.