Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes.

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."

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

The only royal road to elementary geometry is ingenuity.

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.

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.