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.

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.

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.

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

Time makes fools of us all. Our only comfort is that greater shall come after us.

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."