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

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.

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

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

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

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.

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