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

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.

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

'Obvious' is the most dangerous word in mathematics.

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.