If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

Fashion as King is sometimes a very stupid ruler.

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

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.

The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting importance who has not also been an innovator.

The only royal road to elementary geometry is ingenuity.

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.