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.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

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.

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.

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.