The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

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.

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.

Pick the assumptions to pieces till the stuff they are made of is exposed to plain view - this is the cardinal rule for understanding the basis of our beliefs.

Obvious is the most dangerous word in mathematics.

Fashion as King is sometimes a very stupid ruler.

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.