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

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.

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.

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

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

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

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.