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

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

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.

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.

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.

I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.

The only royal road to elementary geometry is ingenuity.