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.

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

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

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.

Obvious is the most dangerous word in mathematics.

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

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.