Obvious is the most dangerous word in mathematics.

The only royal road to elementary geometry is ingenuity.

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

Fashion as King is sometimes a very stupid ruler.

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.

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

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