Science makes no pretension to eternal truth or absolute truth.

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

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.

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

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

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.

The only royal road to elementary geometry is ingenuity.