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 i….

Fashion as King is sometimes a very stupid ruler..

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nin….

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

Galois read the geometry from cover to cover as easily as other boys read a pirate yarn..

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which w….

Science makes no pretension to eternal truth or absolute truth..

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of ph….

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 o….

Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along wit….

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 ou….

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

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences..

The only royal road to elementary geometry is ingenuity..

Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attemp….

The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting im….

Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the pre….

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

Time makes fools of us all. Our only comfort is that greater shall come after us..

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..