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

Although he was a limited mathematician with no pretensions to scientific greatness, Crelle was a broadminded man, in fact a great man.

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

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.

The only royal road to elementary geometry is ingenuity.

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.

The Handmaiden of the Sciences.

Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.

Fashion as King is sometimes a very stupid ruler.

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 importance who has not also been an innovator.