Mathematicians are used to game-playing according to a set of rules they lay down in advance, despite the fact that nature always writes her own. One acquires a great deal of humility by experienceing the real wiliness of nature.
A mathematician is a machine for turning coffee into theorems.
The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood.
I have hardly ever known a mathematician who was capable of reasoning.
Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was one which does not now seem very impressive; it was, that some people can do sums.
Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs Aristotle to keep her mouth open while he counted.