For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

Mathematicians are born, not made.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

Thought is only a flash between two long nights, but this flash is everything.

A small error in the former will produce an enormous error in the latter.

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.