Mathematicians are born, not made.

Mathematicians do not study objects, but the relations between objects.

One does not ask whether a scientific theory is true, but only whether it is convenient.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.