The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.

Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

The progress of mathematics can be viewed as progress from the infinite to the finite.

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist.

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.