Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

The infinite! No other question has ever moved so profoundly the spirit of man.

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.