I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.

No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.

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

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

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

I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.

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