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

However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.

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.

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

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.