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.

As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.

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

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.

Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.

We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know.

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