For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We must know - we will know!"

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

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.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.

Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

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