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

One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it

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.

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

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.