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

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

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.

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

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.

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.