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.

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Physics is becoming too difficult for the physicists.

Physics is much too hard for physicists.

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.

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

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