The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.

[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

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.

He who seeks for methods without having a definite problem in mind seeks in the most part in vain.

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