We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know.

If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.

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

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.

Geometry is the most complete science.

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

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