Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

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

For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We must know - we will know!"

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

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.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.