I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

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.

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

One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs

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

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.

However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.