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.

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

The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

Some people have got a mental horizon of radius zero and call it their point of view.

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

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!"

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.