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.

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

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

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!"

I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.

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.

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