Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific result will establish itself.

But above all I wish to designate the following as the most important among the numerous questions which can be asked with regard to the axioms: To prove that they are not contradictory, that is, that a definite number of logical steps based upon them can never lead to contradictory results.

Galileo was no idiot. Only an idiot could believe that science requires martyrdom – that may be necessary in religion, but in time a scientific result will establish itself.

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.

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

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

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

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

No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.

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