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

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

Physics is becoming too difficult for the physicists.

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.

In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.

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

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