Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.

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

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

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

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

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.

Geometry is the most complete science.