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.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

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 tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

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!"

One hears a lot of talk about the hostility between scientists and engineers. I don't believe in any such thing. In fact I am quite certain it is untrue... There cannot possibly be anything in it because neither side has anything to do with the other.

We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know.