David Hilbert Quotations

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

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.

No one shall expel us from the paradise which Cantor has created for us. Expressing the importance of Cantor's set theory in the development of mathematics.

I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bathhouse. Objecting to sex discrimination being the reason for rejection of Emmy Noether's application to join the faculty at the University of Gottingen.

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.

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

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

Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.

Keep computations to the lowest level of the multiplication table.