David Hilbert

Wir müssen wissen. Wir werden wissen.

We must know. We will know.

Mathematics is an art.

No one shall expel us from the paradise that Cantor has created for us.

The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought... The role that remains for the infinite is solely that of an idea, if one means by an idea a concept of reason which the mind is able to go beyond all experience and which completes the understanding of experience by means of the understanding of the whole.

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

The object of mathematics is the discovery of the laws of nature and the laws of the human mind.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Physics is too hard for physicists.

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

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

The problems are not solved, but they are clearly stated.

The further a mathematical theory is developed, the more beautiful and more harmonious it becomes.

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

The infinite! No other question has ever moved the human spirit so profoundly; no other idea has so fruitfully stimulated its intellect; yet no other concept stands in greater need of clarification than this.

For the mathematician there is no 'ignorabimus', and, in my opinion, not at all for natural science either. In contrast to the foolish 'ignorabimus', our slogan shall be 'Wir müssen wissen, wir werden wissen!'

The problems of mathematics are not isolated, but are connected with each other, and the solution of one problem often leads to the solution of others.

Mathematics is the queen of the sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

The value of a science is not to be measured by its immediate practical application, but by its intrinsic beauty and by the intellectual satisfaction it affords.