David Hilbert

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.

— David Hilbert

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

— David Hilbert

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

— David Hilbert

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

— David Hilbert

"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.

— David Hilbert

If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.

— David Hilbert

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

— David Hilbert

One of the supreme achievements of purely intellectual human activity.

— David Hilbert

But he (Galileo) was not an idiot,... Only an idiot could believe that scientific truth needs martyrdom — that may be necessary in religion, but scientific results prove themselves in time.

— David Hilbert

Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

— David Hilbert

Keep computations to the lowest level of the multiplication table.

— David Hilbert

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 bath-house.

— David Hilbert

Good, he did not have enough imagination to become a mathematician.

— David Hilbert

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

— David Hilbert

To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts.

— David Hilbert

If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.

— David Hilbert

This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.

— David Hilbert

The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!

— David Hilbert

An old French mathematician said: 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. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

— David Hilbert

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

— David Hilbert