David Hilbert Quotes

48 Sourced Quotes

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
No one shall expel us from the Paradise that Cantor has created.
In German: Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.

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

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

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
Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended.

David Hilbert
One of the supreme achievements of purely intellectual human activity.

David Hilbert
The importance of a scientific work can be measured by the number of previous publications it makes it superfluous to read.

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
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
History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future.

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
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
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.

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

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

David Hilbert