David Hilbert Quotes

48 Sourced Quotes

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

David Hilbert
Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.

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
Arithmetical symbols are written diagrams and geometrical figures are graphic formulas.

David Hilbert
For mathematics hoch — hoch — hoch [hip, hip hooray]

David Hilbert
Physics... is much too hard for physicists.

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
It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.

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

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
It has become perfectly clear that physics does not deal with the material world or with the contents of reality, but rather, what it perceives is merely the formal constitutions of reality.

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

David Hilbert
The reason that I am now almost completely swimming in physical waters is because here at the moment as a pure mathematician I am the only feeling heart among the wraiths. So for now... in order to have points in common with other mortals, I have surrendered myself to magic — that is to say, physics.

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

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
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
It is difficult and often impossible to judge the value of a problem correctly in advance; for the final award depends upon the gain which science obtains from the problem.

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
One of the supreme achievements of purely intellectual human activity.

David Hilbert