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
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
Keep computations to the lowest level of the multiplication table.

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

David Hilbert
Three-dimensional geometry becomes a chapter in four-dimensional physics.

David Hilbert
Mathematics must be cherished and strengthened as a unified, vital branch in the broad river of science; it dares not trickle away in the sand.

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

David Hilbert
The tool which governs the mediation between theory and practice, between thought and observation is mathematics; it builds the bridge and carries more and more of the load. It thereby happens that the basis of our entire present day culture, in so far as it is based on investigations dealing with nature, can be found in mathematics.

David Hilbert
Living mathematics rests on the fluctuation between the antithesis powers of intuition and logic, the individuality of "grounded" problems and the generality of far-reaching abstractions. We ourselves must prevent the development being forced to only one pole of the life-giving antithesis.

David Hilbert
A problem in number theory is as timeless as a true work of art.

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

David Hilbert
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

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
Mathematics is not a popular subject, even though its importance may be generally conceded. The reason for this is to be found in the common superstition that mathematics is but a continuation, a further development, of the fine art of arithmetic, of juggling with numbers.

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

David Hilbert
Mathematics... is nothing more than a game played according to certain simple rules with meaningless marks on a paper.

David Hilbert
No one will drive us our of this paradise that Cantor has created for us!

David Hilbert
From time immemorial the infinite has stirred men's emotions more than any other question. Hardly any other idea stimulated the mind so fruitfully. Yet no other concept needs clarification more that it does.

David Hilbert
We have reformed mathematics, the next thing is to reform physics, and then we'll go on to chemistry.

David Hilbert
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?

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
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
Existence proofs carried out with the help of the principle of excluded middle usually are especially attractive because of their surprising brevity and elegance. Taking the principle of excluded middle from the mathematician would be the same...[as] proscribing the telescope to the astronomer or to the boxer the use of his fists.

David Hilbert
The infinite, like no other problem, has always deeply moved the soul of men. The infinite, like no other idea, has had a stimulating and fertile influence upon the mind. But the infinite is also more than any other concept, in need of clarification.

David Hilbert
He who seeks for methods without having a definite problem in mind seeks for the most part in vain.

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
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
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