David Hilbert quotes

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
 David Hilbert 
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
 David Hilbert 
Begin with the simplest examples.
 David Hilbert 
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science
 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 
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 
Galileo was no idiot. Only an idiot could believe that science requires martyrdom  that may be necessary in religion, but in time a scientific result will establish itself
 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 

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.
 David Hilbert 
Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
 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 
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
 David Hilbert 

The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
 David Hilbert 
Geometry is the most complete science.
 David Hilbert 
The art of doing mathematics consists in finding that special case which contains all the germs of generality
 David Hilbert 
Physics is becoming too difficult for the physicists.
 David Hilbert 

We must know. We will know.
 David Hilbert 
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
 David Hilbert 
Some people have got a mental horizon of radius zero and call it their point of view.
 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 

One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it
 David Hilbert 
No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite
 David Hilbert 
One must be able to say at all timesinstead of points, straight lines, and planestables, chairs, and beer mugs
 David Hilbert 
The infinite! No other question has ever moved so profoundly the spirit of man.
 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. The very effort for rigor forces us to find out simpler methods of proof.
 David Hilbert 
He who seeks for methods without having a definite problem in mind seeks in the most part in vain.
 David Hilbert 
Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.
 David Hilbert 
No one shall expel us from the paradise which Cantor has created for us. Expressing the importance of Cantor's set theory in the development of mathematics.
 David Hilbert 

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups iv as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.
 David Hilbert 
Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.
 David Hilbert 
Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.
 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 bathhouse. Objecting to sex discrimination being the reason for rejection of Emmy Noether's application to join the faculty at the University of Gottingen.
 David Hilbert 

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
 David Hilbert 
Physics is much too hard for physicists.
 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 PoincarÃ©, 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 
Keep computations to the lowest level of the multiplication table.
 David Hilbert 

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
 David Hilbert 
[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
 David Hilbert
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