(source) 
David Hilbert
(23 Jan 1862  14 Feb 1943)

[Cantor’s set theory:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
— David Hilbert
Meine Herren, der Senat ist doch keine Badeanstalt.
The faculty is not a pool changing room.
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.
The faculty is not a pool changing room.
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
Wir mussen wissen. Wir werden wissen.
We must know. We will know.
We must know. We will know.
— David Hilbert
~~[No known source]~~ Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
Eine jede Wissenschaft fällt, hat sie erst eine gewisse Reife erreicht, automatisch der Mathematik anheim.
Eine jede Wissenschaft fällt, hat sie erst eine gewisse Reife erreicht, automatisch der Mathematik anheim.
— 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
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
After seeking in vain for the construction of a perpetual motion machine, the relations were investigated which must subsist between the forces of nature if such a machine is to be impossible; and this inverted question led to the discovery of the law of the conservation of energy, which, again, explained the impossibility of perpetual motion in the sense originally intended.
— David Hilbert
Anything at all that can be the object of scientific thought becomes dependent on the axiomatic method, and thereby indirectly on mathematics, as soon as it is ripe for the formation of a theory. By pushing ahead to ever deeper layers of axioms … we become ever more conscious of the unity of our knowledge. In the sign of the axiomatic method, mathematics is summoned to a leading role in science.
— David Hilbert
As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.
— David Hilbert
Before beginning I should put in three years of intensive study, and I haven’t that much time to squander on a probable failure.
— 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
Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
— David Hilbert
From time immemorial, the infinite has stirred men's emotions more than any other question. Hardly any other idea has stimulated the mind so fruitfully. Yet, no other concept needs clarification more than it does.
— 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
Geometry is the most complete science.
— David Hilbert
He who seeks for methods without having a definite problem in mind seeks for the most part in vain.
— 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
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
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
In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly
— David Hilbert
In mathematics there is no ignorabimus!
— David Hilbert
In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
— David Hilbert
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.
— David Hilbert
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
— David Hilbert
Mathematics is that peculiar science in which the importance of a work can be measured 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
Meine Herren, 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.
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
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.
Expressing the importance of Cantor's set theory in the development of mathematics.
— 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
Physics is becoming too difficult for the physicists.
— David Hilbert
Physics is much too hard for physicists.
— David Hilbert
Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
— David Hilbert
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
— David Hilbert
The farther 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
The infinite! 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
The most suggestive and notable achievement of the last century is the discovery of NonEuclidean geometry.
— David Hilbert
The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms. From this it has come about that our entire contemporary culture, inasmuch as it is based on the intellectual penetration and the exploitation of nature, has its foundations in mathematics. Already Galileo said: one can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are mathematical figures.
— 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
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? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?
— David Hilbert
With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out 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
Quotes by others about David Hilbert (5)
But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.
To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
Plenty of mathematicians, Hardy knew, could follow a stepbystep discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
Das ist nicht Mathematik, das ist Theologie!
This is not mathematics; this is theology.
[Remark about David Hilbert's first proof of his finite basis theorem.]
This is not mathematics; this is theology.
[Remark about David Hilbert's first proof of his finite basis theorem.]
I found out at an early age that science is a haven for the timid, the freaks, the misfits. That is more true perhaps for the past than now. If you were a student in Göttingen in the 1920s and went to the seminar “Structure of Matter” which was under the joint auspices of David Hilbert and Max Born, you could well imagine that you were in a madhouse as you walked in. Every one of the persons there was obviously some kind of a severe case. The least you could do was put on some kind of a stutter. Robert Oppenheimer as a graduate student found it expedient to develop a very elegant kind of stutter, the "njumnjumnjum" technique. Thus, if you were an oddball you felt at home.
See also:
 23 Jan  short biography, births, deaths and events on date of Hilbert's birth.
 The Theory of Algebraic Number Fields, by David Hilbert, I.T. Adamson.  book suggestion.
 Booklist for David Hilbert.