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David Hilbert
(23 Jan 1862 - 14 Feb 1943)
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[Cantor’s set theory:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
— 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
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
Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
— 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
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
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 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
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
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.