David Hilbert quotes

David Hilbert was a German mathematician who made fundamental contributions to many areas of mathematics. His work shaped the formalization of mathematical logic and influenced the development of modern mathematics. He developed the famous list of 23 unsolved problems that guided mathematical research in the 20th century. Here are 40 of his quotes:

Physics is becoming too difficult for the physicists. (David Hilbert)
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. View quote
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. View quote
David Hilbert
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. View quote
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? View quote
David Hilbert
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it. View quote
David Hilbert
The art of doing mathematics consists in finding that special case which contains all the germs of generality. View quote
David Hilbert
Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics. View quote
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. View quote
David Hilbert
Keep computations to the lowest level of the multiplication table. View quote
David Hilbert
A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. (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. View quote
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. View quote
David Hilbert
No one shall expel us from the paradise that Cantor has created. View quote
David Hilbert
Begin with the simplest examples. View quote
David Hilbert
Mathematics is a game played according to certain simple rules with meaningless marks on paper. View quote
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. View quote
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. View quote
David Hilbert
[M]athematics is not a popular subject... The reason for this is to be found in the common superstition that [it] is but a continuation... of the fine art of arithmetic, of juggling with numbers. [We] combat that superstition, by offering, instead of formulas, figures that may be looked at and that may easily be supplemented by models which the reader may construct. This book... bring[s] about a greater enjoyment of mathematics, by making it easier... to penetrate the essence of mathematics without... a laborious course of studies. View quote
David Hilbert
In mathematics, as in any scientific research, we find two tendencies... [T]he tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects... a live rapport with them... which stresses the concrete meaning of their relations. ...[I]ntuitive understanding plays a major role in geometry. ...[S]uch concrete intuition is of great value not only for the research worker, but... for anyone who wishes to study and appreciate the results of research in geometry. View quote
David Hilbert
The various branches of geometry are all interrelated closely and quite often unexpectedly. This shows up in many places in the book. Even so... it was necessary to make each chapter...self-contained... We hope that... we have rendered each chapter taken by itself... understandable and interesting. We want to take the reader on a leisurely walk... in the big garden that is geometry, so that each may pick for himself a bouquet to his liking. (David Hilbert)
We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: We must know - we will know! View quote
David Hilbert
Good, he did not have enough imagination to become a mathematician. View quote
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. View quote
David Hilbert
The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples! View quote
David Hilbert