Top 42 David Hilbert Quotes
#2. One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
David Hilbert
#3. However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.
David Hilbert
#4. 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.
David Hilbert
#5. 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
#6. 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
#7. Mathematics is a game played according to certain simple rules with meaningless marks on paper.
David Hilbert
#8. 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
#10. 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
#11. The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
David Hilbert
#12. Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
David Hilbert
#13. Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches? ... Mathematics is, in my opinion, an indivisible whole ... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.
David Hilbert
#14. 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
#16. The infinite! No other question has ever moved so profoundly the spirit of man.
David Hilbert
#17. 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
#18. We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.
David Hilbert
#19. Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
David Hilbert
#20. 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
#21. He who seeks for methods without having a definite problem in mind seeks in the most part in vain.
David Hilbert
#22. Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
David Hilbert
#23. Some people have got a mental horizon of radius zero and call it their point of view.
David Hilbert
#24. 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
#25. The art of doing mathematics consists in finding that special case which contains all the germs of generality.
David Hilbert
#26. 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
#27. 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
#28. 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
#29. 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
#30. 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
#31. Keep computations to the lowest level of the multiplication table.
David Hilbert
#32. One must be able to say at all times
instead of points, straight lines, and planes
tables, chairs, and beer mugs
David Hilbert
#33. 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
#35. No one shall expel us from the paradise which Cantor has created for us.
{Expressing the importance of Georg Cantor's set theory in the development of mathematics.}
David Hilbert
#36. Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
David Hilbert
#37. 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
#38. Physics is becoming too difficult for the physicists.
David Hilbert
#39. 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
#40. [On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
David Hilbert
#41. I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.
David Hilbert
#42. 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
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