David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
David Hilbert Quotes
1. “We must know. We will know.”
— David Hilbert
2. “Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”
— David Hilbert
3. “Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.”
— David Hilbert
4. “Mathematics is a game played according to certain simple rules with meaningless marks on paper.”
— David Hilbert
5. “The art of doing mathematics consists in finding that special case which contains all the germs of generality.”
— David Hilbert
6. “He who seeks for methods without having a definite problem in mind seeks in the most part in vain.”
— David Hilbert
7. “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
8. “Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.”
— David Hilbert
9. “Physics is becoming too difficult for the physicists.”
— David Hilbert
10. “Begin with the simplest examples.”
— David Hilbert
11. “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
12. “The infinite! No other question has ever moved so profoundly the spirit of man.”
— David Hilbert
13. “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
14. “Geometry is the most complete science.”
— David Hilbert
15. “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
16. “No one shall expel us from the paradise that Cantor has created for us.”
— David Hilbert
17. “Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.”
— David Hilbert
18. “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
19. “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
20. “The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.”
— David Hilbert
21. “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
22. “One must be able to say at all times – instead of points, straight lines, and planes – tables, chairs, and beer mugs.”
— David Hilbert
23. “Some people have got a mental horizon of radius zero and call it their point of view.”
— David Hilbert
24. “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
25. “One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.”
— David Hilbert
26. “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
27. “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
28. “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
29. “We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.”
— David Hilbert
30. “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
31. “That Schmidt, he didn’t have enough imagination for mathematics. Now he has become a poet. For that he had just enough.”
— David Hilbert
32. “But above all I wish to designate the following as the most important among the numerous questions which can be asked with regard to the axioms: To prove that they are not contradictory, that is, that a definite number of logical steps based upon them can never lead to contradictory results.”
— David Hilbert
33. “Keep computations to the lowest level of the multiplication table.”
— David Hilbert
34. “Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.”
— David Hilbert
35. “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
36. “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
37. “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
38. “I didn’t work especially hard at mathematics at school, because I knew that’s what I’d be doing later.”
— David Hilbert
39. “We hear within us the perpetual call: There is the problem. Seek its solution.”
— David Hilbert
