25 quotes
One of the supreme achievements of purely intellectual human activity.
No one shall expel us from the paradise that Cantor has created.
Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
Axiomatic Thought (1918)
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Arithmetical symbols are written diagrams and geometrical figures are graphic formulas.
Keep computations to the lowest level of the multiplication table.
Hilbert-Courant (1984)
"Mathematics is a presuppositionless science.
Hilbert's Die Grundlagen der Mathematik (1927)
We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
Mathematical Circles Revisited (1971)
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
Mathematical Mysteries : The Beauty and Magic of Numbers (1999)
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
Mathematical Circles Revisited (1971)
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.
Hilbert-Courant (1984)
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.
Hilbert-Courant (1984)
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.
Mathematical Problems (1900)
But he (Galileo) was not an idiot,... Only an idiot could believe that scientific truth needs martyrdom — that may be necessary in religion, but scientific results prove themselves in time.
Good, he did not have enough imagination to become a mathematician.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
Mathematical Problems (1900)
History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones.
Mathematical Problems (1900)
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.
Comic Sections (1993)
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.