David Hilbert Quotes

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

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.

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

Some people have got a mental horizon of radius zero and call it their point of view.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Begin with the simplest examples.

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!"

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.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

Physics is becoming too difficult for the physicists.

He who seeks for methods without having a definite problem in mind seeks in the most part in vain.

One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs

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.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it

I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.

The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

Geometry is the most complete science.

Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.

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.

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

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.

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.

Keep computations to the lowest level of the multiplication table.

Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.

Physics is much too hard for physicists.

The infinite! No other question has ever moved so profoundly the spirit of man.

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

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.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.