David Hilbert Quotes

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

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.

Keep computations to the lowest level of the multiplication table.

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

Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.

Good, he did not have enough imagination to become a mathematician.

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.

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

Wir dürfen nicht denen glauben, die heute mit philosophischer Miene und überlegenem Tone den Kulturuntergang prophezeien und sich in dem Ignorabimus gefallen. Für uns gibt es kein Ignorabimus, und meiner Meinung nach auch für die Naturwissenschaft überhaupt nicht. Statt des törichten Ignorabimus heiße im Gegenteil unsere Losung:

One of the supreme achievements of purely intellectual human activity.

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

No one shall expel us from the paradise that Cantor has created.

Begin with the simplest examples.

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.

[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.