David Hilbert > Quotes

“We must know. We will know.”
― David Hilbert

“The infinite! No other question has ever moved so profoundly the spirit of man.”
― David Hilbert

“Wir müssen wissen, wir werden wissen.”
― David Hilbert

“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

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

[Upon hearing that one of his students had dropped out to study poetry]”
― David Hilbert

“Wir mussen wissen. Wir werden wissen. (We must know. We will know.)

[Inscribed on his tomb in Gottingen.]”
― David Hilbert

“Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is one country.”
― David Hilbert

“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

“The art of doing mathematics consists in finding that special case which contains all the germs of generality.”
― David Hilbert

“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

“… he who seeks for methods without having a definite problem in mind seeks for the most part in vain.”
― David Hilbert

“That Schmidt, he didn’t have enough imagination for mathematics. Now he has become a poet. For that he had just enough.”
― David Hilbert

“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

“No one shall expel us from the paradise that Cantor has created for us.”
― David Hilbert

“Only an idiot could believe that scientific truth needs martyrdom; that may be necessary in religion, but scientific results prove themselves in due time”
― David Hilbert (1862-1943)

“We hear within us the perpetual call: There is the problem. Seek its solution.”
― David Hilbert, Mathematical Problems

“Wir müssen wissen, wir werden wissen.
Dobbiamo sapere, sapremo.”
― David Hilbert (1862-1943)

“… the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.”
― David Hilbert

“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

“Wir dürfen nicht denen glauben, die heute mit philosophischer Miene und über-legenem Tone den Kulturuntergang prophezeien und sich in dem Ignorabimus gefallen. Füruns gibt es kein Ignorabimus, und meiner Meinung nach auch für die Naturwissenschaftüberhaupt nicht. Statt des törichten Ignorabimus heisse im Gegenteil unsere Lösung: Wir müssen wissen. Wir werden wissen. (translation: We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. 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.)”
― David Hilbert

“It is difficult and often impossible to judge the value of a problem correctly in advance; for the final award depends upon the gain which science obtains from the problem. Nevertheless we can ask whether there are general criteria which mark a good mathematical problem. An old French mathematician said: “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.” This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.”
― David Hilbert

“If, apart from proving consistency, the question of the justification of a measure is to have any meaning, it can consist only in ascertaining whether the measure is accompanied by commensurate success. Such success is in fact essential, for in mathematics as elsewhere success is the supreme court to whose decisions everyone submits.”
― David Hilbert

“In the joy of discovering new and important results, mathematicians paid too little attention to the validity of their deductive methods. For, simply as a result of employing definitions and deductive methods which had become customary, contradictions began gradually to appear. These contradictions, the so-called paradoxes of set theory, though at first scattered, became progressively more acute and more serious. In particular, a contradiction discovered by Zermelo and Russell had a downright catastrophic effect when it became known throughout the world of mathematics. … Too many different remedies for the paradoxes were offered, and the methods proposed to clarify them were too variegated. Admittedly, the present state of affairs where we run up against the paradoxes is intolerable. Just think, the definitions and deductive methods which everyone learns, teaches, and uses in mathematics, the paragon of truth and certitude, lead to absurdities! If mathematical thinking is defective, where are we to find truth and certitude?”
― David Hilbert

“We have established that the universe is finite in two respects, i.e., as regards the infinitely small and the infinitely large.”
― David Hilbert

“Geometry is nothing more than a branch of physics; the geometrical truths are not essentially different from physical ones in any aspect and are established in the same way.”
― David Hilbert

“Someone who wished to characterize briefly the new conception of the infinite which Cantor introduced might say that in analysis we deal with the infinitely large and the infinitely small only as limiting concepts, as something becoming, happening, i.e., with the potential infinite. But this is not the true infinite. We meet the true infinite when we regard the totality of numbers 1, 2, 3, 4, … itself as a completed unity, or when we regard the points of an interval as a totality of things which exists all at once. This kind of infinity is known as actual infinity.”
― David Hilbert

“Let us consider that we as mathematicians stand on the highest pinnacle of the cultivation of the exact sciences. We have no other choice than to assume this highest place, because all limits, especially national ones, are contrary to the nature of mathematics. It is a complete misunderstanding of our science to construct differences according to peoples and races, and the reasons for which this has been done are very shabby ones.
Mathematics knows no races. . . . For mathematics, the whole cultural world is a single country.”
― David Hilbert

“Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought…”
― David Hilbert

“Every science takes its starting point from a sufficiently coherent body of facts is given. It takes form, however, only by organizing this body of facts. This organization takes place through the axiomatic method, i.e., one constructs a logical structure of concepts so that the relationships between the concepts correspond to relationships between the facts to be organized.
There is arbitrariness in the construction of such a structure of concepts; we, however, demand of it:
1) completeness, 2) independence, 3) consistency.”
― David Hilbert

“Wir dürfen nicht denen glauben, die heute mit philosophischer Miene und über-legenem Tone den Kulturuntergang prophezeien und sich in dem Ignorabimus gefallen. Füruns gibt es kein Ignorabimus, und meiner Meinung nach auch für die Naturwissenschaftüberhaupt nicht. Statt des törichten Ignorabimus heisse im Gegenteil unsere Lösung: Wir müssen wissen. Wir werden wissen.”
― David Hilbert