Frases de David Hilbert

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David Hilbert

Fecha de nacimiento: 23. Enero 1862
Fecha de muerte: 14. Febrero 1943

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David Hilbert fue un matemático alemán, reconocido como uno de los más influyentes del siglo XIX y principios del XX. Estableció su reputación como gran matemático y científico inventando o desarrollando un gran abanico de ideas, como la teoría de invariantes, la axiomatización de la geometría y la noción de espacio de Hilbert, uno de los fundamentos del análisis funcional. Hilbert y sus estudiantes proporcionaron partes significativas de la infraestructura matemática necesaria para la mecánica cuántica y la relatividad general. Fue uno de los fundadores de la teoría de la demostración, la lógica matemática y la distinción entre matemática y metamatemática. Adoptó y defendió vivamente la teoría de conjuntos y los números transfinitos de Cantor. Un ejemplo famoso de su liderazgo mundial en la matemática es su presentación en 1900 de un conjunto de problemas que establecieron el curso de gran parte de la investigación matemática del siglo XX.

En la pugna por demostrar correctamente algunos de los errores cometidos por Einstein, en la teoría general de la relatividad, David Hilbert se adelantó a las correcciones de Einstein, sin embargo nunca quiso otorgarse el mérito.

Frases David Hilbert

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„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
Context: 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. Eine mathematische Theorie ist nicht eher als vollkommen anzusehen, als bis du sie so klar gemacht hast, daß du sie dem ersten Manne erklären könntest, den du auf der Straße triffst.

„To new concepts correspond, necessarily, new signs.“

— David Hilbert
Context: To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts.

„Only an idiot could believe that scientific truth needs martyrdom“

— David Hilbert
Context: 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. Hilbert (2nd edition, 1996) by Constance Reid, p. 92

„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.“

— David Hilbert
Context: 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. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future.

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

— David Hilbert
Context: 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.

„A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts.“

— David Hilbert
Context: 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.

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„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
Quoted in Mathematical Mysteries : The Beauty and Magic of Numbers (1999) by Calvin C. Clawson, p. 258

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