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David Hilbert

Data de nascimento: 23. Janeiro 1862
Data de falecimento: 14. Fevereiro 1943

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David Hilbert foi um matemático alemão. Foi eleito membro estrangeiro da Royal Society em 1928.

David Hilbert é um dos mais notáveis matemáticos, e os tópicos de suas pesquisas são fundamentais em diversos ramos da matemática atual.

David Hilbert nasceu em Königsberg, atualmente Kaliningrado, onde estudou na Universidade de Königsberg. Em 1895 foi nomeado professor para Göttingen, onde lecionou até se aposentar, em 1930. Está sepultado no Stadtfriedhof de Göttingen.

Hilbert é frequentemente considerado como um dos maiores matemáticos do século XX, no mesmo nível de Henri Poincaré. Devemos a ele principalmente a lista de 23 problemas, alguns dos quais não foram resolvidos até hoje, apresentada em 1900 no Congresso Internacional de Matemáticos em Paris.

Suas contribuições à matemática são diversas:

Consolidação da teoria dos invariantes, que foi o objeto de sua tese.

Transformação da geometria euclidiana em axiomas, com uma visão mais formal que Euclides, para torná-la consistente, publicada no seu Grundlagen der Geometrie .

Trabalhos sobre a teoria dos números algébricos, retomando e simplificando, com a ajuda de seu amigo Minkowski, os trabalhos de Kummer, Kronecker, Dirichlet e Dedekind, e publicando-os no seu Zahlbericht .

Criação dos espaços que levam seu nome, durante seus trabalhos em análise sobre equações integrais.

Contribuição para as formas quadráticas, bases matemáticas da teoria da relatividade de Albert Einstein.

Citações David Hilbert

„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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„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.

„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.

„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.

„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

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

— David Hilbert
Upon hearing that one of his students had dropped out to study poetry, as quoted in [http://books.google.com/?id=nnpChqstvg0C&pg=PA151 The Universal Book of Mathematics (2004) by David J. Darling, p. 151 <!-- publisher=John Wiley and Sons|isbn=978-0-471-27047-8 -->

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„Begin with the simplest examples.“

— David Hilbert
Hilbert-Courant (1984) by Constance Reid, p. 104; German version quoted in Algebra by Michael Artin

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

— David Hilbert
"Axiomatic Thought" (1918), printed in From Kant to Hilbert, Vol. 2 by William Bragg Ewald

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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

„Physics is too difficult for physicists!“

— David Hilbert
This quote has many variants. An early version attributed to the Göttingen School appears in a book review by Heinrich Wieleitner in Isis, Volume 7, No. 4, December 1925, p. 597: Ach, die Physik! Die ist ja für die Physiker viel zu schwer! (Oh, physics! That's just too difficult for the physicists!).

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