Questions tagged [hilbert]

David Hilbert (1862-1943) was a German mathematician and one of the most influential and universal mathematicians of the 19th and early 20th centuries.

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David Hilbert's paper: Substitution of the group of cyclotomic field

A question about a notation in David Hilberts's "Ein neuer Beweis des Kroneckerschen Fundamentalsatzes über Abelsche Zahlkörper" (here a german online available source, not sure if there ...
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What were people looking for when they started to study bounded linear functionals?

Very briefly, my understanding of the initial motivations for studying $L^p$ spaces included interest in the $\ell_2$ space, due to relationships with quadratic forms that arose from searching for ...
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Did J. W. Gibbs “invent” Hilbert spaces before Hilbert formulated the notion of such spaces?

I was surprised to see a reply to a comment on his answer to a Quora question by a research mathematician claiming that Hilbert spaces were actually due to J. W. Gibbs rather than to D. Hilbert. The ...
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What are Weber class field's weak points?

These days, I'm interested in class field theory. I know that Weber first made his own 'class field' and then Hilbert made his own field, 'Hilbert class field'. By the way, were there so many weak ...
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Historical background with Weber and Kronecker's Jugendtraum

https://mathoverflow.net/questions/74073/the-first-complete-proof-of-the-kronecker-weber-theorem I searched above link, and I was so interested about this post. Today, I have a question about ...
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Why did Hilbert believe consistency implies existence?

I am reading Sieg's "Hilbert's programs and beyond" and I am having difficulty understanding this quote by Hilbert on page 74: In the Paris Lecture Hilbert re-emphasized and expanded this ...
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Hilbert's criticism on the first version of Einstein's field equations

Crossposted at Physics Stack Exchange I have read once that Hilbert had some reservations regarding the first form of the field equations $$ R_{\mu\nu} = k T_{\mu\nu} $$ because it was not possible ...
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Is Edmund Whittaker claim that Hilbert proved General Relativity days before Einstein valid?

Are the claims of Sir Edmund Whittaker regarding David Hilbert's derivation of the general relativity theory predated that of Einstein by five days? This Wikipedia article that I found contains the ...
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Hilbert's problem list did not include Fermat's last theorem. Why?

Fermat's Last Theorem was open for more than 350 years until Andrew Wiles proved it in 1995. Are there possible (historical or other) reasons why David Hilbert did not include this famous open problem ...
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What paradoxes did David Hilbert propose?

Google just won't tell me about any other than "the grand hotel". I know of the Turing paradox but did he propose any other? If yes, which?
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Background on the Stone-von Neumann theorem

I'm a mathematician. I'm required to give a lecture on the Stone-von Neumann theorem. I already have all the mathematical details figured out, but I wish to make the lecture more interesting by giving ...
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Why is Hilbert's Seventeenth Problem important?

I'm self-learning about Model Theory and I just got to the proof of Hilbert's 17th Problem via Model Theory of Real Closed Fields. The 17th problem asks to show that a non-negative rational function ...
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Was Hilbert ambivalent about set theory?

There is the well-known quote of Hilbert: "No one shall drive us from the paradise which Cantor has created for us." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (...
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Are there any records that show how Hilbert came to "invent" or "discover" Hilbert spaces?

I think it's fuzzy as to whether or not this question is appropriate to ask on this site. The reason I ask it that the characteristics of Hilbert spaces are very much used in expressing quantum ...
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Why did Einstein get a better hearing in Göttingen than Berlin?

On page 326 of his 2008 book, Jeremy Gray writes matter-of-factly that Albert Einstein "found he got a better hearing from Hilbert and Klein in Göttingen than he did from his colleagues in Berlin&...
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What were Hilbert's weekly 1933 lectures on "matters of general intellectual interest" about?

Saunders Mac Lane says he attended Hilbert's weekly lectures on "matters of general intellectual interest" around 1931 or 1933 (Saunders Mac Lane: A Mathematical Autobiography p. 44). I believe these ...
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Is there any reason why Hilbert's problems are ordered in the way they are?

Is there any reason why Hilbert's problems are ordered in the way they are? Also, from whom does this ordering come? I know that Hilbert talked about several problems on his list, namely 1, 2, 6, 7, ...
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Hilbert's problems

Hilbert presented ten of his 23 problems at the Paris conference of the International Congress of Mathematicians, speaking on August 8 in the Sorbonne 1900. In which of the 23 or 24 problems was ...
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Did Hilbert really have dyscalculia?

One of the comments on this Math.SE question states that Hilbert had dyscalculia. However I have not been able to find a reliable source that confirms this, and I do not really believe it. Of ...
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David Hilbert and the limits of science

David Hilbert wrote a couple of anecdotal paragraphs regarding "the limits of science." He recalled that in the early 19th Century the position of a philosopher - or philosophy in general - was that ...
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Source for Hilbert's famous quote "Mathematics in Göttingen? There really is none anymore"

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
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Hilbert's reaction to Gödel's incompleteness theorems

Is it known how Hilbert initially reacted to Gödel's incompleteness theorems upon their announcement at the Königsberg conference in 1930, or their publication in 1931?
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What was the connection between David Hilbert and Stefan Banach?

The so-called "Hilbert space" is named after mathematician David Hilbert. Later, this was generalized into "Banach spaces" by Stefan Banach. My understanding is that Hilbert was ...
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