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Former good articleDavid Hilbert was one of the Mathematics good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones
August 25, 2007Good article reassessmentDelisted



ARCHIVED: May 7, 2009 Editing session Hilbert/Physics/Relativity with Jwy, Salix, Wvbailey, Pie are round, concluded with the revision of a paragraph under category "Physics" concerning Einstein, Hilbert, and the 1915 development of the field equations of General Relativity. --Pie are round (talk) 18:51, 7 May 2009 (UTC)[reply]



This claim, previously present on this page, is obviously false:

Gödel's incompleteness theorems show that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove.

If we take the axiomatic system, and extend it by adding a single new axiom, which says that the logical proposition is true, then the extended system immediately proves the logical proposition in question, directly from the new axiom. The extended system may have become inconsistent, but in that case it proves every proposition, including the one under question.

When we do this, a new Goedel sentence can be formed in the extended system, which in its turn cannot be proven within the extended system (but is provable in an infinitude of other, yet-more-extended systems). And so on ad infinitum.

I believe the correction I just made in the page is strictly correct, but would like checking by a professional mathematician:

Gödel's incompleteness theorems show that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove within that system. — Preceding unsigned comment added by 2403:5808:B368:0:6D2F:CF23:9832:A61B (talk) 03:04, 30 September 2022 (UTC)[reply]

Hilbert in the 1930's


Hilbert is said to have made a pro-Nazi remark in the 1930's. —Preceding unsigned comment added by (talk) 17:04, 3 July 2009 (UTC)[reply]

That has been suggested before, but I've never seen any sources of it. Do you have a good source? (John User:Jwy talk) 17:14, 3 July 2009 (UTC)[reply]
See Constance Reid's biography, mentioned in the "Secondary Literature". —Preceding unsigned comment added by (talk) 10:14, 8 July 2009 (UTC)[reply]
There was a plebiscite in Germany on the 19/8/1934. A pro-Hitler declaration appeared in a German paper,
made by German scientists, on the previous day. Unfortunately, I have no access to copies of German newspapers, going back to
18/8/1934.See http://arxiv.org/abs/physics/0505235 Hilbert is not mentioned as being one of those refusing to make a
pro-Hitler declaration.
The link didn't work for me -- the paper doesn't exist? Bill Wvbailey (talk) 14:06, 8 July 2009 (UTC)[reply]

I agree, that the link does not work directly. Search arxiv.org for "Ivan Todorov" and you might find his paper on Heisenberg. A PDF is involved, which might account for the difficulty. —Preceding unsigned comment added by (talk) 13:59, 9 July 2009 (UTC)[reply]

Sorry, but WERNER HEISENBERG mentions Hilbert directly only as Courant's colleague. I couldn't see any indirect mention, although I may not have read closely enough. Since it appears to be a notable exception when a professor avoided the Hitler salute, I suspect Hilbert participated in that - but that is as notable as saying he kept his job. But thanks for pointing to that site. A lot of good information there. (John User:Jwy talk) 18:06, 9 July 2009 (UTC)[reply]

See "Hilbert" by Constance Reid, published by Springer-Verlag, in 1996. On page 207 it says, "An election was scheduled for August with the alternatives, yes or no. The day before the election, the newspapers carried a proclamation announcing that Hitler had the support of German science. The list of signatures included the name of Hilbert. Whether Hilbert actually signed the proclamation is not known." —Preceding unsigned comment added by (talk) 12:13, 13 July 2009 (UTC) I think the same passage appeared in the 1970 edition of the biography of Hilbert. —Preceding unsigned comment added by (talk) 12:18, 13 July 2009 (UTC)[reply]

An uncertain signature among a long list that did not reflect (as it indicates later in the paragraph) his apparent core beliefs does not, in my opinion, warrant mention here unless the context is made very clear - which would take some careful research and writing. There is no sign that he was an active supporter of the Nazis. That someone in Germany didn't resist openly is not really notable. Resistance seems to have been rather limiting in many ways - and he did complain about the loss of his Jewish colleagues. (John User:Jwy talk) 19:06, 13 July 2009 (UTC)[reply]



Often accused


Hilbert was often accused of being a *** by the Nazis, because of his name "David". He seems to acquired the name from Lutheran ancestors, who often used Hebrew names. —Preceding unsigned comment added by (talk) 08:18, 5 May 2010 (UTC)[reply]

Early accounts and connections


It seems that emitting his ancestry and speaking about "Hebrew names" without giving any proof, the interest in Greek Philosophy and Thimaeos in particular, a central topic studied by the first and second generation of assimilated Jews in Germany, raises the suspicion that actually Hilbert (and Heisenberg !) where actually of self-denied Jewish descent. פשוט pashute ♫ (talk) 18:02, 12 August 2020 (UTC)[reply]

At the time it was considered common knowledge. See here page 423. It seems the writer is saying that it seems to be only an impression.פשוט pashute ♫ (talk) 18:08, 12 August 2020 (UTC)[reply]

Hilbert's alleged anger


Numerous wiki pages are assorted with an allegation that Hilbert got angry when he heard of Goedel's work. The main source for this seems to be the somewhat sensationalistic biography by Reed. Such an allegation is not very informative, and I suggest we delete it thoughout. It is particularly irrelevant in the context of the debate against Brouwer, and gives the impression of a gleeful editor siding with Brouwer propagating this information throughout Hilbert-related pages. Tkuvho (talk) 12:33, 5 May 2010 (UTC)[reply]

There is a little bit of research on Hilbert's reactions here. (talk) 03:57, 28 April 2011 (UTC)[reply]
Indeed, the discussion there reveals that the only source for the alleged anger is Reed's personal recollection of a conversionation with... Bernays. Reed's sensationalistic dramatisations have no respectable source and should be deleted. Please log in and you agree we can delete this unreliable material. Tkuvho (talk) 04:05, 28 April 2011 (UTC)[reply]

finiteness theorem


http://people.math.jussieu.fr/~harris/theology.pdf tell a somewhat different version of the "theology" story. Parking it here for now. I'll add something about it to the article unless someone gets to it before I do (please feel free). (talk) 08:07, 27 April 2011 (UTC)[reply]

Is COLIN MCLARTY's piece published? Why does it appear in pdf form at Harris's page? What's the relation between Harris and McLarty? If this has been published, it is yet another "dramatic" distortion of history perpetrated by Reed and Eric Temple Bell. This should certainly be clarified. Tkuvho (talk) 04:17, 28 April 2011 (UTC)[reply]
The article will appear in the book "Circles disturbed: the interplay of Mathematics and Narrative", edited by Apostolos Doxiadis and Barry Mazur, Princeton University Press, 2011. Harris was at the meeting where I presented the paper, and he put up the pdf because the book is not out yet. It is based on comments by Hilbert, and Felix Klein and others close to the event. You could especially look at Gerhard Frei editor, "Der Briefwechsel David Hilbert Felix Klein (1886--1918)", Vandenhoeck & Ruprecht, Goettingen, 1985.
Also, I am unsure who this Reed is. Should it be (Constance) Reid?Colin McLarty (talk) 14:59, 10 September 2011 (UTC)[reply]

Strange gender issue in the introduction??


"the first of two children and only son of Otto and Maria Therese (Erdtmann) Hilbert"

OK what is that supposed to be? Why is it significant that the second child was a female, is it that the Hilberts only had one 'good one'? Ridiculous sentence. (talk) 21:27, 17 October 2011 (UTC)[reply]

Dunno, making the change. A13ean (talk) 21:37, 17 October 2011 (UTC)[reply]
It's a very common form in encyclopedic entries :P Jorgen W (talk) 00:43, 18 October 2011 (UTC)[reply]

It is really somehow derogatory to know that his sibling was a sister? Colin McLarty (talk) 20:59, 26 January 2012 (UTC)[reply]

I assume someone paraphrased a very old biography without thinking about it. a13ean (talk) 16:50, 1 June 2013 (UTC)[reply]
I agree with @Colin McLarty: here. There is nothing wrong with that statement. Logically, if he is the only son of a couple with two children, the other is female. Shrugs. Nerd271 (talk) 23:16, 26 July 2019 (UTC)[reply]



"Ignorabimus" is translated as "we cannot know" but it means "we will not know". — Preceding unsigned comment added by (talk) 13:37, 5 May 2012 (UTC)[reply]

Significant nuances to the English translation are not conveyed in the literal interpretation. This leaves the reader uninformed about the true meaning of the debate between Hilbert and du Bois-Reymond. As it is commonly stated in many English sources, it has the flavor of an interrogation. Definitely not the idea Hilbert intended to be conveyed to his audience of educators and mathematicians.

Hilbert's quote calls to mind the educational ideals described by Wilhelm von Humboldt, as well as the self fulfilling actualization that good education brings. This link to the greatness of the German educational tradition is missing in the literal translation. — Preceding unsigned comment added by Ab3517 (talkcontribs) 18:13, 30 April 2016 (UTC)[reply]

As Wikipedia editors, we do not do our own direct translations nor do we attempt to correct what we might think of as common misunderstandings. In order to bring up this view of Hilbert's quote, you must find and cite a reliable secondary source that discusses this issue. We can then point to and possibly explain (but not amplify) this point of view. Material that is not grounded in good references is subject to being reverted; which might seem like an unfair and somewhat nasty procedure, but it is how we keep Wikipedia from degenerating into a collection of personal blogs. Bill Cherowitzo (talk) 18:46, 30 April 2016 (UTC)[reply]
The English text is a literal translation of the German text. There is no mention of educational ideals or Humboldt in either of them. Both convey exactly the same nuances. (However, I cannot assess the Latin text.) - Jochen Burghardt (talk) 21:49, 30 April 2016 (UTC)[reply]
I find it hard to believe that they "both convey exactly the same nuances" or even how one would confirm that. But it doesn't matter for the immediate discussion. --John (User:Jwy/talk) 00:00, 1 May 2016 (UTC)[reply]

I'm saying: legalistic arguments aside, you're missing the actual point of the translation, and robbing future generations of the greatness of Hilbert's work. If you read yourself, Hilbert's 1930 speech, you will notice that significant ideas are missed in a literal translation into English. This is a fact with ANY literal translation from one language to another. Each language has its own idioms, or ways of speaking, which are of different forms. The translation into colloquial English is not quite correct. The way it appears to speakers of English is very negative towards speakers of Germans. This is an image I think you would not want to convey, as it is not quite correct. It fails to convey the full beauty of the German language as Hilbert speaks it. — Preceding unsigned comment added by Ab3517 (talkcontribs) 23:33, 30 April 2016 (UTC)[reply]

For a fuller view of the inter-relationship between English and German, and especially German intellectual development in all areas, I suggest, "The German Genius" by Peter Watson. He speaks specifically, in the introduction, of how, many people revert to stereotypes, when discussing German history, and this is an obstacle to understand the great contributions that German Science has made to World History. — Preceding unsigned comment added by Ab3517 (talkcontribs) 23:37, 30 April 2016 (UTC)[reply]

Hilbert's greatness lies in the fact that he encouraged many scientists throughout the world to not accept arbitrary limitations, but to investigate wholeheartedly, and find answers. And these answers are well within human ability to find. — Preceding unsigned comment added by Ab3517 (talkcontribs) 23:40, 30 April 2016 (UTC)[reply]

While I applaud your rigor, I was deeply moved by the true meaning of Hilbert's words, which are not fully translated into English. Future generations, and people around the world, could greatly benefit, by the very positive image of German Science that Hilbert portrays. His speech has the beauty and poetry that, as English speakers, we proverbially attribute to French. — Preceding unsigned comment added by Ab3517 (talkcontribs) 23:46, 30 April 2016 (UTC)[reply]

As an example, I would suggest examining the literal and meta-linguistic interpretation of koan 7 of the Mumonkan. There is clearly more than one meaning to the concept of "rice bowl." It would not be a stretch to state that Hilbert was aware of such things.

I would suggest you channel your energy, perhaps, into expanding the article itself with further information (from reliable sources) about how Hilbert epitomizes "German Science" as you describe. A footnotes to translations won't do this justice anyway! --John (User:Jwy/talk) 00:00, 1 May 2016 (UTC)[reply]



I've removed one of the references for Hilbert's atheism as the quote appears to be a response to Kroenecker's "God invented integers" approach, not a statement of Hilbert's more general religious stance - and is a primary source. The remaining reference is a bit dubious. Most of the references in it are from Wikipedia and there is no reference for the atheism statement. If it were "famously atheist," we should be able to find a better reference. --John (User:Jwy/talk) 19:07, 25 July 2012 (UTC)[reply]

The two references just added have the same issue. They discuss Hilbert's refusal to include God in his discussion of mathematics (and geometry), but do not indicate he did not believe in God. --John (User:Jwy/talk) 20:16, 25 July 2012 (UTC)[reply]

I think 4 citations more than suffice to make the claim that Hilbert was an atheist. These citations are created by academics from universities, not some random user making questionable claims. You could send an email to these academics to ask for clarification to these articles as you wish. I posted links to these citations in order for skeptics to look at these citations for themselves. Anyway, a person does not have to deny the existence of God in order to become an atheist. Just because a person doesn't explicitly states that he/she is an atheist does not mean he/she is not an atheist. American physicist, Steven Weinberg states this comment about scientists who don't call themselves atheists: "Most scientists I know don't care enough about religion even to call themselves atheists.". This statement can be also applied to mathematicians as well. Hilbert, as a mathematician, was known to be against intuitionism of any kind and demanded rigorous proofs for any claims whatsoever. (Read the wiki article, Brouwer–Hilbert controversy for more details.) Whether in terms of mathematics or theology. Here is one example, "Also, when someone blamed Galileo for not standing up for his convictions Hilbert became quite irate and said, “But he 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 due time." - David Hilbert. Anton Z. Capri, Quips, quotes, and quanta: an anecdotal history of physics (2007), page 135. If a person does not have proof of any kind to their claims, it does not make any sense to believe in it. This is what most atheists' stance is in terms of theology. For example, Richard Dawkins himself, has said before that he was an agnostic. World's most notorious atheist Richard Dawkins admits he is in fact agnostic. Daily Mail.co.uk However, that does not rule out the fact that he stills considered himself to be an atheist. Just because a person is unsure about the existence of God, doesn't forbid the person to not believe in him as well. For example, I'm unsure about the existence of the Tooth fairy, however, due to lack of any evidence for this entity, I don't tend to believe in it. If there is evidence (or proof) of a statement or claim, a scientist may be more likely to believe in it. Ninmacer20 (talk) 20:27, 25 July 2012 (UTC)[reply]

Only one of the four quotes you list indicate explicitly that Hilbert was an atheist. The statement needs to be more explicit in the sources. I could argue against the conclusions you derive from them, but since since the conclusions are not explicit in the source, they are original research and should not be included here.

Alright, I made a mistake by labeling him an atheist considering two of those sources are considered "original research". After finding an another source and based on his other statements, I think it's safest to say that he was an agnostic. I'll leave it as that. Ninmacer20 (talk) 02:03, 26 July 2012 (UTC)[reply]

Note also, that Hilbert was a supporter of Cantor, who believed in a deep connection with set theory, and what one might call the higher power and beauty of the universe. Hilbert's quote, "Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.", leads one to think that he was deeply sympathetic to such a view. — Preceding unsigned comment added by Ab3517 (talkcontribs) 04:26, 1 May 2016 (UTC)[reply]

Hilbert's Son's Mental Illness


I would like to know more about Hilbert's son's mental "illness." It sounds like his son was mentally handicapped which I don't think is considered mental illness.

The whole phrasing and description seems imprecise and awkward and I think could be improved if more information is available.

Hilbert was a great man and I take his biography seriously -- please help with this.--Jrm2007 (talk) 04:30, 4 March 2014 (UTC)[reply]

changing "one of the most influential and universal mathematicians of the 19th and early 20th centuries." to ",along with Hermann Minkowski, is the most influential and universal... "


pls? i shouldn't even have to ask, given what i've done and the reliance on his work. i'd be nowhere if roweis didn't make the method, if david hilbert didn't study the peano curve/arithmetic, if hermann minkowski didn't study the geometry of numbers.

hilbert and minkowski must go down as THE MOST influential mathematicians of the 19th and 20th centuries. can't see how the generality of their work, especially with the unbelievable geometric interpretations, this isn't true.

just sayin — Preceding unsigned comment added by (talk) 04:52, 27 January 2015 (UTC)[reply]



Why is there a whole page devoted to the Entscheidungsproblem and then no mention of it on here? He is the person directly related to that said thing. I would have thought that a large amount of people only know of him because of the Entscheidungsproblem - especially within the computer science community.-- (talk) 18:56, 21 April 2016 (UTC)[reply]

hi, this is a fair point and i hope someone else will add more about it. however i wanted to take this time to inform you about the controversy surrounding some of Hilbert's best work, given it implicitly accommodates Cantor's work. if you read Controversy over Cantor's theory, you'll see that many people were upset. even though those (like Kronecker and Poincare) who refuted Georg Cantor's theory were inferior mathematicians to Hilbert, there are many so-called mathematicians today chasing the dead ends they set out. it has snowballed because of the persistence of Foundational crisis in Mathematics. i agree there should be more, but we're going to have to wait until Hilbert's work is appreciated the way it should be. along with Hermann Minkowski, Constantin Carathéodory and Andrey Kolmogorov, David Hilbert reigns as one of, if not THE, premier mathematician of his era. (talk) 00:35, 27 April 2016 (UTC)[reply]

An excellent, and very valid point, if I may say so. The topic known as "Hilbert's Problems" might more beneficially be called, "Hilbert's 23 Open Questions." This conveys the true flavor of his ideas. — Preceding unsigned comment added by Ab3517 (talkcontribs) 00:18, 1 May 2016 (UTC)[reply]


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I think that a link may be add to the page Geometry and the Imagination. — Preceding unsigned comment added by P. Potiron (talkcontribs) 22:00, 27 November 2017 (UTC)[reply]

 Done I put the link in the See also section since it didn't seem to fit anywhere else. This can be lifted into the article if an appropriate sentence or two can be crafted. --Bill Cherowitzo (talk) 23:06, 27 November 2017 (UTC)[reply]

50 kilometers


There are about 50 kilometers between Znamensk and Kaliningrad. — Preceding unsigned comment added by (talk) 07:11, 20 September 2018 (UTC)[reply]

What is your point? Hrodvarsson (talk) 21:18, 20 September 2018 (UTC)[reply]
Hilbert is said to have been born in both. — Preceding unsigned comment added by (talk) 14:20, 25 September 2018 (UTC)[reply]
It is unclear whether Hilbert was born in Königsberg (today called Kaliningrad) or Wehlau (Znamensk), so the article mentions both possibilities. Yes, they are about 50 km apart. Certes (talk) 15:19, 25 September 2018 (UTC)[reply]

Correspondence with Einstein


This article does not appear to mention Hilbert's correspondence with Einstein. Vorbee (talk) 09:11, 24 January 2019 (UTC)[reply]

It seems that the German article on Hilbert doesn't either. Conversely, correspondence with Hilbert is mentioned neither in the English nor the German article on Einstein. - Do you have some source? - Jochen Burghardt (talk) 11:48, 24 January 2019 (UTC)[reply]



The "distinction between mathematics and metamathematics" isn't a major innovation by Hilbert. In particular, the cited source doesn't claim Hilbert invented it. The distinction between physics and metaphysics, wherever you want to draw it, was already of long standing in Hilbert's time. These are my reasons for removing this dubious assertion from the lead, where it is clearly being given too much importance. Eleuther (talk) 07:34, 30 October 2019 (UTC)[reply]