Talk:Georg Cantor

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Christian or Jewish?[edit]

Georg cantor is listed both in List of Jewish scientists and philosophers and in List of Christian scientists. Which one is right? Was he Christian or Jewish? --Fibonacci 04:00, 25 Oct 2004 (UTC)

Well, according to footnotes in http://www.jinfo.org/Philosophers.html,
4. In Men of Mathematics, Eric Temple Bell described Cantor as being "of pure Jewish descent on both sides," although both parents were baptized. In a 1971 article entitled "Towards a Biography of George Cantor," the British historian of mathematics Ivor Grattan-Guinness claimed (Annals of Science 27, pp. 345-391, 1971) to be unable to find any evidence of Jewish ancestry (although he conceded that Cantor's wife, Vally Guttmann, was Jewish). However, a letter written by Georg Cantor to Paul Tannery in 1896 (Paul Tannery, Memoires Scientifique 13, Correspondance, Gauthier-Villars, Paris, 1934, p. 306) explicitly acknowledges that Cantor's paternal grandparents were members of the Sephardic community of Copenhagen. In a recent book, The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (Four Walls Eight Windows, New York, 2000. pp. 94, 144), Amir Aczel provides new evidence in the form of a letter, recently uncovered by Nathalie Charraud, that was written by Georg Cantor's brother Louis to their mother. This letter seems to indicate that she was also of Jewish descent, as Bell had claimed originally.
In other words, good question. --jpgordon{gab} 04:08, 25 Oct 2004 (UTC)
Depends on your definition of "Jewish", right? Some definitions would make your question have an exclusive "or". Dauben, the reigning Cantor expert, mentions the info Jpgordon gives above, but he also adds that Cantor was not Jewish "in an orthodox rabbinical sense, since his mother was a Roman Catholic". This is from Dauben's book on Cantor. However, as the whole book makes clear, Cantor was a very devout Christian, making theological researches into the nature of the Trinity even. He was also baptized a Lutheran. So Cantor should definitely be listed as a Christian. I don't know whether all this makes him Jewish --C S 03:45, Dec 5, 2004 (UTC)
My definition makes that an exclusive "or". I'm asking about his beliefs, not about his heritage. But you have already answered my question. --Fibonacci 15:41, 12 Apr 2005 (UTC)
I put him on the new and improved List of Christian thinkers in science. He could be Jewish, by culture or Jewish law of maternal inheritance, but still fit that considering his theological research. In fact I think I put one or two other Jewish scientists there as you can be both.--T. Anthony 13:28, 23 January 2006 (UTC)

Cantor was a Christian, born of Christian parents. He never referred to himself as a Jew. Moreover, he was far more enthusiastic about Christianity in his intellectual activities than was in any way required. If Jewishness is defined by beliefs and practices, Cantor was not a Jew at all.

Nevertheless, the name Cantor is very Jewish. Evidently, he descended from Jews who had converted to Christianity, a situation not all that rare then or now. If Jews are seen as a human tribal community related by descent, than he was a Jew of sorts. That his father was a stockbroker, and that he pursued abstruse mathematics are facts consistent with this. The high level of musical and literary culture in the Cantor home are consistent with this. So was Cantor's friendship with Edmund Husserl, a Jew who converted to Lutheranism in 1887. Keep in mind here that there are a few Jews who recognize Christ as the Messiah and who revere the New Testament, but who proudly describe themselves as Jews. Quite a few Jews in their day-to-day lives accept Jewish converts to Christianity as fellow Jews for certain purposes. You would not necessarily want your Jewish son to marry one but... In any event, I submit that a tribal understanding of Jewishness has more predictive power than a faith one.202.36.179.65 23:43, 16 February 2006 (UTC)

I do not see why Cantor is a specially Jewish name. "Kantor" is the title of a singer in a church service, both in Protestant churches, Catholic churches and Jewish synangogues. There are many Germanys called "Kantor", "Kenter" etc. who are not of Jewish origin. —Preceding unsigned comment added by 79.178.137.236 (talk) 12:40, 25 February 2009 (UTC)

I find the above ad nauseum discussion about the religion of his family irrelevant and racist. Are there several paragraphs in the Wiki biographies for all famous people discussing arguments for and against their inclusion in certain ethnic or religious groups? Why not? Unless it sheds light on some aspect of his beliefs or works (and CLEARLY if it is moot it does not rise to the level of inclusion here) it should not be included. boo for Wikipedia69.40.250.129 (talk) 03:00, 3 September 2010 (UTC)

Weyl[edit]

H. Weyl generally supported Cantor, while admitting that "at the furthest bounds of set theory, some contradictions did show up." —Preceding unsigned comment added by 86.137.170.8 (talk) 11:43, 25 July 2009 (UTC)

BBC doco[edit]

Cantor was one of four subjects (along with Boltzmann, Gödel and Turing) in the 2008 BBC doco called "Dangerous Knowledge". (see here). Not sure if this belongs in the article but I thought I'd pass it along. Manning (talk) 03:00, 25 September 2009 (UTC)

Don't even try[edit]

Whether Cantor was or wasn't Jewish is a question that assumes that there are definite boundaries to the set "Jewishness." This assumption of non–continuity can neither be proved nor disproved using standard Zermelo–Fraenkel set theory plus the axiom of choice.Lestrade (talk) 19:46, 24 February 2010 (UTC)Lestrade

What was the need for this comment? No one has brought up the question in more than a month. There is no need to go looking for trouble. --Trovatore (talk) 20:55, 24 February 2010 (UTC)

Lol I believe he was being facetious. Lestrade was simply applying relevant theorems of Cantor's study area (e.g. Zermelo-Fraenkel) and applying it to knowledgability within discussions of "Jewishness" or anything that goes into wikipedia. Genius comment, sir. —Preceding unsigned comment added by 155.31.173.86 (talk) 20:20, 7 October 2010 (UTC)

Poincare Criticism?[edit]

I am not sure that the statement Poincare disliked Cantor's work is correct. Reference Marcus du Satoy's recent TV Program on the story of mathematics where he claims Poincare publically supported the efforts. Also in Engines of Logic by Martin Davies claims the statement from Poincare, "a disease from which one has recovered", is apocryphal. —Preceding unsigned comment added by 82.69.53.110 (talk) 11:33, 24 September 2010 (UTC)

See the Wikipedia article on Henri Poincare. His opposition to the transfinite and the like is fully referenced in refs. 40 and 41. — Preceding unsigned comment added by 92.26.2.17 (talk) 13:57, 11 September 2012 (UTC)

School named after him[edit]

Does it make sense to mention somewhere in the article that in Halle (the city where he died) a school is named after him (Georg-Cantor-Gymnasium)? Or maybe just link it in the "See Also" section? TFTD (talk) 07:36, 7 October 2010 (UTC)

To tell the truth, I am not very enthusiastic about doing either. Most notable historical personalities have at least one school named after them, and it's not really relevant to him, while he is of course relevant to the school.
By the way, I have reverted your edit to his death place. Our general convention is to use countries and geographical subdivisions as they existed at the time. Since Saxony-Anhalt is a post-war creation he never had anything to do with it. If you think it's very important, the section "Teacher and researcher" looks like a natural place to say something like "Halle in the province of Saxony (now Saxony-Anhalt)", but I am not sure if that wouldn't be undue weight. It looks like a borderline case to me. Hans Adler 10:14, 7 October 2010 (UTC)
Thx for the fast response and sry about the edit on the Saxony. I should have guessed that but since you changed it to Province of Saxony it's more clear and less misleading (before it stated just Saxony).
To the school thing, I totally agree with you. The intention was that the school article is marked as an Orphan, but I don't want to force anything. TFTD (talk) 09:30, 8 October 2010 (UTC)
Yes, I saw the orphan tag but neglected to mention it. I am not sure that a link from Halle, Saxony-Anhalt is appropriate either, but one could of course create something similar to de:Portal:Halle/Einrichtungen. But we would do it as a list here, and one would have to verify first that we have already enough other links for such a list. The tag is a bit silly on that article anyway, and I see it was added by an editor who was blocked last year for insisting on this kind of nonsense and vanished this April. As it disfigured the article for no discernible purpose I have simply removed it now. Hans Adler 09:52, 8 October 2010 (UTC)

Harvrefcol -> Citation[edit]

This article uses a very unusual citation templates, {{harvrefcol}}, which produces an output which is (usually) identical to {{Citation}}. (The only difference is the way that the journal volume, issue and number appear).

{{Harvrefcol}} appears in only five articles. Obscure templates such as {{harvrefcol}} tend to be poorly maintained and often have incomplete functionality. {{Citation}}, on the other hand is used in more than 56,000 articles, and is uses the same core as the {{cite *}} family of templates, which are used several million articles. This family of templates is very well maintained and well documented.

Any objections to converting {{harvrefcol}} to {{citation}}? ---- CharlesGillingham (talk) 19:10, 20 December 2010 (UTC)

I don't have any objections. Your reasoning makes sense. However, you may want to hear from some others first, if only out of courtesy to those editors responsible for this excellent article (and one of the relatively few to be a "Featured Article"). I've made only one or two insignificant additions to this page, so I'm not in the loop here. Good luck Christian Roess (talk) 20:33, 20 December 2010 (UTC)
Yes check.svg Done Mark Hurd (talk) 16:22, 30 September 2011 (UTC)

Letter from Cantor in Russell's Autobiography[edit]

Not to bring up a potentially very silly subject that has already been beaten to death, but shouldn't the section "Cantor's ancestry" (which maybe, on the other hand, need not even exist) include that nice paragraph in Cantor's letter to Russell (the one where he says that he is not "full germain" (sic)) and proceeds to give an account more or less orthogonal to everything currently said in our page)? Feketekave (talk) 19:30, 21 December 2010 (UTC)

I am not familiar with Cantor's comment. What did he say? Tkuvho (talk) 21:13, 21 December 2010 (UTC)
Ah, here I have it. Feketekave (talk) 18:42, 27 September 2011 (UTC)

On a different matter, shouldn't we make it clearer in the lead that Wittgenstein lived quite a bit later than Cantor, at a time when Cantor's work had already become accepted by mathematicians? Some readers will be confused. Feketekave (talk) 18:52, 27 September 2011 (UTC)

Changes related to Cantor's 1874 article[edit]

I have rewrote the material on Cantor's 1874 article to agree with the Wikipedia article Cantor's first uncountability proof. Most of my changes are in the first two paragraphs of Georg_Cantor#Set_theory. The second paragraph uses Cantor's 1874 proofs.

In the first paragraph, I took out the unreferenced statement: "The paper, published in Crelle's Journal thanks to Dedekind's support (and despite Kronecker's opposition)… ." I have been unable to find any evidence to support this statement. On the other hand, Cantor's first uncountability proof mentions the article's "quick acceptance (only four days after submission)." Here's the timeline:

December 23, 1873: Cantor submits his article.

December 25: Cantor writes Dedekind that he has submitted a short article to Crelle's Journal containing titled On a Property of the Collection of All Real Algebraic Numbers. He says the article contains results that appear in his recent letters. Dedekind writes back and advises Cantor "to drop the restriction to the field of all real algebraic numbers." (Quote from Cantor-Dedekind correspondence, Ewald 1996, vol. 2, p. 850.) In other words, Dedekind advises Cantor to publish the stronger theorem: The collection of all algebraic numbers (both real and complex) is countable.

December 27: Cantor writes to Dedekind that Borchardt, the editor-in-chief of Crelle's Journal, has accepted the article.

By the way, Dedekind had no influence with the Berlin mathematicians, who controlled Crelle's Journal. As Ferreirós 2007, p. 185, points out: "There is some evidence that Kronecker and Kummer were angered with Dedekind after the publication of his theory of algebraic numbers in 1871." (Ferreirós then gives the evidence.) Kronecker had an equivalent theory of algebraic numbers that he did not publish until 1882. Also, Kronecker did not like Dedekind's approach since Dedekind's ideals are infinite sets of algebraic integers.

I should probably add a little on Cantor's 1878 article since it contains a proof that the set of real numbers and the set of irrational numbers have the same power. This proof can be easily modified to prove that the set of transcendental numbers has the same power as the set of reals. Before adding more, I would like to see reader's reactions (either in comments or changes) to the changes I've just made.

Also, I added an on-line link to Cantor's 1874 article. I found that the on-line link to Cantor's Gesammelte Abhandlungen mathematischen und philosophischen inhalt no longer works (at least on my computer). Does this link work for other readers?--RJGray (talk) 19:22, 29 December 2010 (UTC)

Kronecker's opposition was documented by Dauben who connects it to the weak title. Edwards has pursued the line that Kronecker did not oppose Cantor vigorously, but Dauben's research tends to refute Edwards. Tkuvho (talk) 19:52, 29 December 2010 (UTC)
Thank you for your comment. The weak title is an excellent point, and it has generated some controversy. When I was writing Cantor's first uncountability proof#Why does Cantor's article emphasize the countability of the algebraic numbers?, I realized that Wikipedia's NPOV policy required both Dauben's viewpoint (the title was caused by Kronecker's influence) and the opposing viewpoint that points to Weierstrass' influence.
For the opposing viewpoint, I used José Ferreirós' 2007 book Labyrinth of Thought: A History of Set Theory and Its Role in Mathematical Thought. Ferreirós' book covers the pre-history and early history of set theory as well as central parts of its modern history. It is well researched, contains lots of references, and it contains information that does not appear in Dauben's work. Ferreirós provides evidence that Weierstrass' influence was responsible for the title of Cantor's article. I'm interested in what you think about his arguments. Personally, I'm most interested in the NPOV aspect of the controversy, and letting people decide for themselves.
In any case, if Kronecker made any complaints about the 1874 article, most likely Cantor would have mentioned it — he certainly let Dedekind know about his worries concerning Kronecker and his 1878 article. Also, the article's quick appearance shows that there was no publication delay.
Thanks for pointing out Edwards' point of view. Where do Edwards arguments appear? Are they contained in his Essays in Constructive Mathematics?--RJGray (talk) 22:25, 31 December 2010 (UTC)
I don't remember anymore, sorry. I am pretty sure I found this online in a popular magazine, perhaps american math monthly. Tkuvho (talk) 15:16, 14 April 2011 (UTC)

Cantor's paradox[edit]

I wonder if someone who's taken the trouble to do such a nice job on this page might look at Cantor's paradox, and edit it so that it will be tied more closely to this one. (Lorenzo Traldi (talk) 15:08, 14 April 2011 (UTC))

Did Poincare call set theory a "grave disease"?[edit]

Some sources dispute this. DHN (talk) 09:29, 14 April 2013 (UTC)

University of Zurich or ETH?[edit]

"Youth and Studies" says University of Zurich, Infobox says alma_mater = ETH Zurich. Neither has a citation. Garymm (talk) 23:35, 1 February 2014 (UTC)

Encyclopædia Britannica says "University of Zürich". - Jochen Burghardt (talk) 23:51, 1 February 2014 (UTC)
... while Astroseti.org (the other link reachable from www-history.mcs.st-andrews.ac.uk, found via Mathematics Genealogy Project) says "Politécnico de Zurich" (which probably translates "ETH"). All of de:Georg Cantor#Leben, www.deutsche-biographie.de, and leopoldina say "University". Neither the wikipedia article on ETH Zurich nor that on University of Zurich lists Cantor among their famous students. To summarize, "University" seems to have the majority of votes. - Jochen Burghardt (talk) 00:11, 2 February 2014 (UTC)

Millerites[edit]

Does anyone know whether there's anything to the claim that the Millerites (presumably adherents of Millerism) were interested in Cantor's work? For me, a web search doesn't find much, and one of the things it does find is the same claim in this article from several years back.

So there seem to be several possibilities:

  1. Just a hoax, with a persistent perpetrator.
  2. Someone trying to add something he/she thinks is really true, but can't substantiate.
  3. An actual tidbit about the Millerites, potentially sourceable if we found the right sources.

Now, even in case 3, I kind of doubt it's appropriate for this article, but the matter could be discussed. (Might be more appropriate at Millerism, which doesn't mention Cantor.) --Trovatore (talk) 03:11, 11 July 2014 (UTC)

I think you have expended too much time researching this already. It's clearly a little bit of promotion. I don't spend much time on wikipedia, but I've seen heaps of these little bogus promotions for various causes. So I'm sure you've seen a thousand. I imagine someone who wanted to promote millerism has done a search in wikipedia for certain keywords which appear on the Cantor page. If Cantor had been a major influence on Millerism, that could be worthy of comment on the Cantor page, but then it would surely show up on the Millerism page. But really, the Cantor page is big enough and comprehensive enough already. It doesn't need to be padded with introspective musings. Just my 2¢ worth....--Alan U. Kennington (talk) 05:36, 11 July 2014 (UTC)

Clarifying an edit summary[edit]

I wrote a rather confusing summary for this edit. I wrote:

I do not think his first proof is more complex or less elegant than the original. I think the original is more elegant.

What I actually meant was:

I do not think his first proof is more complex or less elegant than the later (1891) proof (the diagonal argument). I think the original is more elegant (than the later diagonal argument).

The original proof is applicable to all densely ordered sets that have at least two members and that have no gaps. Michael Hardy (talk) 18:18, 11 December 2014 (UTC)