Talk:Georg Cantor

Memorial in Halle

There is a memorial bust of him in Halle - https://thalesandfriends.org/wp-content/uploads/2012/03/monument.pdf — Preceding unsigned comment added by 82.16.72.221 (talk) 18:32, 23 September 2024 (UTC)

unsourceable quotations attributed to Kronecker?

I’m concerned about the repetition in this article of Dauben’s (1977) claim that Kronecker directly called Cantor a "scientific charlatan", a "renegade" and a "corrupter of youth". I looked up Dauben’s source and it does not seem that Kronecker ever actually said that. The source for all of these quotations is supposed to be Schoenflies (1927) “Die Krisis in Cantor's mathematischem Schaffen”, but Dauben doesn’t list specific page numbers or precise sourcing. (Dauben also cites a Poincaré talk under the same footnote number, but as far as I can tell it does not mention any comments from Kronecker about Cantor.)

The relevant part from the page number he does cite from Schoenflies is:

Bei Kronecker hatte er den schärfsten Gegensatz gefunden. Es übersteigtnicht das erlaubte Mass, wenn ich sage, dass die Kroneckersche Einstellung den Eindruck hervorbringen musste, als sei Cantor in seiner Eigenschaft als Forscher und Lehrer ein Verderber der Jugend.

I don’t speak German but Google Translate renders this as:

In Kronecker he had found the sharpest contrast. It does not go beyond the permissible limit to say that Kronecker's attitude must have produced the impression that Cantor, in his capacity as researcher and teacher, was a corrupter of youth.

Saying that Kronecker “must have produced the impression” that Cantor was a corruptor of youth is not at all the same thing as claiming he literally said those words to someone. As far as I am concerned this kind of invention of a quotation is pure libel.

I would try to get Google translate to handle the whole Schoenflies paper, but the existing OCR of the German is poor, turning all of the umlauts into gobbledygook, so it takes a lot of manual effort to retype it, and I can’t be bothered.

Can someone who reads German go through the above source and look carefully for direct statements that Kronecker explicitly called Cantor a “renegade” or “charlatan”? Otherwise, I would recommend striking this whole section from the article. Such apparently poor scholarship makes me doubt Dauben as any kind of reliable source. –jacobolus (t) 18:33, 1 February 2022 (UTC)

Here is what Harold Edwards has to say (Edwards 1995, “Kronecker on the Foundations of Mathematics”):

Another thing everyone knows about Kronecker is that he made vicious and personal attacks on Georg Cantor. I used to know this too, but a colleague alerted me some years ago to the lack of primary sources for the story, and I began to look for evidence of the attacks. I asked various friends and scholars about the matter, including Joesph Dauben, the author of a well-known biography of Cantor, but no one seemed to have any evidence. I wrote to one author in Germany, who newly published the time-honored assertions about Kronecker's attacks on Cantor some years ago, and, after a long delay, he wrote back saying that his source was Dauben's biography of Cantor. But there is no evidence in Dauben's book of vicious and personal attacks. The word "attack" is used once or twice, but I take this to mean attacks on Cantor's philosophical positions, not personal attacks, and even for these, no evidence is offered. The worst Dauben accuses Kronecker of is attempting to prevent Cantor from publishing any of his work in Crelle's Journal, but this accusation is not backed up by any evidence. The one thing of this nature that we do know from a contemporary source is that, according to Heine, Kronecker held up publication of a paper of Heine until he had a chance to meet with Heine personally and explain his objections to it. Evidently Heine did not find Kronecker's arguments persuasive, because Heine's paper was published with little delay.

I should mention one other item in the matter of Kronecker's alleged attacks on Cantor, one I learned about from another of Cantor's biographers, Walter Purkert. Purkert directed my attention to a letter written by Cantor in 1891 in which he says that by chance he had come into possession of some notes of a course Kronecker had given that summer, and that in these notes Kronecker called some of Cantor's works "mathematical sophistry." This is indeed strong evidence that Kronecker did publicly oppose Cantor's theories, if not, as Cantor says in the same letter, evidence that Kronecker had been trying for 20 years to harm Cantor. There is of course no doubt that Kronecker disagreed totally with Cantor's theories. The question is whether he opposed them maliciously and with personal attacks on Cantor. To call the views of another professor "mathematical sophistry" before a student audience may have been regarded as a malicious attack in the cultural context of the Germany of 1891, but it is not what most of us had in mind when we imagined Kronecker's attacks on Cantor.

–jacobolus (t) 19:58, 1 February 2022 (UTC)

Nice work, jacobolus! Very impressed! I wouldn't dismiss Dauben in general for one point of insufficient checking, though; he's probably the best secondary source we have and would be pretty hard to replace. --Trovatore (talk) 23:21, 1 February 2022 (UTC)

I am not at all an expert, and have not read widely here, but my vague impression from what I have seen is more along the lines of: «Kronecker was philosophically opposed to Cantor’s foundations and methods of proof and said so publicly; Cantor was psychologically fragile and somewhat paranoid, and came to the (exaggerated/mistaken) conclusion that Kronecker was out to get him personally, and this led to a breakdown of their relationship.» It’s not entirely clear to me to what extent Cantor/Kronecker later reconciled. That Schoenflies paper quotes a letter from Cantor where he says he got a warm and friendly reply from Kronecker in 1884, but the Edwards bit I just quoted makes it sound like there was still some bad blood by 1891. It would be pretty helpful to find someone literate in German to check out the relevant papers from Schoenflies (which contain a bunch of Cantor’s letters, etc.) and try to write a fair and source-supported summary. Maybe there is some relevant material from Purkert? –jacobolus (t) 02:50, 2 February 2022 (UTC)

It occurs to me that Dauben himself might be persuaded to comment. According to his WP bio he'd be 77 years old; no idea how active he is these days. I don't have direct contact info to him but I could probably find someone who does. --Trovatore (talk) 04:16, 2 February 2022 (UTC)

While we’re here, is there any primary-source evidence for this article’s claim that Worse yet, Kronecker, a well-established figure within the mathematical community and Cantor's former professor, disagreed fundamentally with the thrust of Cantor's work ever since he intentionally delayed the publication of Cantor's first major publication in 1874, or Whenever Cantor applied for a post in Berlin, he was declined, and it usually involved Kronecker? If none can be found, then those should perhaps also be stricken or relegated to a footnote explaining that secondary sources make these claims without evidence but there is some controversy about their truth. Or if the ultimate source turns out to be “Cantor speculated such-and-such in a letter”, that should be explicitly stated. –jacobolus (t) 18:09, 3 February 2022 (UTC)

Generally Wikipedia editors aren't expected to be competent historians who can make these sorts of determinations about primary sources. It seems to me we have a secondary source, namely the Edwards paper, than can be used to counterweight the criticisms of Kronecker sourced to Dauben, and maybe we should simply represent both of these, in "Dauben says... but Edwards says..." kind of style. Any claims that don't have a secondary source should be removed. --Trovatore (talk) 18:32, 3 February 2022 (UTC)

Fine, but Wikipedia also shouldn’t perpetuate defamatory myths just because a secondary source once said something with no evidence and then was widely quoted/cited by miscellaneous other secondary sources none of which bothered to check the original claim. It can’t be that hard to find a Wikipedian who can read German willing to skim through Schoenflies (1927) looking for support for Dauben’s claims (it’s only ~20 pages). The burden of proof should be pretty high for making claims that trash someone’s reputation, and hiding behind a “we can’t investigate this directly, but need to rely on secondary sources” excuse seems ethically dubious to me. –jacobolus (t) 23:04, 5 February 2022 (UTC)

I just read through Schoenflies, which mainly consists of Cantor letters, e.g. to Mittag-Leffler. I found no clear evidence of anything Kronecker ever did or said to Cantor, except for (a) a claim that Cantor saw a letter from Kronecker to Hermite “in which he tries to belittle my work with his poisonous pen and to discredit me” (p. 8) without any further specifics, and (b) a claim that Kronecker criticized Cantor’s work in front of students in 1891 (»Six months ago I offered [Kronecker] the opening lecture in our mathematical section and he accepted this offer with great satisfaction. ¶ Now I believed that my courtesy would persuade him to cease his hostilities against me, at least this summer. On the contrary! I happen to have in my possession a transcript of his public lecture on the concept of number, which he gave this summer semester at the University of Berlin, and I have here black and white proof that he disparaged my mathematical work in the most shameless way and without any attempt at scientific justification before his immature, impartial listeners. What do you think?», p. 13 via Google translate). What I also found was that in 1884 Cantor exchanged some nice letters with Kronecker, went to visit him, and had a polite and pleasant 6 hour conversation during which neither side was convinced. I also found several other letters where Cantor calls Kronecker various insulting names. The thing that comes across to me most strongly in the letters is a clingy desperation from Cantor, who was clearly going through a bad time and was grasping for validation. It reminded me of the conversations a depressed lonely person might have with a friend after a bad romantic breakup. The more I investigate the more it seems like there were never any quotations like "scientific charlatan", "renegade" or "corrupter of youth", and that Dauben perhaps misunderstood some other source or just made them up. Cantor clearly personally believed for a decade + that Kronecker was secretly plotting against him (denying him publication in Crelle's Journal, blocking him from academic jobs, gossiping about him behind his back, etc.) but while there might be some truth to these speculations I don’t see any direct evidence and it also seems plausibly an invention of a paranoid depressed person. –jacobolus (t) 05:42, 6 February 2022 (UTC)

Jacobulus, you weave a plausible narrative, and I wouldn't bet at all against you being right. I think it's nice work and I personally thank you for making me aware of it.

That said, I have the sense that you might be taking this a tiny bit personally. Our function here is not to right great wrongs, particularly on behalf of persons who aren't so much living as the other thing. (Note in passing that Dauben is a living person, and we have a higher duty of care in his regard, even on talk pages.)

The term "original research" is often used on Wikipedia as a euphemism for "crankery", but I don't think your work looks crankish. But I do think it's at least borderline original research. What I think we should do is represent the Edwards source. If that opinion becomes the mainstream view, then we can present it as such, but it's not our role to make that happen. --Trovatore (talk) 22:32, 6 February 2022 (UTC)

(By the way, I haven't managed to get in touch with Dauben yet, but I haven't given up. I'd really like to hear his take on this.) --Trovatore (talk) 22:36, 6 February 2022 (UTC)

It’s hardly “original research” to follow one secondary source’s link to another secondary source, and check if the attributed quotation actually occurs there. Especially since Edwards apparently tried to do the same check. Perhaps a fair summary would be something along the lines of: For over a decade Cantor believed he was being persecuted by his former teacher Kronecker, who he believed to be “plotting” against him. Cantor believed that Kronecker had blocked the publication of his papers in Crelle’s journal, blocked him from academic jobs, and unfairly attacked his work in letters to other mathematicians and public comments. While Cantor’s grievances have been repeated as fact in secondary sources, the only claim for which there is clear evidence is that Kronecker called one of Cantor’s arguments “mathematical sophistry” in a lecture to students in 1891. Then some of the controversy can be elaborated in a footnote. –jacobolus (t) 23:20, 6 February 2022 (UTC)

(Note in passing that Dauben is a living person, and we have a higher duty of care in his regard, even on talk pages.) – fair enough, and sorry. I am not trying to accuse Dauben of deception or misconduct. It’s entirely plausible that he had a source, and it just wasn’t clearly cited in his paper (e.g. maybe Cantor directly said Kronecker had called him these names in some letter other than those reprinted by Schoenflies, or maybe one of Kronecker’s letters to another mathematician had these names printed in it). Mostly I’m frustrated as a reader to find something written as a direct quotation, reprinted widely (including in Wikipedia) as a quotation, but then not be able to track down any place where the supposed quotation occurred. It makes it impossible to figure out if the quotation was real and if so what the context was, who the audience was, etc. I don’t think Wikipedia should ever uncritically reprint quotations from secondary sources where the quotation cannot be validated in any way and where the citation in the secondary source doesn’t actually lead to the words quoted. (At that point, can it even be considered a secondary source for the quotation?) –jacobolus (t) 23:43, 6 February 2022 (UTC)

Chronic depresson

What is the source for the claim of chronic depression? 73.193.148.242 (talk) 15:37, 17 August 2022 (UTC)

Is that in "Dauben 1979, pp. 283–284"? Which sentence(s) this is a source for is unclear to me. The Crab Who Played With The Sea (talk) 01:28, 23 August 2022 (UTC)

Quote from Dauben on Bell

The quote from Dauben in the Biographies section has no connection to the preceding paragraph - it doesn't even mention Bell. Unhandyandy (talk) 20:16, 19 March 2023 (UTC)

Article presents Cantor's results as unconditional truth, despite finitist school existing.

> Cantor ... proved that the real numbers are more numerous than the natural numbers

The article should clearly state that Cantor's proof is only valid within the (nowadays mainstream) trans-finitist school, but invalid in the views of finitist / intuitionalist / Aristotelean schools. Article states Cantor's axioms are printed in college curriculums worldwide - but that in not a proof of truthfulness, just suppression of valid alternative schools of mathematics. 94.21.160.96 (talk) 94.21.160.96 (talk) 22:43, 16 November 2024 (UTC)