Wikipedia:Featured article candidates/Georg Cantor


 * The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was promoted 21:04, 31 July 2007.

Georg Cantor

 * Self-nom by Ling.Nut but many others contributed significantly.
 * This article has an A-rating in WikiProject Biography,WikiProject Mathematics, WikiProject Germany and WikiProject Philosophy. It had a positive Peer Review. It has been collaborated on by several mathematicians and other editors. It is well-developed and has a boxful of references (plus more stored away in case of challenges). Ling.Nut 16:19, 23 July 2007 (UTC)
 * oppose. I am extremely disappointed by what has happened to the section on ancestry since I wrote it; I attempted to be factual and non-tendentious; this is neither. The rest of the article will require more consideration; this can be discussed on its talk page. Septentrionalis PMAnderson 19:34, 23 July 2007 (UTC)
 * Comment The relevant discussion regarding this 'Oppose' vote is on the article's Talk, here. FA reviewers can judge for themselves whether or not these are valid grounds for opposing Featured Article status. Ling.Nut 20:37, 23 July 2007 (UTC)
 * I may simply edit it again; but I offer an oppotunity to justify the changes. The rest of the article has been thoroughly revised, and I intend to comment on that when I have perused it. Septentrionalis PMAnderson


 * Edited; I think it's improved, and am withdrawing the oppose; but the edit history should be checked before it is put on the main page. Septentrionalis PMAnderson 01:23, 24 July 2007 (UTC)


 * Comment Articles that depend strongly on a single source, as Dauben here, have been failed from both GA and FA for citing their source as rarely as this article does, and indicating it no better. This is not an oppose, because I think those decisions were wrong; but it should be borne in mind. Septentrionalis PMAnderson 21:07, 23 July 2007 (UTC)
 * It has more than thirty cites to the main source (which is well indicated in footnote 2). I would be shocked if such a well sourced article had been failed previously for such a reason. Geometry guy 00:24, 27 July 2007 (UTC)
 * Comment Does anyone have any input on making Georg Cantor the selected biography for the Logic Portal for the month of August? I suppose it might be a good mark for it. Perhaps the timing is an issue, and some time down the road would be better? Please advise. Gregbard 10:20, 25 July 2007 (UTC)
 * Support. I had some concerns about the mathematical sections, but I fixed them. This article is in excellent state, well referenced and sourced. Geometry guy 00:24, 27 July 2007 (UTC)
 * Support with misgivings I like this article a lot, and I recognize the love and care that have been lavished on it. However, I fear that it does not reach out to lay-people in the way that a general encyclopedia should; most of it reads like a biographical sketch written for the mathematical cognoscenti. I really wish that there were a section describing in simple terms for the lay-person why the real numbers are not countable, and that that result were described with appropriate emphasis in the lead section.  Bonus points for a discussion of the rationals! :)  If Scientific American can do it, then so can we, no?  At least perhaps someone should write a daughter article that does all that and then include a link to the daughter article.  Non nobis solum — we do not write Wikipedia articles for ourselves, but for earnest students who wish to learn; please build a bridge to them, lest our work be in vain. Willow 01:39, 27 July 2007 (UTC)
 * PS. Minor point: can one make a link to non-standard analysis from transfinite numbers? It occurs to me that there is a 1-to-1 mapping between a finite repeating decimal such as

\frac{1}{3} = 0.33333\ldots = 3*10^{-1} + 3*10^{-2} + 3*10^{-3} + \cdots $$
 * and an infinite number, by inverting the signs of all the exponents

3*10^{1} + 3*10^{2} + 3*10^{3} + \ldots $$
 * which, when inverted, should give an infinitesimal. One might be able to define an ordering on the infinitesimals based on the ordering of the finite decimals.  Just a stray thought, Willow 01:39, 27 July 2007 (UTC)
 * Comment from non-mathematician: Cantor thought infinitesimals were evil (not literally), and resisted attempts to define them using transfinite numbers. I'm not exactly sure what hat means, but it might mean that connecting the two in this article won't work....? Ling.Nut 01:52, 27 July 2007 (UTC)
 * Further comment/request clarification: If I understand Willow 's reservations correctly, it seems she is wanting the article to explain the logic of Cantor's diagonal argument (which mathematicians find so swoon-inducingly elegant) ...? Ling.Nut 02:59, 27 July 2007 (UTC)
 * Hi Ling.Nut, thanks for your note! :) I'm not particular about the method, although I agree that the diagonal argument seems like the rigorous proof most likely to be intelligible.  The main thing is to clarify the uncountability of the reals; there are probably many ways of doing it.  You might begin with a simpler, non-rigorous, intuitive argument, then move to the rationals, and thence to the reals.  If you stick to arguments that seem ridiculously kindergarten-simple to you, then the rest of us might have a chance of understanding them. ;) Ramp up gradually; keep the simpler arguments close to the beginning of the article, so that readers don't drift away before they get to the good stuff :) Good luck and best wishes, and I know you'll have good help Willow 03:49, 27 July 2007 (UTC)
 * This should be done in Cantor's diagonal argument. The article on Georg Cantor is a biography, not an introduction to transfinite set theory. Geometry guy 09:43, 27 July 2007 (UTC)
 * I see your point and whatever you all decide is fine; the purely biographical material is excellently written and you definitely have my support either way. But please consider that readers will want to understand why they should care about Georg Cantor, what did he do important?  The article has a section on his "Work", which to me seems as though it would be rough sledding for many readers.  I would suggest either to (1) simplify the language throughout that section — which, unfortunately, would make it less accurate, I guess — or (2) choose one or two core concepts (e.g., power sets or that there are different types of infinity) and explain that/them in detail, either here or in a linked daughter article.  Perhaps more Figures might help, e.g., illustrating the power set, and a more lay-friendly Figure for the bijection?  I suspect that the two ovals with the symbols and arrows may be mysterious to many readers.  There's the more picturesque metaphor of comparing the number of grains of sand in two buckets, or (say) matching parents and children at a very large adoption agency; perhaps do the finite case and then extend to the infinite?  I just think readers would be happier if they came away understanding one thing well, rather than five things vaguely; grasping one concept might also inspire them to try to learn more, which would be a Good Thing, no?  Willow 10:45, 27 July 2007 (UTC)

(undent) Comment: In response to Willow's comments, we added a new super-top-level intro to his Works, which is extremely abbreviated/simplified. IMHO, the nuts and bolts of actually explaining his work in a digestible fashion should be done in the relevant articles which are dedicated to aspects of his work &mdash; see e.g. Cantor's diagonal argument. I agree that article and others need work, but that fact should not penalize this article. Ling.Nut 18:33, 28 July 2007 (UTC)
 * Comment -
 * I think the second sentence under Youth and studies would be better if worded as "Georg, the eldest of six children, was an outstanding violinist, having inherited his parents' considerable musical and artistic talents ."
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Perhaps I am reading this incorrectly, but the 7th paragraph under Teacher and researcher reads, "Cantor suffered his first known bout of depression in 1884.[18] This emotional crisis led him to apply to lecture on philosophy rather than on mathematics. He also began an intense study of Elizabethan literature in an attempt to prove that Francis Bacon wrote the plays attributed to Shakespeare; this ultimately resulted in two pamphlets, published in 1896 and 1897.[19] Every one of the fifty-two letters he wrote to Gösta Mittag-Leffler in 1884 attacked Kronecker. A passage from one of these letters is revealing of the damage to Cantor's self-confidence:" - This seems to jump into information about letters to G M-L. The way it is worded is as if these letters have been previously mentioned, however, they have not. Additionally, I recommend removing the "on" before "mathematics".
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Following the previous, "Cantor soon recovered in 1885, and subsequently made further important contributions, including his famous diagonal argument and theorem, but he never attained again the high level of his remarkable papers of 1874–84." - This prose could use some work. Possibly, "*Cantor soon recovered and, in 1885, made further important contributions including his famous diagonal argument and theorem, but he never again attained the high level of his remarkable papers of 1974-84. "
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Under Late years, "After Cantor's 1884 hospitalization, there is no record that he was in any sanatorium again until 1899.[21] Later that same year," - Later which year? 1884 or 1899?
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Following the previous, "and this tragedy finally drained Cantor of much of his passion for mathematics." - "Finally" seems out of place.
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * "The events of 1904 preceded a series of hospitalizations at intervals of two or three years." - "two or three years" or "two and three years"?
 * Not fixed, the original seems acceptable. Ling.Nut 10:54, 29 July 2007 (UTC)
 * Second paragraph under Set theory, "... transcendental numbers is nondenumerable (that is, not countable)." - The meaning of nondenumerable has already been explained a couple times. I recommend removing the info in parenthesis.
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Following the previous, "Cantor had shown that union of two denumerable sets must be denumerable." - Is there a word missing? Such as "that the union"?
 * Fixed thanks. Ling.Nut 10:45, 29 July 2007 (UTC)
 * Under Continuum hypothesis, "there exists no set whose power is greater" - Should that be "whose" or "thats"?
 * Not fixed, the original seems acceptable. Ling.Nut 10:54, 29 July 2007 (UTC)
 * Unable to complete review at this time. Lara  ♥Love  07:14, 29 July 2007 (UTC)


 * Comment: This is a fine article and deserves to be an FA. However, I have some problems with the lead section. It should summarise the article, but unfortunately there are some interesting "teasers" in the lead that are not fully explained in the article. For example, Poincaré's quote is quite strong, but is not explained. Kronecker's opposition is explained well, but I cannot see the connection between his opposition on a mathematical basis and the quote that Cantor is a "corruptor of youth". There is also a mismatch between the lead section and the philosophy section. Wittgenstein is mentioned in the lead, but there are no details in the philosophy section. Some additional sentences on the Christian theologians' objections with Cantor's theory would be nice. As it is, both sections just state that there were objections without any details. Finally, it would be great to add details, if the sources provide it, on the motivations behind Cantor's philosophical beliefs (why did he believe in direct communication from God, why was he the only person in Halle that did not believe in a deterministic universe, etc.). This addition would make this a better biography article as well as a mathematics/philosophy article. The last point isn't a big deal though, but please fix the mismatch of the lead and the rest of the article. --RelHistBuff 15:40, 29 July 2007 (UTC)
 * Reply: OK the quote regarding Poincare is explained in a new paragraph beginning "Debate among mathematicians grew out of...". More to come... Ling.Nut 20:35, 29 July 2007 (UTC)
 * Further reply: amplified "corrupter of youth"
 * Further reply: I really thought the Catholic argument was clear before this, but I added 1 more sentence to make it (hopefully) even more perspicuous: see "God's exclusive claim to supreme infinity". As for Wittgenstein, explaining his thought is of course difficult, but I gave a (probably inadequate) 1-sentence summary at the end of the paragraph beginning "Debate among mathematicians...". I hope this satisfies RelHistBuff's concerns Ling.Nut 23:10, 29 July 2007 (UTC)
 * You have my Support. Very nice article on a complex man. --RelHistBuff 06:39, 30 July 2007 (UTC)


 * Support - All issues I found were addressed or explained. I feel it now meets the criteria. A very well-written article. Lara  ♥Love  03:34, 30 July 2007 (UTC)
 * The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.