Wikipedia:Articles for deletion/The ugly theorem

This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was DELETE. (by Francs2000 2005-07-11 22:21:11)

[edit] The ugly theorem

Non-notable theorem. Gets no Google hits, and since it applies to only two real numbers, is not exactly powerful. Denni☯ 2005 July 2 00:43 (UTC)

• Delete. Somewhat interesting, but doesn't belong in an encyclopedia. --Canderson7 July 2, 2005 00:50 (UTC)
• Keep Rename to Ugly number since this is a property not a theorem(see comment below ↓). If it has been proven that it applies to only 2 natural numbers, it is extraordinarily notable, and the concept is any case encyclopedic. The article associated with the discoverer is very short, too, but that's not up for VfD because Google easily establishes notability. Not wishing to judge one article by another, but it seems that a theorem/concept from a notable mathematician has a fair shot at being notable itself (though is not guaranteed to be so). -Splash July 2, 2005 00:54 (UTC)
• Delete in light of the discussion that has ensued; particularly the children's book thing. -Splash 5 July 2005 22:39 (UTC)
• Keep. noteable Billhpike July 2, 2005 00:56 (UTC)
• Keep. That's a pretty interesting little mathematical trivia piece. COuld do with some more history or how the guy came up with it. Has it been proven that there are only three numbers that work? Harro5 July 2, 2005 01:03 (UTC)
  • I've not managed to find any references to this idea anywhere yet. After longer consdieration, I think perhaps this article is misnamed — without some result, it's hardly a theorem and more a property of numbers, like the perfect numbers. I'd be tempted to move it to Ugly number in consequence. I've amended my vote. Splash July 2, 2005 01:58 (UTC)
• Delete. The information cannot be verified. Oleg Alexandrov 2 July 2005 02:00 (UTC)
• Delete. As Splash noted, not a theorem, and there is no reason to believe anyone calls this "ugly number", so you can't move it there either IMO. It's possible that there is something here that is encyclopedia-worthy, but in order to decide, we need a real name for the category, and some cites. Dcarrano July 2, 2005 02:23 (UTC)
• As per Oleg Alexandrov and Dcarrano, citations are vital, in particular for the proof that the article asserts has been found that only those three numbers have this property. (If the proof has the shape that I suspect it to have, I can understand why some mathematicians would consider it to be ugly.) If sources are cited and the content can be verified, then Keep at whatever name turns out to be the one used in the sources; otherwise, as the article stands, Delete. Uncle G 2005-07-02 03:42:09 (UTC)
  • In response to my comment about a lack of an ISBN, an ISBN was supplied. The research by Nabla and Scimitar below convinces me that "ugly" is just an arbitrary adjective used for a property in a mathematics book for students, just as it apparently is used (for a different mathematical property) in the mathematical exercise that Nabla found. This is just a nonce definition of a minor mathematical property, therefore. And at best, what we have here is an erratum for the book, mentionable in Masahiko Fujiwara. Delete. (That was the shape that I suspected, by the way.) Uncle G 8 July 2005 15:04 (UTC)
• Delete. Folks voting should note that this was discussed on Wikipedia talk:WikiProject Mathematics. The consensus was to bring it here because the mathematicians don't believe it exists. Isomorphic 2 July 2005 03:48 (UTC)
• Delete as it stands (without citations or real classification)Onlyemarie 2 July 2005 05:08 (UTC)
• Delete It seems to be a little mathmatical trick. If it only applies to 2 numbers, then it holds no real promise to the world of Mathmatics and has no place in an Encyclopidia. Vipersp51 2 July 2005 5:16 (UTC)
• Delete I doubt this is true because 1458 is also "ugly". (1+4+5+8 = 18, 18 x 81 = 1458) Althought it seems there are no more of these through 1 million... Rangek July 2, 2005 18:00 (UTC)
  • Ha. Now the text says 1458 too. Nice. You know, it only took me like 5 minutes (well, 10 if you count the time it took to write the program) to search from 1--10000000 and uncover 1458. Does this "professor"'s "proof" mention 1458 or not? Since no one has cited any references, I guess we'll never know. Rangek July 2, 2005 20:37 (UTC)
  • Yeah, I added 1458 to the article since it was already there, but in the midst of a bunch of off-the-wall silly stuff. -Splash July 2, 2005 21:07 (UTC)
• delete: On the basis of the text "This theorem is refuted since 1458 was repoted to happen," this is not a theorem, and therefore this article is nonsense. If the article can be fixed and the notability established, perhaps I would vote keep. Brighterorange 2 July 2005 19:30 (UTC)
• Delete. Since the theorem is falsified by 1458, it fails the verifiability requirement. Quale 2 July 2005 22:14 (UTC)
  • Actually, the proof that there were only 3 such numbers being wrong would not make the article unverifiable. This is not mathematical verification, but encyclopaedic verification. What makes the article unverifiable is that so far no source has been proferred (apart from a vague statement that Masahiko Fujiwara published this theorem in "a book which became a best-seller in Japan", which entirely fails to state the ISBN of the book or any way of determining what book is being referred to) for the theorem's publication by anyone anywhere. It's less about whether the proof is correct, and more about whether the statement that such a (fallacious) proof was published is correct. The only thing that the addition of 1458 does is cast yet further doubt on the existence of any actual source material. Peer-review of a mathematical article would have caught that error within minutes, as demonstrated here. It looks like what is actually happening is that the original publication and peer-review of this mathematical assertion is happening here in Wikipedia, which is not what Wikipedia is for. Uncle G 2005-07-03 00:06:09 (UTC)
    • I don't fully agree with you. It's true that a false theorem could be encyclopedic, but that requires special circumstances. As you note, there's no evidence of that here. It is absolutely not verifiable that the information in the original article is correct, because in fact it was wrong. An encyclopedia article that simply stated "1+1=3" would fail verifiability even if there is someone somewhere who claims that it's true. You could instead say "Japanese mathematician xxx claims 1+1=3" and that might be verifiable, although it would probably be doubtful that it was notable. The article I voted on fit into the former category (made a claim that was demonstrably false), thus not verifiable. Quale 3 July 2005 06:27 (UTC)
      • Actually the article that you voted on was of the "Japanese mathematician xxx claims 1+1=3" type. See this version, for example. However, given that the author has been incorporating results derived from this very VFD discussion into the article (See this edit and this edit.) it still appears as though the peer review is happening here in Wikipedia. Uncle G 8 July 2005 15:04 (UTC)
• Delete, WP:NOR. Radiant_>|< July 2, 2005 22:31 (UTC)
• Comment The ISBN number now listed is a genuine book (in Japanese) which has a sales rank of 92 on Amazon.co.jp. I think further checking needs to be done about the contents of the book. Although it does seem strange to be called "the ugly theorem", it could be due to poor translation from the book. Bobbis 3 July 2005 01:25 (UTC)
• Delete, WP:NOR. --Idont Havaname 3 July 2005 04:21 (UTC)
• Comment. Besides 1, 81, 1458, and 1729, there are no "ugly numbers" up to 10⁹. It's also interesting that 1729 is the Hardy-Ramanujan number. Eric119 3 July 2005 04:32 (UTC)
  • Also, I would hazard that the article is more or less correct. The result is natural because the number of digits grows logarithmically with respect to the number itself and so the product eventually falls short of the original number. Of course this isn't a rigorous proof. Eric119 3 July 2005 04:47 (UTC)
• Anon comment. Nothing relevant mentioned in David Wells' The Penguin Dictionary of Curious and Interesting Numbers, which is full of just this sort of stuff. 82.210.118.102 3 July 2005 18:25 (UTC)
• Iff the book is valid, then I see nothing wrong with keeping this article, albeit probably under the name Ugly number. I also note that the article on 1729 cites 91 as having relevance as far as the Hardy-Ramanujan number is concerned, which is at the very least an interesting coincidence. Grutness...wha? 4 July 2005 02:11 (UTC)
• Keep (pending further facts), but rename to (for instance) Fujiwara's ugly theorem, or perhaps Fujiwara's ugly property. An ISBN number is now given, so it's falsifiable (see this page on amazon.co.jp as evidence that the book exists), the current sales rank seems to be 132 which would certainly make it notable, especially if it turns out to be wrong. Masahiko Fujiwara is a mathematician at Ochanomizu University with 22 publications on MathSciNet. I also note that nobody seems to have checked the book. The name Ugly theorem reminds me of a fragment in Hardy's A Mathematician's Apology, in which he states that some theorems, while true, are devoid of any interest. -- Jitse Niesen (talk) 4 July 2005 14:15 (UTC)
  • Comment. Perhaps, if people feel that the result an sich is not important enough, we should merge the article with Masahiko Fujiwara or Mathematical beauty? -- Jitse Niesen (talk) 4 July 2005 14:19 (UTC)
  • Changing to abstain. Based on the available information, it's on the borderline of notability for me. -- Jitse Niesen (talk) 7 July 2005 15:38 (UTC)
• Delete, as per Vipersp51, and also because:

1. Its almost an insult having such a thing as a mathematicians only referenced work.
2. What is the relevance of such property?

Why is it almost an insult? Because it took me less than 15 min to find that this is true for 1, 81, 1458 and 1729, and no other number up to 5 digits.

Its easy to show that any number with 5 digits can't have this property:

The sum of the digits would have a maximum of 45(=5*9), a reversal of such number would at most 93 (reversing 39<45), so any such product is less than 4185, which as 4 digits, thus is smaller than the target value.

This can be performed by any high school student studying math. A generalization of this for any number of digits is also relatively simple, yet quite boring to post on VfD.

Last, but not least, a Google search shows Ugly numbers as a completely different thing: Ugly numbers are numbers whose only prime factors are 2, 3 or 5.

--Nabla 2005-07-04 15:31:58 (UTC)

• Delete. The book is for junior high students (thank you, Babelfish!) as is evident by looking at the classifications at the bottom of the amazon page linked to above. Thus, this ceases to be a theorem, and more of a math game for junior high students. --Scimitar 5 July 2005 21:57 (UTC)
• I would say keep, but I ought to reveal that Masahiko is a friend of mine from way back. This material is also perhaps not quite stand-alone. Merge into the article on MF. Who, by the way, is quite prominent in Japan for other things, such as opposing the government on education reform. Charles Matthews 20:42, 10 July 2005 (UTC)
• Masahiko is your friend! Is it true? Masahiko has been giving his opinion on how education in Japan ought to be. It seem as though he has a conservative idea. His main opinion is that Japanese children should not

learn English while they're young.Instead, they should go back to Japanese classic literature. As I said in the article, Masahiko thinks great Math comes from the sense of beauty. So he thinks what children should do is to learn and memorize beautiful Japanese poems and phrazes. Have you heard from him about those ideas?User:DYLAN LENNON 21:42, 10 July 2005 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.