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V. A. Gorbatov claims that he solved 4-color problem in 1964, and he repeats this claim in his book which appears in 2000. (The paper and the book are in Russian; the book is also translated to Spanish --- see refs below.) Obviousely, I doubt that it is true, but I do NOT want to read the book...

Question: Did anyone checked this proof?

Why do I care. This claim appears in Russian wikipedia and I would be happy to have a good reason to remove it. (At the moment ru.wikipedia states Gorbatov's claim and says that nobody checked his proof.)

  • Горбатов В. А. Фундаментальные основы дискретной математики.
  • Gorbatov, V. A. Fundamentos de la matemática discreta.
  • Горбатов, В. А. О минимальной раскраске графа // Доклады НТК. МЭИ, Подсекция вычислительной техники. --М.: МЭИ, 1964. -С. 17.

Summary of answers: I have got few answers, roughly stating that there is no sign that Gorbatov is a serious mathematician. I agree with that, but it is not an answer to my question...

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I haven't heard this claim before, but the earliest paper by V.A. Gorbatov in MathSciNet is from 1970, Zentralblatt mentions 2 more papers before 1970, Zbl 0218.94008 (1967) is in graph theory, but not about 4-color problem (is there more in РЖ "Математика"?). So it seems to be a reference to an unpublished "proof" at best. Based on my understanding of WP policies, you can remove the claim if the only reference is to his own book, because it's a "primary source", as opposed to a "secondary source", such as a textbook, monograph, or survey article independently reporting on it. –  Victor Protsak Aug 22 '10 at 19:25
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Andrey, I think the chances are low of there being a wikiwar since his own wikipedia page doesn't say anything about such a claim (see my answer below). Anton could flag that line as needing a real source and then if nothing changes in a week or two it is probably safe to remove the line. –  KConrad Aug 22 '10 at 20:13
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It might be instructive to go through the history to find out who added that comment, then to look at their editing history to see if they are likely to be edit warriors or just do drive-bys. –  JBL Aug 22 '10 at 20:27
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If Gorbatov proved it before, it is unlikely exactly the same as the known proof. If it also works with unavoidable reducible set, then it is likely not the same set, or he directly found the minimal set (but that is also unlikely). So, if he found it earlier, he should come with papers how he did it and it is probably not very difficult to see if those papers are genuine or not. –  Lucas K. Aug 22 '10 at 21:16
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Anton, It is clear that the answer to your question is that nobody, either on MO and in the larger mathematical community, seriously looked through his proof, checked its validity, and commented thereon. On the other hand, there is highly compelling argument that it was not valid. Namely, he had plenty of opportunity to share his work with experts in Russia, who could have checked it and disseminated it. But, says a skeptic, maybe he didn't care about such things (a precursor to Pereleman, perhaps). Aha - but he did care about such things, repeating the claim 36 years later. QED –  Dev Sinha Sep 5 '10 at 4:13
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3 Answers 3

Check out the page http://community.livejournal.com/science_freaks/1639427.html.

The whole thing seems bizarre. The MathSciNet review of the book you mention says nothing about a claimed proof of the 4-color theorem. The earliest MathSciNet reference to a paper by any Gorbatov is from 1970; nothing from 1964. Did he write a proof and stuff it in a drawer or something? He's listed at http://www.newportuniversity.eu/faculty.php as having "degrees of the Doctor and Grand Doctor of Philosophy and a Rank of the Full Professor of the World Information Distributed University." That seems to be some strange academic structure between Belgium and Russia. (The description of certification of diplomas at WIDU on their page http://www.webspawner.com/users/eduardevreinov/index.html is hilarious: "Organization of the preparation and defense of theses in WIDU shall correspond to the common rules applied in the most of famous universities of the world. The Harvard and Yell Universities can be named as examples of these universities... The important difference of WIDU is an opportunity to study and defend thesis in the native language... A more perfect credit system is available, compared to the famous universities.")

Gorbatov's own wikipedia page (the fifth person listed at http://ru.wikipedia.org/wiki/Горбатов) says nothing about this 4-color "achievement" and it also shows you're not exactly going to be getting any complaints from him: he passed away in June.

All in all, the evidence supporting his claim is very weak, so it seems fair to cut it.

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Does MathSciNet index all the Russian journals? I'm wondering if its possible that the 1964 proof appeared in an obscure journal not indexed by MathSciNet. –  alex Aug 22 '10 at 20:17
    
Never mind...I posted the 1964 reference below. –  alex Aug 22 '10 at 20:31
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From Gorbatov's book this seems to be the original reference:

Горбатов, В. А. О минимальной раскраске графа // Доклады НТК. МЭИ, 27 марта - 10 апреля 1964 г. Подсекция вычислительной техники. --М.: МЭИ, 1964. -С. 17.

I'm not familiar enough with Russian journals to make sense of it. What is "НТК. МЭИ"? And is this a peer-reviewed journal or is this more in the nature of a technical report or unrefereed conference proceedings?

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From a web search on initials it is Научно-техническая конференция and Московский Энергетический Институт. (Scientific-Technical Conference, Moscow Energy Institute.) –  KConrad Aug 22 '10 at 20:42
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That's exactly the kind of place a serious proof in pure math should be published. –  KConrad Aug 22 '10 at 20:44
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I am not sure but may be this page (in Russian) http://community.livejournal.com/ru_math/191138.html will be useful for find a good reason.

Fon-Der-Flaass Dmitrii Germanovich lj-user flaass (http://flaass.livejournal.com/) http://www.mathnet.ru/php/person.phtml?personid=30297&option_lang=eng well-qualified mathematician gave some comment to this book and author.

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Unfortunately, Flaas died recently. –  Mark Sapir Sep 6 '10 at 17:49
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