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February 3

Bhargava-Hanke 290 theorem

The 290 theorem is cited in that article as "Invent. mth., to appear" and cited in various places[1] as "Invent. Math. 2005". I was hoping to update the article with an exact reference but don't seem able to find the paper through Inventiones' own search form.[2] (other searches don't work either). Does anyone know how to find if the paper was actually published? There's no doubt of its validity, it is just a question of a proper cite, though maybe I shouldn't care since it's a Springer journal. Thanks. 73.93.153.74 (talk) 01:35, 3 February 2020 (UTC)

Apparently it has not yet been published. On his own website, Jon Hanke writes: "the paper should appear in the near future";[3] the statement has not been updated since September 21st, 2011. His "Math Papers" page only mentions the preprint.  --Lambiam 08:54, 3 February 2020 (UTC)

The proof of the theorem was announced in Fall 2008, so 2005 is made of whole cloth.  --Lambiam 09:06, 3 February 2020 (UTC)

I found a paper from last year that was still citing the preprint, so presumably if it has been published then it was 2019 at the earliest. It's an awkward situation as far as WP:RS is concerned since WP articles are only supposed to cite articles published in peer reviewed journals and not random web pages. (An over simplification but that's the gist of it in this case.) On the other hand it does seem like a significant result and a number of papers which have appeared in peer reviewed journals do cite it. But the article only says the proof was announced, so maybe just cite one of the published papers just mentioned to support that weaker claim. One of the objectives of WP:RS is to keep Joseph T. Crackpot from adding to the article on the Collatz conjecture that he's proved it and citing his post on blogspot.com as his source. So while there may be no doubt of the validity of the Bhargava-Hanke result, it sets a bad precedent when a self-published source is used as the only reference. Btw, the article has an ESL vibe to it imo; anyone feel like doing a copy edit on it? --RDBury (talk) 13:49, 3 February 2020 (UTC)

Apparently, Bhargava used the occasion of his receiving the 2005 SASTRA Ramanujan Prize to announce that he and Hanke had cracked the 290 conjecture; the preprint with the details of the proof followed later.[Article (paywall)]&[PDF] This can be used to source the first sentence of the last paragraph of the lead. If we replace the sentence about the proof going to appear in Inventiones Mathematicae by "A write-up of the proof is available as a preprint." and strike "Invent. Math., to appear." from the ref, the primary source can serve as acceptable direct evidence for this statement (that is, not requiring analysis or interpretation).  --Lambiam 15:30, 3 February 2020 (UTC)

Thanks all. I wouldn't worry about the RS angle for this. The 290 theorem was part of Bhargava's Fields medal citation and a zillion other sources cite it too, so I'm sure it's fine. Perelman's proof of the Poincaré conjecture was never in a journal either, but his being awarded the Fields medal and the Millenium prize for it is good enough documentation that he really did it, even though he declined both awards. In the case of the 290 theorem, there was just what looked like an outdated reference to a paper then still in Inventiones' pipeline, so I thought it would have appeared by now. Apparently not, but no big deal under the circumstances. Added: for most math topics I wouldn't worry about formalities too much. Joseph T. Crackpot's work is focused mostly on a few major open problems like the Collatz conjecture. Topics with less glamour don't attract as many unreliable claims, so we can rely more on editorial judgment to identify the stuff that readers should want to see. 2601:648:8202:96B0:0:0:0:E118 (talk) 19:56, 3 February 2020 (UTC)

I agree that once you get away from the top five most famous unsolved problems you don't get many outlandish claims. But we have to deal with Mr. Crackpot at the help desk occasionally and my experience is that it's not wise to underestimate his persistence. The idea of relying on the RS policy rather than editorial judgment is WP editors can just point to the policy when they remove questionable claims; this helps avoid arguments. My worry was that Mr. Crackpot would point to the self-published cite in this article and say "This reference was self-published so why can't I use my self-published paper?" In any case, I'm going to go ahead and add Lambiam's information and cite into the article, and that should resolve everything. --RDBury (talk) 03:22, 4 February 2020 (UTC)

Your edit is fine, and those situations with J. T. Crackpot do come up once in a while, but not often enough that we should make unaffected articles suffer for them. In the case of the 290 theorem, you could also mention that the IMU noted it when they gave Bhargava the Fields medal.[4] That establishes its significance, among other things. I'm cool with citing Crackpot's self-published preprints in Wikipedia, conditional on Crackpot getting the Fields medal or Millenium prize the way Bhargava and Perelman did for their preprints, lol.

More seriously, I'm satisfied if some established experts take a claimed result seriously, like here, citing blog writeups by some noted specialists. Wikipedia isn't a formal system--it's a textual work written for human readers and its value is in the relevant knowledge that it delivers to those readers. Its policy machinery is a means to that end, not something to pursue for its own sake. It's consistent with other observed practice to be stricter about the Collatz conjecture than about less flaky topics. See e.g. here, scroll down to "Editorial policy on submissions concerning famous problems". Just go by common sense and experience. 2601:648:8202:96B0:0:0:0:E118 (talk) 07:10, 4 February 2020 (UTC)