Talk:Inter-universal Teichmüller theory

Inter-universal geometry?

Various media and blogs, e.g. New Scientist & MathOverflow, suggested when the ABC-proof came out that he used “Inter-universal geometry” (for which we have no article or redirect as of 2015-05-10), others that his papers on “Inter-universal Teichmüller theory” are where he proves it. Is this a mix-up on someone’s part? He does have papers on both, but IUG is a handwritten PDF ([1]) of what look like lecture notes, while those on IUTT (I to IV under References in the article) are cleanly type-set papers. The fourth of these does indeed include the claim to prove ABC, so that the reference in ABC-conjecture is correct. What is the difference between the subjects? Some googling on my part found various references, but left me unclear what the relevance of IUG is. Given these references to IUG, a mention in this article and an appropriate stub or redirect would be helpful.
N.B.

This is an editted copy of Talk:Abc_conjecture#Inter-universal_geometry.3F_or_IU_Techm.C3.BCller_theory.3F (sic :( ).

I have also posted this question on math.stackexchange.com.

PJTraill (talk) 14:21, 10 May 2015 (UTC)

   Maybe this article helps you... Ishnigarrab (talk) 16:28, 8 December 2016 (UTC)

Inference is not a reliable source, eg see [2] Doug Weller talk 16:25, 14 April 2019 (UTC)

What are the stars on the external links?

As it says in the title, why are there stars after many of the external links? Is it just a mix-up with the markup, or does it mean something? If the latter, the list should be preceded by an explanation (legend) as it is a convention I do not recall seeing elsewhere in Wikipedia, and which I am sure will confuse the casual reader. PJTraill (talk) 21:53, 18 February 2018 (UTC)

I think the asterisks are there by mistake, maybe they were intended as bulletpoints but whoever added those ELs didn't check before saving. I will remove them. Hrodvarsson (talk) 22:21, 18 February 2018 (UTC)

Revision following COI

It appeared obvious that the page had been edited by puppets of somebody with a personal interest in this topic (see SPI [3]). As a result it clearly violated NPOV. The new version hopefully resolves these issues. I did not remove the tags yet, I'll do so soon if nobody objects. jraimbau (talk) 17:42, 19 March 2018 (UTC)

Recent developments concerning the understanding of Inter-universal Teichmüller theory

The article states in the last sentence of its history section that: "A number of mathematicians who have examined Mochizuki's argument in detail (including Peter Scholze and Brian Conrad) point to a specific point which they could not understand.[7][8]"

Suggested addition I suggest that the following text or a similar text is added to the article after the statement above: "In December 2017 they became aware, that the explanation to the point the could not understand, had been significantly expanded earlier in 2017."

Motivation: As is seen in the discussion in reference [8] in the article (https://plus.google.com/+DavidRoberts/posts/PQLbe2gKaEA), "A number of mathematicians who have examined Mochizuki's argument" (including Ivan Fesenko, +h motomura on google+ and @math_jin on Twitter) show that the point which Scholze and Conrad could not understand has been further explained since the time they last studied Mochizuki's IUT papers.

Conrad and Scholze, at the time of voicing their concerns, were not aware of the expanded explanation of the point in question. This is evident from their discussions, specifically from:

• the statement of Scholze that "no more details are given" on the point in question, and
• the statement of Conrad that "It came to my attention this morning from someone else via email that Remark 3.12.2 has been very much expanded since earlier versions (I don’t know when that change occurred), and that this Remark (not just its part (ii)) should address some aspects of how 3.12 follows from 3.11. The wider awareness about this due to the discussion on Frank Calegari’s blog and this one has helped in this direction. I immediately brought this to the attention of several other people who have looked a lot into the IUT papers; hopefully it will clarify things. But the coming days are a time of travel and vacation for many people, so don’t hold your breath.".

Specifically, Remark 3.12.2 of IUTeich III was expanded from approx. 12000 characters in May 2017 to approx. 19000 characters in August 2017. The revisions are listed in the revision history on Mochizuki's webpage. It remains to be seen if this expanded explanation has increased or will increase the understanding of Mochizuki's proof. — Preceding unsigned comment added by 80.250.30.194 (talk) 07:42, 2 April 2018 (UTC)

References

Unless we have published secondary sources by other people than the researchers working on this, reporting on this expansion, then it is off-topic here. We can only report on what published sources say, not our own evaluation of what the primary researchers are doing. —David Eppstein (talk) 15:57, 7 April 2018 (UTC)

Deletion suggestion

I suggest deleting the last sentence in the history section: "A number of mathematicians who have examined Mochizuki's argument in detail (including Peter Scholze and Brian Conrad) point to a specific point which they could not understand.[7][8]"

Motivation: The sources [7][8] are only discussion posts to some blog posts by some not clearly defined contributors, they are not secondary sources. — Preceding unsigned comment added by 80.250.30.194 (talk) 20:53, 13 April 2018 (UTC)

To me this suggestion appears to be part of a pattern of promotional editing (and already-proven sockpuppetry) surrounding this article, in which any hint that the proof is deficient is minimized and removed. The sources are indeed not good, but that's true of everything but the Ball Nature source here. Why is it only the negative sources that are suggested to be removed? For that matter, why has another good (but negative) source, Revell's New Scientist article, not been used? —David Eppstein (talk) 21:42, 13 April 2018 (UTC)

I agree the sources are not ideal. For some reason number theorists seem to be reluctant to write formally on the topic. I added a citation to Revell's NS news article, which is better with regard to sourcing hygiene but does not include as much detail about the issues mathematicians have with Mochizuki's work. jraimbau (talk) 07:05, 14 April 2018 (UTC)

It seems that editing rules are applied both inconsistently in this article and in a way which is favors negative comments about the theory.

Motivation: A suggestion to add a text (see section "Recent developments concerning the understanding of Inter-universal Teichmüller theory" above) was turned down on the grounds, that the sources quoted and referenced to were not secondary sources. At the same time a deletion suggestion (see section "Deletion suggestion" above) was also turned down, although the sources quoted in the text that was suggested to be deleted, were not secondary sources, indeed, they were rather comments on blog posts, where the commenters were assumed, but not unambigously confirmed, to be Scholze and Conrad. — Preceding unsigned comment added by 80.250.30.194 (talk) 23:52, 15 April 2018 (UTC)

I removed Scholze and Conrad's names since the comments were made semi-anonymously (though without doubt they were not misattributed by the editor who added them). Feel free to include a line or two which neutrally mention of the modifications to Mochizuki's preprints if you want (the draft you (?) wrote above is much too long and its style is rather melodramatic). jraimbau (talk) 14:02, 28 April 2018 (UTC)

I would go for the deletion suggestion as the mathematicians actually all stopped the discussion about "a specific point which they could not understand", when it came to their knowledge, that Remark 3.12.2 of IUTeich III had been expanded in August 2017. See

If you do not want to delete, then I guess the following text could be added after the sentence I propose should be deleted: "This discussion ended, when it emerged, that the explanation to the point in question had been significantly expanded earlier in 2017."

I agree it sounds maybe a bit comic, but that is the current state of affairs, all those mathematicians missed the update. — Preceding unsigned comment added by 80.250.30.194 (talk) 19:26, 2 May 2018 (UTC)

Your wording suggests a motivation for the lack of continued discussion (namely, that the point was already satisfactorily answered) that the sources do not support. It could equally well be that the mathematicians making this point felt that, once they had made it, it became unnecessary to belabor the point even though the updates did not satisfy them. They could have seen an unsatisfactory update as evidence that this was never going to become clear and there was no point even trying. (I am not suggesting that it is actually true that the updates did or did not satisfy them; only that we don't know and we shouldn't imply anything like that with our wording.) —David Eppstein (talk) 21:02, 2 May 2018 (UTC)

References

Extended-confirmed-protected edit request on 3 June 2018

The word outstanding is spelled wrong (oustanding) at the beginning of the article.CalliopeMuse (talk) 04:18, 3 June 2018 (UTC) CalliopeMuse (talk) 04:18, 3 June 2018 (UTC)

fixed, thanks. --JBL (talk) 11:27, 3 June 2018 (UTC)

Abbreviations and Teichmüller

Joel B. Lewis & Jean Raimbault: Why do you want to withhold information on alternately used abbreviations and the namesake person [4]? --KnightMove (talk) 19:22, 21 September 2018 (UTC)

First let me say that adding this information without context to the introductory paragraph is not a very good way to go about it.

Regarding the alternative abbreviations: IUT is not by any means a part of standard mathematics and there is essentially no references to it outside of Mochizuki's circle, and blog posts or divulgation articles which all essentially say that people do not understand it (with the exception of Scholze and Stix's recent report which says that they understand enough of it to claim that it cannot prove ABC in its present state). It seems thus premature to list any number of alternate names, as it is not clear whether the theory will not fade away quietly, and if it does not then standard ways of referring to it will emerge in due time.

Regarding the link with "classical" Teichmüller theory: it was named thus because of Mochizuki's previous (uncontroversial as far as I am aware) work on so-called p-adic Teichmüller theory. I think that the links of IUT with the analytical study of moduli spaces of Riemann surfaces are tenuous enough as to make the claim that IUT "is rooted in [the] concept of the Teichmüller space" preposterous. The name should probably be explained somewhere, but not in the lede and with a reference to Mochizuki's p-adic Teichmüller theory rather than O. Teichmüller and the theory named after him by L. Bers.

Finally, this article has a bit of a special status among math articles on wikipedia as it has been the subject of a long campaign of targeted editing and sockpuppeting, which is why some editors pay special attention to it and your edits were reversed so fast. Sorry if that gave you the impression that we wanted to "withhold information". Cheers, jraimbau (talk) 07:17, 22 September 2018 (UTC)

I am in full agreement with jraimbau. --JBL (talk) 12:56, 22 September 2018 (UTC)

I get your points, but:

1. A basic question of any uninformed reader here is "Now who was that Teichmüller guy?", and I don't think it's in the sense of an encyclopedia to leave them alone with the question. Well, far down in the text there is the link p-adic Teichmüller theory, from there a link to Teichmüller theory, which is a redirect to Teichmüller space, and there finally is a link to Oswald Teichmüller. This is not exactly user-friendly. Of course articles whose topic has a namesake person explain who that person was. Imagine the articles Hubble Space Telescope, Tesla, Inc., Foley (filmmaking), Molotov cocktail or Ruy Lopez not mentioning the namesakes... that would be even ridiculous. There is hardly a reason to make an exception in this case. If there is a better way, I'm open to it. What about quoting Mochizuki's own description of attempting "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve" in the introduction? At least this gives a more direct connection, and the reader will accurately expect to find the person in this other article.
2. As of the abbreviations: IUTT and IUTeich have been redirects here for years now. These abbreviations are used in papers discussing the topic, and those papers will remain part of human knowledge and heritage. Whether the theory will maybe be refuted and fading into relative obscurity later, and whether only one abbreviation will be used to name it as a curiosity, is open future. As even a bunch of alternate abbreviations appears not to do any harm (see e.g. Bachelor of Science), I do not get the point of omitting them. --KnightMove (talk) 07:26, 24 September 2018 (UTC)

re. 1: I think the situation is different here wrt. the examples you quote as Teichmüller himself had no direct influence on what is discussed in the article. I think it's a good idea to use Mochizuki's quote above in the body of the article, for example as the second sentence of the "history" section we could add "The theory was named in analogy with the Teichmüller theory of Riemann surfaces by Mochizuki, whose aim was to develop "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve"".

re. 2: I don't think it is useful to add transparent abbreviations to the article, even if they are used in primary sources they are not necessary to understand anything that it said here or anywhere else, and they are not relevant by themselves. I don't agree that "they do no harm" for the reasons I described above. Cheers, jraimbau (talk) 15:33, 24 September 2018 (UTC)

As of "Teichmüller himself had no direct influence on what is discussed in the article": That's also the case for the majority (not all) of my examples, especially the Tesla corporation, named thus for no other reasons than marketing. But - ok, I like your text suggestion, and let's leave it that way. --KnightMove (talk) 15:41, 24 September 2018 (UTC)

References

Extended-confirmed-protected edit request on 30 September 2018

Regarding the last paragraph under the section titled "History", wherein it says "[...] in detail point to a specific point which they could not understand", I thought it would do good to replace the vagueness of 'a specific point' with a more exact description to the location of the point of contention. Specifically, to mention that its "near the end of the proof of Corollary 3.12, in paper three of four". The reference for this comes from a quanta magazine article [which already exists in the references as ref. #9 (https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920)]

  This identifies 1) the paper, 2) the corollary and 3) the location within the corollary, which is convenient. Although, admittedly, conveniently locating the section in question is no way going to facilitate the understanding sought regarding the question of the objection's validity.

Thanks, DrBurningBunny (talk) 22:04, 30 September 2018 (UTC)

@DrBurningBunny: That edit is now  Done, thank you for requesting it. Fish+Karate 10:45, 1 October 2018 (UTC)

Lots of Gossip, Little Math

Sorry for posting in the incorrect place. I didn't know where to write these things.

This article is not very mathematical. Perhaps this should be a moved to an IUT Flame War page.

The statement: "However, these did not lead to broader understanding of Mochizuki's ideas and the status of his claimed proof was not changed by these events.[8]" is false. I attended both of these and gained a lot. Also, Brian was interrupting the speaker for most of the time so it was hard for people to talk. The difference in understanding of IUT2 from the Oxford to Kyoto was staggering. Nobody at the first conference understood it.

There was also workshop at the University of Vermont "Kummer Classes and Anabelian Geometry". This was positively received. Also, there have been seminars in Nottingham and Paris.

The statement "In 2017, a number of mathematicians who had examined Mochizuki's argument in detail pointed to a specific point which they could not understand, near the end of the proof of Corollary 3.12, in paper three of four.[9][10]" is misleading. If something is claimed there should be a pinpoint reference. Also, referencing a single Corollary or Theorem in Mochizuki's papers are meaningless because they run for multiple pages.

"In March 2018, Peter Scholze and Jakob Stix visited Kyoto University for five days of discussions with Mochizuki and Yuichiro Hoshi; while this did not resolve the differences, it brought into focus where the difficulties lay.[9][11]" I take issue with the last part. Also, Scholze and Stix used a number of references they did not cite. Fucheng Tan's unpublished manuscript for example. The notation from the two papers and the discussion of "copies of the real numbers" is strikingly similar.

"In 2017, a number of mathematicians who had examined Mochizuki's argument in detail pointed to a specific point which they could not understand, near the end of the proof of Corollary 3.12, in paper three of four.[9][10]" This is vague.

The statement "One issue with Mochizuki's arguments, which he acknowledges, is that it does not seem possible to get intermediate results in his proof of abc using IUT. In other words, there is no smaller subset of his arguments more easily amenable to an analysis by outside experts, which would yield a new result in Diophantine geometries.[19]" This is mathematically meaningless. There are plenty of anabelian theorems in the paper, are those intermediate results? Also, from the volume inequalities in the fourth paper you can derive things. Does this count? If you only work with the last capsule you get weaker version of the exponent in Szpiro (exponent 10). Does this count?

The statement "The first step is to translate arithmetic information on these objects to the setting of Frobenioid categories. It is then claimed that extra structure on this side then allows to deduce statements which translate back into the claimed results.[18]" This doesn't even parse. The second sentence is so vague.

This is Taylor Dupuy posting this. — Preceding unsigned comment added by 69.5.115.207 (talk) 07:25, 12 October 2018‎ UTC

In my opinion it is fitting that this article be, as you aggressively put it, "gossip", since most of the discussion in mathematical circles around IUT has been nonmathematical and so it is natural that this article should reflect that. In purely mathematical terms IUT has no reason to be included in wikipedia, its notability derives entirely from the claim to proving ABC which so far---and I don't see any comment in your post above that contradicts this---has not been confirmed by anybody outside Mochizuki's circle. Cheers, jraimbau (talk) 10:46, 12 October 2018 (UTC)

I have touched up the English as "It is claimed that extra structure on this side allows one to deduce statements which translate back into the claimed results", which can at least be parsed; it is still vague, but at this level that may be unavoidable; it is guarded, as seems reasonable so long as there is disagreement. I understand that you take issue with "it brought into focus where the difficulties lay", which I wrote based on Mochizuki's own remarks that "the … discussions … constitute the first detailed, … substantive discussions concerning negative positions … IUTch." (p. 4) and the way he sums up (pp. 4-5) the issues discussed – would you care to suggest a more appropriate formulation of the result of the discussions? PJTraill (talk) 22:50, 12 October 2018 (UTC)

Extended-confirmed-protected edit request on 20 December 2018

Please change this text: "a series in four preprints"

to: "a series of four preprints"

This is a grammatical correction which I hope is self-evident. - TienShan0 (talk) 14:30, 20 December 2018 (UTC)

 Done, thanks! ‑‑ElHef (Meep?) 15:19, 20 December 2018 (UTC)

"Has not been accepted by the mathematical community"

...is this still considered true? His work is still controversial, from what I understand, but this seems at best a simplistic assessment of the current situation. Twin Bird (talk) 03:03, 5 April 2020 (UTC)

The brand-new Nature article used prominently as a new reference makes clear that this assessment has not changed. —David Eppstein (talk) 04:30, 5 April 2020 (UTC)

The discussions with Peter Scholze and others on Peter Woit's blog, cited in the abc conjecture article, make it clear that the quoted assertion is an understatement. The work isn't just not accepted, it is widely considered to be content-free, an embarrassment, and the upcoming publication to be corrupt if it does not address and resolve criticisms of the online preprints. 73.149.246.232 (talk) 00:38, 25 May 2020 (UTC)