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 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 (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  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 |here). 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)


 * 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)

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 ? --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:
 * 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.
 * 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)

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)
 * That edit is now ✅, 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)


 * Nevertheless, the article should at least attempt to explain the mathematical content of IUT, even if its content is not the reason for its notability. The article is about IUT first and foremost after all, as is reflected by the name of the article. Either the article needs a lot more details on mathematics, or it needs to just be moved under a different name altogether. BlueBanana (talk) 00:49, 18 June 2023 (UTC)
 * The sections "Scope of the theory" and "Consequences in number theory" do attempt to explain the mathematics. If you're hoping for something more comprehensible, I don't see any hope for producing such a thing, as there are no reliable sources that explain the ideas even at the level of experts in number theory, much less at the level of the larger Wikipedia audience. Interestingly both proponents and critics agree that the ideas are impossible to explain, the proponents because the ideas are so revolutionary that they can only be appreciated after a lengthy immersion, the critics because the ideas simply don't work.
 * It's unfortunately probably inevitable that Wikipedia will have an article on IUTT, given how much ink has been spilled on the topic, even though there's little chance of turning the article into something useful and interesting. Will Orrick (talk) 17:04, 18 June 2023 (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)


 * Yes check.svg Done, thanks! &#8209;&#8209; El Hef  ( 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 in mid-April 2020 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 with no salvageable new result, 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)

If I may, it looks like this statement reflects the situation in 2018 and does not include the latest academic developments (the papers have been peer-reviewed and published, there have been international workshops organized, there is a refined version of the theory with application to FLT). Don't get me wrong, the theory is still controversial and this point must be explicitly mentioned. But it is also misleading not to report on a peer-reviewed process and on blog post discussions only. Below is a suggestion which I hope provides a better balance.

Edit suggestion: "The most striking application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture. After some intense debates within the mathematical community and a 8-years peer-reviewed process, Mochizuki's work is now published while still a controversial theory for some.

There are also some inaccuracies that give a false impression regarding the (allegedly non) academic nature of Mochizuki's work. I will bring it to the attention of the community with some edit suggestions so that you can judge what is the best decision to reach.2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 13:57, 2 October 2021 (UTC)

Very bad article
What Inter-universal Teichmüller theory has to do with Peter Scholze and Jakob Stix visiting Kyoto University? Their visit was about the proof of abc conjecture. Even if this proof is wrong it still does not invalidate the theory itself. This article here, even though it would still sound politically motivated, would be ok if the title is Proof of abc conjecture by Mochizuki. It is very wrong to think that all that there is to this theory is abc and derived conjectures. This article is disseminating a popular and simplistic belief, depending on which side of the globe you are, and with that the utter ignorance. (What is it all about this attempt to enforce the opinion that the proof is invalid, by the way? So nobody would invest his time into analyzing it. But then it is a self-fulfilled prophecy.) Really IUT is not just about abc conjecture. — Preceding unsigned comment added by 158.248.76.166 (talk) 11:05, 15 March 2021 (UTC)

The sentence, "[This work], which has..." is unclear and seems like a potential mischaracterization.
"This work, which has been peer-reviewed and well-received by the mathematical community," is a bit confusing because IUTT was the subject of the previous sentence, but the end of the sentence refers only to work done prior to IUTT. I'd like to assume 'this' here refers only to his pre-IUTT work, yet referring to all previous work is vague and it seems clear that at least some of the remainder of the paragraph refers to IUTT in specific. Additionally, the section is labeled 'Scope of the theory' which implies this is about the totality of IUTT. This feels questionable to me because "well-received by the mathematical community" is perhaps not the most accurate way to characterize the controversy around claims attached to IUTT, and even "peer-reviewed" (while technically true) is a bit misleading. If this characterization is only intended to refer to his previous work, then it should probably say something like, "The author's work prior to IUTT," (or something more specific than this) before continuing the puffery claiming legitimacy. Then the rest of the paragraph should only discuss work from that pre-IUTT period. TricksterWolf (talk) 01:50, 30 July 2021 (UTC)

"Mochizuki made his work public [...] in a rather unusual manner"
Nb. This discussion is the first of a few, whose goal is to submit a few inaccuracies in this article to the attention of the Wikipedia community. While they support the academic nature of Mochizuki's work, their goal is not to minimize the debate and controversy around IUT theory.

Source: "Mochizuki then made his work public in 2012 in a rather unusual manner, only making the papers available on his RIMS webpage and avoiding announcements or posting to a prepublication server."

Comment: The first announcement of IUT was in an international conference in 2010 in front of a broad panel of experts. The manuscripts were available on the RIMS preprint server (that has the same value as ArXiv). As every anabelian geometer knows, this is nothing unusual since it is the main channel of communication of the Japanese anabelian community.

Edit suggestion: "The first public announcement of IUT theory was made by Mochizuki in front of a broad panel of experts during the ``Development of Galois-Teichmüller Theory and Anabelian Geometry" conference in 2010. He then made his manuscript available on the official RIMS preprints server in 2012. Following the community feedback, he maintainted some contant updates on his RIM webpage.2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 14:35, 2 October 2021 (UTC)

History - additional sectioning
This is a minor suggestion whose goal is to give a more precise overview on the place of IUTT with respect to the mathematical community (i.e. the goodwill and efforts for digesting the theory, the academic debate, the latest developments, etc.)

"The reception of the claim was at first enthusiastic..."

Edit suggestion 1:  "=== First encounter with the theory (2012-2017) === The reception of the claim was at first enthusiastic..."

"In March 2018, Peter Scholze and Jakob Stix visited Kyoto University..."

Edit suggestion 2:  "=== Academic discussion period (2018-2020) === In March 2018, Peter Scholze and Jakob Stix visited Kyoto University..."2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 15:12, 2 October 2021 (UTC)

History - updates 2020-2021
According to some comments on Peter Woit's blog in 2020, Scholze position has not changed since 2018. This does not mean that IUTT is dead since there have been some additional activities (publication, workshops, preprints). This Wikipedia article should give a better overview of these points.

Edit suggestion:(new section in History) "=== Development of IUTT (2021-) === After a 8-years peer-reviewed process, the IUTT manuscript have been accepted for publication in a special volume by a special editorial committee.

While debates continue outside of the academic on the comment section of Peter Woit's blog (incl. Peter Scholze), the arithmetic geometry community continues its effort for assimilating the ideas of IUTT: in 2020 a 1-semester seminar was organized between RIMS and Lille University , in 2021 a one-year RIMS-project``Expanding Horizons of IUT theory'' took place with a series of four online workshops.

A refinement of IUT theory led to the application of the theory to Szpiro conjecture and to a new proof of Fermat Last Theorem (preprint) that relies on and motivates new estimates from Preda Mihăilescu.

A few words to conclude: I hope that this series of suggestions will be useful for the Wikipedia community; feel free to edit!2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 15:44, 2 October 2021 (UTC)

These proposed edits are too favorable to IUTT, presenting it as mainstream, accepted, and published, when in contrast my strong impression is that it is by now largely viewed as a fringe topic with a dubious publication process that failed to address objections from mainstream mathematicians. Or, stated another way: The fact that Scholze remains convinced of its failure should not in any way be viewed as evidence that it is a success, and the steadfastness of his views on the issue cannot be used to discount those views. Incidentally, it is false that Scholze has done nothing on this since 2018: he is the author of a Zbl review published this summer,. —David Eppstein (talk) 19:02, 2 October 2021 (UTC)

[Reply of 05:03, 3 October 2021 moved below by the author to follow Wikipedia talk-page etiquette]2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 15:57, 3 October 2021 (UTC)


 * I had the same response. The impression is reinforced by the fact that there is exactly one source in all of the IP's proposed edits that is independent of Mochizuki or RIMS (the Nature article by Castelvecchi); reading that article, one finds a broad array of mathematicians expressing serious and substantial doubts about the work, and the IP wants to summarize this by saying that it is "a controversial theory for some".  Hard to treat this seriously. --JBL (talk) 22:27, 2 October 2021 (UTC)


 * I am sorry if my edit suggestions give a wrong impression. If the formulation "a controversial theory for some" sounds too weak, please feel free to reformulate. On the other hand, why should we ignore the interest of the ~150 participants in the 2020-21 IUT events?
 * Note btw that the fact that this will be a series of edits by one person was clearly stated (nothing suspicious here I hope).
 * If I may, my *impression* is that a handful of Wikipedia editors want to protect, in good faith and complete honesty, the quality of this article from the internet turmoil. This is however no ground for refusing *documented mistake corrections or updates*; I hope that we can all agree on that.2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 05:04, 3 October 2021 (UTC)
 * Please invest some effort in learning basic Wikipedia talk-page etiquette: you have inserted your later comment above mine in a discussion, giving the false impression that I was responding to you. This page explains proper use of indentation.  Since your responses completely fail to grapple with the problems in your proposals, I have nothing substantive to say except to refer you to my previous comment. --JBL (talk) 12:11, 3 October 2021 (UTC)
 * Apologize for the Wikipedia talk-page etiquette and thanks for the link. Re my responses, it could be helpful if you could state why you choose to ignore (1) a peer-reviewed publication, (2) a legitimate academic activity in France and at MIT.2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 15:57, 3 October 2021 (UTC)


 * [Original Reply to David Eppstein of 05:03, 3 October 2021] Thank you for your frank reply. However, I do not understand how it answers the new documented modifications that are proposed. Let us try to meet and communicate:

Mathematicians often publish papers in journals for which they are editors. As long as the authors recuse themselves from the peer-review process, “such a case is not a violation of any rule, and is common” [...] Mehrmann confirms that this would not violate EMS guidelines.
 * Favorable edits to IUT. These are documented facts; why should they be ignored?
 * Presenting IUT as mainstream. This is incorrect, there is no statement in the suggested edits to support this claim. In particular, the debate and criticism from Scholze and others must stay (and be documented)
 * Publication of IUT as a dubious process. I understand that it is your impression, you should update with a precise reference. Note that the 2020 Nature paper states:


 * Also, note that support for a *study* of the theory has been given by Kashiwara, Tamagawa and Ribet (see with attendance among others of Vojta and Hartshorne). I would suggest also add this fact.


 * Scholze has done nothing since 2018. Nothing in my edit suggestions support that claim; I would strongly suggest adding the reference to the Zbl review in the article.

2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 05:03, 3 October 2021 (UTC)


 * I added both the existence of a published version and Scholze's response in the zbl review to the article. Last I looked the MathSciNet review was labeled as "pending"; if it eventually turns into a signed review, or multiple reviews for the multiple papers, we should cite it or them too. —David Eppstein (talk) 19:49, 6 October 2021 (UTC)
 * The header is still strongly misleading (should mention explicitly the IUTT published papers); Zbl and Mathscinet (non-peer-reviewed) reviews give additional context to peer-reviewed papers, they can not be considered as main sources; your statement on Mochizuki being editor-in-chief of PRIMS is correct but strongly misleading since he recused himself during the review of his papers (see excerpt and reference in "Publication of IUT as a dubious process." ~3 lines above).130.54.16.202 (talk) 02:31, 7 October 2021 (UTC)
 * Plenty of other people seems to find the fact that he published the paper in the journal he runs...odd, despite the too-strenuous denials of problematic behavior from the journal. As for your idea that reviews such as the one in Zbl "can not be considered as main sources": in fact, secondary sources such as this are the only kinds of sources we can rely on, or use as our main sources. We should not be relying at all on publications by or associated with Mochizuki; they are primary, non-independent, and because of the controversy cannot be considered reliable (in the sense in which Wikipedia works on the basis of published reliable sources rather than on mathematical proof or real-world factuality) for anything beyond their own existence. And we should probably not be using blog posts such as galoisrepresentations.com, either; they are not reliably published and (because the author is pseudonymous) we cannot rely on the "expert" clause of our guidelines on self-published sources. —David Eppstein (talk) 07:48, 7 October 2021 (UTC)
 * Let me thank you for your explanations regarding Wikipedia (non-)independent source policy; this is very clear and informative. There are however some serious gaps in your arguments:
 * our guidelines on self-published sources. The entire 2018 controversy is entirely based on a non-peer-reviewed, non-published, non-submitted for publication pdf file from Scholze and Stix (initially available on Mochizuki's website, now on Scholze's website). This contradicts the "expert" clause of our guidelines on self-published sources. While it is important to keep the origin of the controversy, the IUTT page should be rewritten accordingly to this clause.
 * Not considering Mochizuki related sources as reliable and independent. An independent editorially peer-reviewed publication does not contradict Independent sources (see also below). Your decision to consider otherwise ignores the work of the editorial committee and of the referees.
 * Plenty of other people seems to(...) odd publication policy. Once again, as documented previously in Nature 2020, Mehrmann the president of the EMS states that it confirms that this would not violate EMS guidelines and such a case is not a violation of any rule, and is common. If you have any documented reference on your impression regarding the odd publication policy, please update the IUTT page. In any case, *both* of these aspects should be mentioned in the controversy. To suspect a well-established academic journal of wrong-doing without proof is not serious. — Preceding unsigned comment added by 130.54.16.202 (talk) 08:38, 7 October 2021 (UTC)
 * The only gap here is between what you want and what is permissible by WP policies (and common sense). --JBL (talk) 10:25, 7 October 2021 (UTC)
 * The z.B. article essentially says that Scholze says the published version of the the papers has the same flaws as the 2018 controversy. The fact that publication didn't violate the EMS's publication ethics does not stop it being irregular: the Nature article goes on to say If the editors of the journal “waved away these criticisms” and published the paper without major revisions, it would reflect badly on them and on Mochizuki himself. &mdash; Charles Stewart (talk) 11:26, 7 October 2021 (UTC)

Neutral point of view inquiry on Noticeboard + RfC
Since it seems that communication is stuck since 2018, a Neutral inquiry with Request for comments has been opened. Let us hope that it will bring some clarity here. 2400:4150:8120:C500:7E87:E20C:2E8E:712 (talk) 18:06, 5 October 2021 (UTC)

RfC: should the documented 2020-2021 academic activity around IUTT be included?
Should the 2020-2021 academic activity around IUTT be included in the page that is protected against sockpuppetry since March 2018?130.54.16.202 (talk) 02:24, 7 October 2021 (UTC) Nb. The RfC has been moved here following the Noticeboard editors' request.

Survey (academic update)

 * Support, a WP page should reflect documented academic activity. 130.54.16.202 (talk) 02:24, 7 October 2021 (UTC)
 * Oppose, since it is not relevant to the 2018 mathematical misunderstanding. 130.54.16.202 (talk) 02:24, 7 October 2021 (UTC)
 * Malformed RFC, speedy close. The 2021 publication is already included, and was before this RFC was posted here. So what the IP posing this RFC wants to happen instead is unclear, so unclear that there is no basis for any kind of RFC or similar decision-making process. And the fact that the IP has also seeded this RFC with three separate contradictory comments makes it appear that they are talking to themselves rather than trying to listen to others. —David Eppstein (talk) 04:34, 7 October 2021 (UTC)
 * There is a misunderstanding: following some WP RfC examples and templates, this section contains the model for the possible answer to the RfC; answers (supports/oppose) are meant to be added in the section below with additional discussions (It is also good behaviour for the initiator of the RfC to initiate the first vote, see below). You choose to believe that the updateS proposal deals with the 2021 publication only while it proposes multiple ones (please refer to the links and the discussion above). Thank you for moving your votes in the section below so that a two-way discussion can take place.


 * Speedy close per David Eppstein. Seemplez 07:34, 7 October 2021 (UTC)
 * Speedy close per David. Proposing something concrete like a specific text for inclusion seems a far simpler approach than what the proposer is doing. RfCs are not so useful when the proponents of the change are anonymous SPAs. Even if the formal problems with this RfC are fixed, this is not going to work. &mdash; Charles Stewart (talk) 08:18, 7 October 2021 (UTC)

Discussion on the 2020-2021 update
Comments or formulation proposals will be most helpful.


 * Support. Grounds for refusal of the editors ("too positive for IUTT" and "sources are RIMS only") are not relevant since updates are documented and Research_Institute_for_Mathematical_Sciences (RIMS) is the international leading research institute in anabelian geometry (the origin of IUTT) and one of the main mathematical research institute in Japan. Updates show a legit international academic activity (e.g in France and the UK 1, 2, 3, | 4). This activity proves that IUTT is *not* a fringe theory (also supported by 1st hand internationally recognized mathematicians (e.g. Minhyong_Kim (link), Jordan_Ellenberg (link), Ken_Ribet (Talk invitation to Berkeley 2020)). The WP page must provide a better balance between academic activity and Scholze (non-peer-reviewed) Zbl and blog post activity. Proposed academic updates in (link1), (link2), (link3), (link4) are documented with non black-and-white sources (initiator of the RfC and author of the update suggestions speaking)130.54.16.202 (talk) 02:24, 7 October 2021 (UTC)

" he is editor-in-chief.[
220.100.45.26 (talk) 07:11, 9 July 2022 (UTC)
 * Red question icon with gradient background.svg Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Padgriffin  Griffin's Nest 09:46, 9 July 2022 (UTC)

Extended-confirmed-protected edit request on 9 July 2022
From: for which he is editor-in-chief.

To: for which Masaki Kashiwara, Akio Tamagawa are Editors-in-Chief

or Deleting descriptions and references.

The reason for correcting or deleting it is because the editors-in-chief are different people. ==> Editors-in-Chief：　Masaki Kashiwara, Akio Tamagawa

According to the description of ”Preface to the Special Issue"

Mochizuki's name is not listed.

Editorial Committee for the Special Issue Editors-in-Chief Masaki Kashiwara, Akio Tamagawa Other Members Tomoyuki Arakawa, Masahito Hasegawa, Takashi Kumagai, Kazuhisa Makino, Takuro Mochizuki, Shigeru Mukai, Hiraku Nakajima, Kenji Nakanishi, Tomotada Ohtsuki, Kaoru Ono, Narutaka Ozawa, Michio Yamada

Preface to the Special Issue It is our great pleasure to publish a special issue of Publications of the Re-search Institute for Mathematical Sciences (PRIMS) for Inter-universal Teichm ?uller Theory, I-IV by Shinichi Mochizuki. There are two main reasons for publishing this series of papers in a special issue. One is their volume and importance. The other is to avoid the conflict of interest that arises because the author is Editor-in-Chief of PRIMS. As a general rule, when a paper is submitted to PRIMS by a member of the Editorial Board, the member should be entirely excluded from the editorial committee charged with handling it. When Mochizuki became Editor-in-Chief of PRIMS in April 2012, the Editorial Board further decided that, in the case of his submission, they would form a special committee to handle it, excluding him and with an Editor-in-Chief substituting for him. When he submitted the present series of papers on August 30, 2012, Akio Tamagawa took the job of Editor-in-Chief of the special committee. Masaki Kashiwara later joined the committee, and he and Tamagawa served as co-Editors-in-Chief. Several mathematicians kindly accepted an invitation to referee the papers; we are extremely grateful to them for their efforts and patience. Based on their reports, we had numerous editorial meetings. In particular because of the total length of the series of papers, it took a long time for the Editorial Committee to arrive at the final decision of acceptance. 2001:240:29E7:DA00:F822:A813:DD32:B841 (talk) 07:45, 9 July 2022 (UTC)


 * In my opinion the proposed new wording is extremely misleading and even contradicts a sentence in the provided quotation from the Preface to the Special Issue. By this I mean the sentence, "The other is to avoid the conflict of interest that arises because the author is Editor-in-Chief of PRIMS", which provides a clear statement that Mochizuki is indeed Editor-in-Chief of PRIMS, something one can, in any event, verify by going to the PRIMS website. It could be added somewhere that a special committee was appointed to handle Mochizuki's papers, which is a fairly normal thing to do in such cases, but to omit that Mochizuki is Editor-in-Chief of the journal would be strange, as that fact has been widely discussed in articles about the controversy.
 * To interject my own views here, if things had panned out the way Mochizuki probably hoped and anticipated back in 2012 when he first submitted the papers to PRIMS, namely if the methods had been widely understood and adopted, and the result heralded as a breakthrough, with widespread acceptance rendering eventual publication almost a formality, his decision to support the local journal by putting his best work there rather than in one of the prestigious international journals where such major results usually end up, would have been seen by many people as admirable, if slightly eccentric. As it was, the members of the editorial board must have found themselves in an impossible situation, having to pass judgement on a close colleague's work amidst acrimonious international controversy. If the work had been submitted to any other prominent journal I believe we'd be in a much better place right now. An independent editorial board with a reputation to uphold would have felt compelled to find a way, without compromising the anonymity of the referees, to provide a mathematical justification to the community of the decision to disregard the critique of Scholze and Stix. Or they would have rejected the papers. In either case the community would have greater clarity than it has now. Will Orrick (talk) 07:49, 10 July 2022 (UTC)
 * I agree with Will Orrick. --JBL (talk) 17:44, 10 July 2022 (UTC)
 * Yes; well said. XOR&#39;easter (talk) 00:44, 11 July 2022 (UTC)

Extended-confirmed-protected edit request on 9 July 2022 (2)
Adding Recent Progress to History：

In April 2022, Mohamed Saïdi, a professor at the University of Exeter, contributed a review in Math Reviews affirming Theorem 3.11 in relation to Corollary 3.12 of the Inter-universal Teichmüller Theory.

In July 2022, Kodai Mathematical Journal, a mathematical journal edited by Tokyo Institute of Technology, published a peer-reviewed paper by Wojciech Polowski, Arata Minamide, Yuichiro Hoshi, Ivan Fesenko, and Shinichi Mochizuki. With this result,they obtain various numerically effective versions of Mochizuki’s Inter-universal Teichmüller theory results, and avoided the obstacles pointed out by Vesselin Dimitrov. 220.100.28.251 (talk) 22:42, 9 July 2022 (UTC)
 * I don't have a mathscinet subscription, but I've read that the mathscinet editors took the unusual step of appending a remark linking to Scholze's negative review in Zentralblatt to Saïdi's review. Someone with access should check this. I'm not sure what he phrase "affirming Theorem 3.11 in relation to Corollary 3.12" means.
 * As for the newer paper, one would need to find reliable sources explaining its significance. In particular, one would need to provide sources justifying the characterization that the paper "avoided the obstacles pointed out by Vesselin Dimitrov." Will Orrick (talk) 08:01, 10 July 2022 (UTC)
 * Yes, the MathSciNet review ends with the following note: "{Editor's note: For an alternative review of the IUT papers, in particular a critique of the key Corollary 3.12 in Part III, we refer the reader to the review by Scholze in zbMATH: https://zbmath.org/1465.14002.}" JBL (talk) 17:30, 10 July 2022 (UTC)
 * ❌. This text is all of the form [assertions about document X][ref: document X].  In particular, the assertions generally are analysis by the author of the paragraph of the content of the documents -- a violation of WP:OR.  --JBL (talk) 17:43, 10 July 2022 (UTC)

Extended-confirmed-protected edit request on 8 July 2023
I would like to add the following paragraph at the end of "History" section with three references. Thank you for your consideration of this matter. QUOTE: In June 2023, the Preparatory Association of The Nippon Foundation and DWANGO Educational Institute (Representative Director: Shinichi Yamanaka) announced that they have established the Inter-universal Geometry Center (abbreviation: IUGC) of ZEN University (provisional name, currently under planning for establishment) to promote and develop the Inter-universal Teichmüller theory. Dr. Fumiharu Kato, Professor Emeritus of the Tokyo Institute of Technology, takes a place of Director of IUGC, and Dr Ivan Fesenko, Professor of University of Warwick and Visiting Professor of Tsinghua University, of Deputy Director as well. Then, in July 2023, they also made the following two statements: 1) They have created two international awards for IUT theory “The IUT Innovator Prize” and “The IUT Challenger Prize”, 2) the 1st IUGC conference on IUT theory will be held in April 2024. The conference will be held in Tokyo, but will be broadcast worldwide via the Internet. UNQUOTE Takaishs (talk) 07:26, 8 July 2023 (UTC)
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. The university's website is not a reliable source because it is not independent (see also WP:PROMOTION). voorts (talk/contributions) 17:42, 8 July 2023 (UTC)
 * The issue is not reliability (the university is not independent, but that doesn't mean it's wrong or untrustworthy) but rather that the inclusion would be WP:UNDUE (as well as the promotional tone). --JBL (talk) 00:00, 9 July 2023 (UTC)
 * Dear Guys, thank you very much for your quick replies. With respect to reliable sources, I found a following newspaper article which reports about the establishment of international awards for IUT theory. Therefore, I would like to add this article as the 3rd reference [3 $1 million offered to the genius who resolves complex math theory (Asahi Shinbun, July 8th, 2023) ] . As for WP:UNDUE matter, as you may know, the "IUT Innovator prize" will be awarded to a paper that contains a new and important development in IUT theory, while the "IUT Challenger prize" will be given to the first mathematician who has written a paper showing an essential flaw in IUT theory. This means that 2 new prizes keep a good balance between pros and cons for IUT theory, and WP:UNDUE criteria do not seem to apply to my request. I hope these explanations will satisfy both of you, and my request will be acceptable. Thanks a lot again for your kind help. Takaishs (talk) 16:14, 9 July 2023 (UTC)
 * The new reference added still does not confirm much of the information in the proposed paragraph. One editor had concerns regarding WP:RS, a second editor had concerns of WP:UNDUE. I don't see how the source authored by Tetsuya Ishikura and provided by the requesting editor surmounts both of those concerns. Regards, Spintendo  03:22, 11 July 2023 (UTC)

New paper by Mochizuki?
A PDF titled ON THE ESSENTIAL LOGICAL STRUCTURE OF INTER-UNIVERSAL TEICHMULLER THEORY IN TERMS OF LOGICAL AND “∧”/LOGICAL OR “∨” RELATIONS: REPORT ON THE OCCASION OF THE PUBLICATION OF THE FOUR MAIN PAPERS ON INTER-UNIVERSAL TEICHMÜLLER THEORY (self-published by Shinichi Mochizuki, September 2023) seems like it ought to be relevant to this article, although I can't personally tell what he's talking about, mathematically speaking. The majority of the PDF seems to be conspiratorial ranting, e.g. [italics, bold, and exclamation points in original] [...] From the point of view of the above discussion, it seems natural, in the case of mathematics, to introduce, especially in the context of issues such as the one discussed above involving logically unrelated fabricated versions of inter-universal Teichmüller theory, the notion of mathematical intellectual property rights [i.e., “MIPRs”]. As the name suggests, this notion is, in some sense, modeled on the conventional notion of intellectual property rights associated, for instance, with trademarks or brand names of corporations. In the case of this conventional notion, intellectual property rights may be understood as a tool for protecting the “reliability” or “creditworthiness” of trademarks or brand names of a corporation from the sort of severe injury to such trademarks or brand names that may ensue from the proliferation of shoddy third-party imitations of products produced by the corporation. Here, we observe that this “severe injury” often revolves around the creation of severe obstacles to the execution of activities that play a central role in the operational normalcy of the corporation.

Unlike this conventional notion, MIPRs should be understood as being associated — not to corporations or individuals for some finite period of time, but rather — to mathematical notions and theories and, moreover, are of unlimited duration [...] or again: [...] This approach of developmental reconstruction may be applied, for instance, to the task of evaluating the level of mathematical or scientific development of ancient civilizations, i.e., not via the direct study of detailed theoretical expositions [which are typically not readily available — cf. the discussion of §1.5!] of the mathematics or science understood by such an ancient civilization, but rather by observing what may be understood as the “fruits” of this mathematics or science, e.g., in the form of architectural achievements such as the famous --Quuxplusone (talk) 17:18, 16 October 2023 (UTC)
 * pyramids of Egypt or
 * Nazca lines and mysterious ruins of Puma Punku in South America [...]


 * The document you reference isn't actually new, having been posted in March 2021. The September 2023 date is a consequence of Mochizuki's habit of continually updating his manuscripts and not doing any form of version control. It's certainly relevant to the subject of this article, but it's hard to see how to make use of it. In part that's because it's unclear what this article wants to be or can be. Should it be (1) a chronicle of the activities of the few people pursuing IUTT? Or (2) an account of the controversy surrounding IUTT's validity? Or (3) a description of the mathematical content of the theory?
 * I would say (1) has no place on Wikipedia. Option (3) would be nice, but who's going to write it? The few people who claim to understand the theory are likely either (A) to write the same kind of conspiratorial material you quote (and are, perhaps, blocked from editing), or (B) not to be active on Wikipedia. That leaves option (2), in which case the referenced manuscript provides some window on the current state of Mochizuki's thinking, but does not, it seems, tell us much that we didn't already know from his earlier writings. Will Orrick (talk) 20:00, 17 October 2023 (UTC)
 * Ah, the date thing is news to me (unsurprising as I don't follow this stuff at all); I agree with everything you wrote, then. :) --Quuxplusone (talk) 13:42, 18 October 2023 (UTC)

Short
Is there any reason why this page is much smaller than its japanese counterpart other than it being protected? Harrydiv321 (talk) 20:04, 14 November 2023 (UTC)


 * Is there any content in the Japanese version that you believe should be in the English version? --JBL (talk) 21:38, 14 November 2023 (UTC)
 * The protection might have something to do with it, but length gives only a first approximation; some parts of our article are much longer than the corresponding parts of the Japanese article. The Japanese version appears to be mostly WP:INUNIVERSE and written by proponents of this work, with a lot of primary-sourced material about media appearances and only a couple of lines about the reception of this work in mainstream mathematics. Our version is primarily based on independent reliable secondary sources and carries over the focus of those sources, which is much more centered on its mathematical reception and less on its hype. —David Eppstein (talk) 21:40, 14 November 2023 (UTC)

Center
There is now a center: https://zen-univ.jp/iugc This seems notable. — Preceding unsigned comment added by 129.2.89.43 (talk) 20:58, 2 February 2024 (UTC)
 * Not unless it has received coverage in independent reliable sources, per WP:DUE. --JBL (talk) 21:07, 2 February 2024 (UTC)

Extended-confirmed-protected edit request on 31 March 2024
Someone please add information for this URL. https://www.newscientist.com/article/2381521-decade-long-struggle-over-maths-proof-could-be-decided-by-1m-prize/ 2400:2411:A1A1:B000:5D36:A5D6:D415:82DC (talk) 22:32, 31 March 2024 (UTC)


 * IP, I presume you are asking for the information about the ITU Challenger Prize to be added? Not quite sure if this event satisfies WP:N and WP:DUE. So far the only independent WP:RS that have reported this are this New Scientist article and The Asahi Shinbun article above in . Also noting that the former request included information on this event and was rejected per WP:DUE too.
 * , you replied to a few other similar requests above. Could you take a look at this? Liu1126 (talk) 23:01, 31 March 2024 (UTC)
 * Red information icon with gradient background.svg Not done: After 20 days there doesn't appear to be progress on this request, and regardless the edit request process requires requestors to provide prose and other specifications for consideration. Gonna mark as answered for now to remove it from the queue. — Sirdog (talk) 04:29, 21 April 2024 (UTC)