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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.
PJTraill ( talk) 14:21, 10 May 2015 (UTC)
Maybe this article helps you... Ishnigarrab ( talk) 16:28, 8 December 2016 (UTC)
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)
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)
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." [1] [2]
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 [3], +h motomura [4] on google+ and @math_jin on Twitter [5]) 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:
Specifically, Remark 3.12.2 of IUTeich III was expanded from approx. 12000 characters in May 2017 [8] to approx. 19000 characters in August 2017 [9]. The revisions are listed in the revision history on Mochizuki's webpage [10]. 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
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)
References
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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)
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)
References
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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)
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
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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)
...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)
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 [1], Mochizuki's work is now published [2] while still a controversial theory for some [3].
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)
References
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)
"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)
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 [1]. He then made his manuscript available on the official RIMS preprints server in 2012 [2]. 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)
References
{{
cite speech}}
: CS1 maint: date format (
link)
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)
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 [1] [2].
While debates continue outside of the academic on the comment section of Peter Woit's blog (incl. Peter Scholze) [3], 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 [4], in 2021 a one-year RIMS-project``Expanding Horizons of IUT theory took place with a series of four online workshops [5].
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) [6] 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, Zbl 1465.14002. — 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)
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.
2400:4150:8120:C500:7E87:E20C:2E8E:712 ( talk) 05:03, 3 October 2021 (UTC)
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)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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.
Comments or formulation proposals will be most helpful.
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220.100.45.26 ( talk) 07:11, 9 July 2022 (UTC)
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From: for which he is editor-in-chief. [1] [2]
To: for which Masaki Kashiwara, Akio Tamagawa are Editors-in-Chief [3]
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)
References
bordg
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Adding Recent Progress to History:
In April 2022, Mohamed Saïdi, a professor at the University of Exeter, contributed a review [1] 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 [2]. 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. [3] 220.100.28.251 ( talk) 22:42, 9 July 2022 (UTC)
References
{{
cite web}}
: Check date values in: |access-date=
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help)
{{
cite journal}}
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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. [1] 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. [2] [3] UNQUOTE
Takaishs ( talk) 07:26, 8 July 2023 (UTC)
References
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
- pyramids of Egypt or
- Nazca lines and mysterious ruins of Puma Punku in South America [...]
-- Quuxplusone ( talk) 17:18, 16 October 2023 (UTC)
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)
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)
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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)
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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.
PJTraill ( talk) 14:21, 10 May 2015 (UTC)
Maybe this article helps you... Ishnigarrab ( talk) 16:28, 8 December 2016 (UTC)
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)
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)
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." [1] [2]
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 [3], +h motomura [4] on google+ and @math_jin on Twitter [5]) 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:
Specifically, Remark 3.12.2 of IUTeich III was expanded from approx. 12000 characters in May 2017 [8] to approx. 19000 characters in August 2017 [9]. The revisions are listed in the revision history on Mochizuki's webpage [10]. 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
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)
References
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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)
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)
References
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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)
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
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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)
...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)
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 [1], Mochizuki's work is now published [2] while still a controversial theory for some [3].
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)
References
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)
"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)
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 [1]. He then made his manuscript available on the official RIMS preprints server in 2012 [2]. 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)
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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)
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 [1] [2].
While debates continue outside of the academic on the comment section of Peter Woit's blog (incl. Peter Scholze) [3], 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 [4], in 2021 a one-year RIMS-project``Expanding Horizons of IUT theory took place with a series of four online workshops [5].
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) [6] 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, Zbl 1465.14002. — 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)
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.
2400:4150:8120:C500:7E87:E20C:2E8E:712 ( talk) 05:03, 3 October 2021 (UTC)
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)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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.
Comments or formulation proposals will be most helpful.
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220.100.45.26 ( talk) 07:11, 9 July 2022 (UTC)
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From: for which he is editor-in-chief. [1] [2]
To: for which Masaki Kashiwara, Akio Tamagawa are Editors-in-Chief [3]
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 (
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References
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Adding Recent Progress to History:
In April 2022, Mohamed Saïdi, a professor at the University of Exeter, contributed a review [1] 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 [2]. 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. [3] 220.100.28.251 ( talk) 22:42, 9 July 2022 (UTC)
References
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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. [1] 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. [2] [3] UNQUOTE
Takaishs ( talk) 07:26, 8 July 2023 (UTC)
References
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
- pyramids of Egypt or
- Nazca lines and mysterious ruins of Puma Punku in South America [...]
-- Quuxplusone ( talk) 17:18, 16 October 2023 (UTC)
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)
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)
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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)