Catch up on the IUT village

(This is a translation of my post on Apr. 17, 2024. Sorry, it is no longer new content.)

I haven’t been following the recent developments since I realised that the IUT is apparently not a significant mathematical achievement, but The Asahi Shimbun has published another strange opinion article, which reminded me of what’s going on these days.

The article says “It is rare for the paper to be so praised, feared and ignored”, and I have no idea that the IUT paper is feared by the math community. I read the paid part which includes claims that the debate is stalled, the unimportant information that Mochizuki is a friendly personality who is also familiar with entertainment stories, and the story of the prize money by Nobuo Kawakami (see below). There is nothing new to talk about.

My own previous writing on this series of issues is posted with the tag ‘abc‘.

To repeat what I have written in the past, there are two main reasons why the IUT has been severely disreputable and abandoned. One is the problem as mathematics and the other is the problem of the academic integrity that Mochizuki and those around him should have. I believe that the latter is the essential reason why the mathematical community has abandoned the IUT, but the innocent people who seem to have high hopes for the IUT, including Mr. Ishikura of Asahi Shimbun, mention the former problem, but for some reason do not mention the latter at all.

The problem as mathematics

It boils down to the following points.

  • In 2018, two experts in arithmetic geometry, Peter Scholze (University of Bonn) and Jakob Stix (University of Frankfurt), pointed out a fatal problem in the core of the Mochizuki paper, “Corollary 3.12”.
  • Scholze and Stix came all the way to Japan to visit Mochizuki at Kyoto University and had a direct discussion for a week, but Mochizuki refused to admit that there was a gap with Corollary 3.12 and the discussion ended in a parallel line.

The Mochizuki paper was also reviewed by Scholze on zbMATH Open, a worldwide mathematical literature database operated by the European Mathematical Society and others, and the paper’s claim that it proved the ABC conjecture was unequivocally denied. As exemplified by this, the Mochizuki paper is perceived negatively outside the Mochizuki group.

Issues of academic integrity

The other problem lies in the fact that, for example:

  • Mochizuki did not cite any of the points made by Scholze and Stix in his paper and published it as if “there were no points made”.
  • The journal in which the paper was published is PRIMS, published by the Research Institute for Mathematical Sciences (RIMS) of Kyoto University, to which Mochizuki belongs, and he himself is the editor-in-chief of this journal. In other words, the paper was submitted to their own journal, peer-reviewed by Mochizuki’s associates and accepted. It is practically self-made. (To be precise, Mochizuki himself is out of editorial duties with regard to this paper, but it would be normal to assume that the peer review team must be trying to please him.)
  • In addition to the main IUT paper, Mochizuki has published IUT-related reports and papers on his website from time to time, but he has consistently avoided mentioning Scholze and Stix’s name in these documents and continues to refer to them derisively as the “RCS (redundant copies school)”. He do not cite their reports in the bibliographies. Failure to properly cite references means that future generations will not be able to follow such discussions from the bibliographic information.
  • Ignoring the situation where the correctness of the IUT is being questioned in a big way, Kyoto University has established an institute called the ‘Center for Research in Next-Generation Geometry‘ under the RIMS in 2019, with Mochizuki as the centre’s director. (In 2022, it will be merged with the Research Center for Quantum Geometry and reorganised as the International Research Center for Next-Generation Geometry. The director of the centre remains the same, Mochizuki.)

Recent developments

There were various matters that I meant to write about but forgot.

Establishment of the Inter Universal Geometry Center at ZEN University

ZEN University is an online university that Nobuo Kawakami (founder of Dwango Co. Ltd.) plans to establish. The announcement that an institute will be set up at a university that does not yet exist is nonsense, but the director is said to be Fumiharu Kato (professor emeritus at Tokyo Institute of Technology) and the vice-director is Ivan Fesenko (Westlake University, China). Of course, they are sympathisers of Mochizuki.

At the same time, they have established an award for researchers who have contributed to the development of IUT.

There are ‘IUT Innovator Prize’ and ‘IUT Challenger Prize’, with the first Innovator Prize going to a 2022 paper by five people, including Mochizuki. Fesenko declined the prize money, so the four people will receive USD 100,000 (instead of USD 100,000 each, the $100,000 is split four ways ?).

This kind of thing would normally be called ‘hand-outs’ – it looks like a scheme by the IUT group to pull money from Kawango (nickname of Kawakami) and put it in their own pockets. Are these people really researchers?

People in the mathematics community outside Japan have observed Mochizuki’s group doing all these fishy things in the name of IUT outreach without dealing with the academic integrity issues I mentioned above. The comments section of the following blog entry by Peter Woit (Columbia University, Mathematical Physics) is constantly filled with numerous comments from readers who appear to be mathematicians and mathematics students, who also write about their disappointment, sadness, anger and pity for Mochizuki and his colleagues’ words and actions.

Work by independent researchers

The Mochizuki paper is unnecessarily long and full of bizarre concepts that are difficult to read, so several researchers are trying to rewrite it in a more existing mathematical language.

One of them, Kirti Joshi (University of Arizona), published a paper at the end of March claiming to have proved the ABC conjecture again, using the existing framework of arithmetic geometry to fill in the gaps in Mochizuki’s Cor. 3.12.

Scholze pointed out in a comment on MathOverflow about this that there were obvious flaws in Joshi’s proof.

On the other hand, Mochizuki also published a text denying Joshi’s paper on his website. Coincidentally, both Scholze and Mochizuki, who are at loggerheads in the IUT, have denied Joshi’s paper.

Scholze’s points on MathOverflow are rational as usual, but Mochizuki’s sentences continue to use boldface and italics in an abusive style. ‘Joshi’s paper is like ChatGPT’s halcynation’ or something like that.

Mochizuki mentions that the number of a key theorem in Joshi’s paper happens to be “Theorem 9.11.xx”, and writes an insensitive joke about whether it is a coincidence that it is “9.11″, or some kind of rhetoric or humour.

[where we note that it is not clear whether or not the number “9.11…” was assigned by the author to these key results in [CnstIII] was purely coincidental or a consequence of some sort of sense of rhetoric or humour that lies beyond my understanding].


If you are a Japanese, you can see the opposite case. Suppose you receive a rebuttal to a paper you wrote and it says: “… By the way, your theorem number here is 8.6, which is the same as the date of the atomic bombing. Does this have an special meaning?” How would you feel if a joke like that was written there?

Well, it would be enough to say that this is the kind of person Mochizuki is, but his childish attitude of mixing this kind of thing into scientific discussion has dampened the will to seriously evaluate his work, and is one of the reasons why the IUT is being abandoned.

If they want to save the IUT (and I don’t think they can save it now), they’d better realise that they’ve had enough. There really is too much dishonesty on various levels on the part of Mochizuki and his crony group. They turn a blind eye to it and say, “IUT is amazing! Japan is amazing! They say it’s too esoteric for people overseas to understand how great it is!” or “We should discuss it more instead of ignoring it”, the sane people have already seen through it and are fed up with it.