The establishment of a new university in Japan has been announced, to be called ZEN University. One component of the new university will be the Inter Universal Geometry Center, with Fumiharu Kato as director, Ivan Fesenko as deputy director. The Center will offer an introductory course on IUTT. There’s a video here.

The website seems to be Japanese-only, here’s what I get via Google Translate:

If you pass all of our courses, you will be better equipped with IUT theory than any mathematics student in any university in the world. A student who blooms his talents that emerges from within. We plan to prepare prizes for such young people and encourage them to continue to participate in the community that seriously researches IUT theory…

Although it is difficult to understand, there are already more than 20 mathematicians in the world who understand and develop the IUT theory. I hope that you will boldly take on the challenge of researching IUT theory together with me so that you can be one of the next.

The problem with this subject though is not the number of people who understand IUTT, but the number who can explain to others in a convincing way the proof of corollary 3.12 in the third IUTT paper. From everything I have seen, that number has always been and remains zero.

**Update**: Another video here.

Oh my God, why is this happening?

It seems to be an online only university, despite the glossy pictures of students on campuses. And probably fairly expensive to attend.

Seems like an attempt to build a pool of innocent japanese students, unaware of the controversy abroad and devoted to IUTT.

Kato has written a popular book (in Japanese) on IUTT. There’s an interesting review of it at zbMATH Open by Hirokazu Nishimura. Choice quote, referring to D. T. Suzuki, who helped popularize Zen Buddhism in the West: “Some cynics say that Daisetz Suzuki became famous by speaking a lot about the unspeakable. The author of this book has written a book for general public on the unspeakable.”

One very small but interesting detail in the second video: at 2:30ish the narrator reads Kato’s name wrong (he says, “Kato Bungen”). Extremely unprofessional.

@Anonymous

Kato has “Bungen” in his Twitter display name (not handle): https://twitter.com/FumiharuKato/

I don’t know what that is and what role it plays in naming him.

Fumiharu and Bungen are alternate pronunciations of the Chinese characters that make up Dr. Kato’s given name. It’s common in the literary world for people to be referred to by the Chinese pronunciation of their given name, even though the official (legal) pronunciation is the Japanese pronunciation. I don’t know how common this is in other academic areas though. Dr. Kato’s first name is given as “Fumiharu” in all the references (e.g. Wikipedia) I noticed.

By the way, the Zen in Zen University doesn’t mean what you think it does. Their motto is “Zen, Zen, Zen Nado”. It consisst of three different Chinese characters, all pronounced “zen”, which mean “All”, “Good”, and “Natural”, respectively. There is no overtone of Buddhism in the slightest. The idea is that each student will experience, deal with, and come to grok a wide range of things “zen”. But not including Buddhism. It makes sense in Japanese, a local expert assures me. So it’s a newly coined version of “Mind and Hand” or “Veritas”. (“Nado” means “and the like”. (Well, actually, it means “The preceeding list defines a set of things with similar characteristics, and that list may or may not be exhaustive”.))

From their long list of _planned_ faculty members (and their website in general), my impression is that the IUTT stuff is but a tiny part of what they’re planning, and that they are not much further than just planning. My guess would be that the IUTT stuff got them government funding. (And, yes, it is an online-only university. Some of the parties involved have been running seminar-like things in public rental spaces in Tokyo, so while most of the photos are stock photos, there are a couple of actual real event photos that I noticed.)

Not sure if we really need to continue this discussion, but since I started it I feel I should (potentially) end it: Kato put up a few tweets about his name being mispronounced and retweeted a tweet of someone else laughing about it.

What is the status of the ABC conjecture in Japan these days, now that the refutation is famous worldwide? Do they consider it proven over there, or are they just being polite to a VIP mathematician, by refusing to challenge the paper?

I mean, if they thought the proof was correct, then the author of the proof would be eligible for glittering prizes worldwide, right?

It seems to me that this has gotten quite out of hand. Either the proof is correct or it is not and no amount of egos or politicking can change that. This is an embarrassment for the whole mathematical field. It is akin to postmodernism in math. We now have the global mathematical community rejecting this proof and a fringe – but well respected before this fiasco – group of mathematicians pressing on as if the proof is correct and self-evident. This was not supposed to happen to mathematics where the rigor and community consensus was to provide a universal mathematical truth.

The only way out of this I can figure is a challenge the fringe group to produce a computer verified proof or a the global mathematical community to produce a computer verified rejection: which seems an absolutely *insane* amount of work either way.

You could get an AI trained on taking human language proofs and translating them to computer verified proofs, but no one would be able to verify that the translation was correct without doing the same or greater amount of work in just writing the computer proof themselves.

I fear that the only way this will end is for egos to die.

Adam Treat,

As far as I can tell, this is over, there’s no significant controversy any more over the Mochizuki abc proof, it’s simply not accepted by experts in the field. There is no embarrassment for mathematics in general, just for RIMS in particular because of the scandal surrounding the publication of a proof experts believe to be incorrect.

As for computer verification, Mochizuki has chosen to not try and produce a clearer version of his original argument that could possibly convince others, instead arguing that those who don’t accept the original argument are incompetent. If he can’t or won’t clarify his argument to answer human objections to it, what reason is there to believe he could clarify the argument to the point it would be computer-checkable?

I’ve asked this before in here but afaik with no answers. Please note that the answer might look obvious to a mathematician, but I assure you that it is not at all for anyone else: Does IUTT have some value, regardless of whether its proof is correct or wrong?

I remember that this is something happening in the past with other theories that were proven wrong; they explored new corners and included new propositions with merit of their own. (Don’t ask me to name such theories though, my general knowledge simply includes the memory of such things happening.) I feel rather surprised that such a large construct is said to be devoid of any value, dependent on a single point of failure.

Hi tulpoeid,

Not sure about its possible significance or value beyond proving abc, but it does not seem possible to get intermediate results in his claimed proof. According to these detailed Notes on the Oxford IUT workshop by Brian Conrad in 2015 (in https://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/), “Mochizuki aims to prove Szpiro’s conjecture for all elliptic curves over number fields, with a constant that depends only on the degree of the number field (and on the choice of epsilon in the statement). The deductions from that to more concrete consequences (such as the ABC Conjecture and hence many finiteness results such as: the Mordell Conjecture, Siegel’s theorem on integral points of affine curves, and the finiteness of the set of elliptic curves over a fixed number field with good reduction outside a fixed finite set of places) have been known for decades and do not play any direct role in his arguments. In particular, one cannot get any insight into Mochizuki’s methods by trying to “test them out” in the context of such concrete consequences, as his arguments are taking place entirely in the setting of Szpiro’s Conjecture (where those concrete consequences have no direct relevance).”

Wikipedia summarizes this in https://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory#cite_note-BC2015-25 by saying that “One issue with Mochizuki’s arguments, which he acknowledges, is that it does not seem possible to get intermediate results in his claimed proof of the abc conjecture 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.”

tulpoeid,

IUTT and similar approaches like Kirti Joshi’s work are probably useful for p-adic/arithmetic Teichmueller theory and anabelian geometry. The issue here is that no mathematician has provided a correct proof of Mochizuki’s Corollary 3.1.2 linking the former fields with the abc conjecture, and the vast majority of mathematicians are mainly interested in the latter.

In a 2017 talk “abc Conjecture and New Mathematics”, Fumiharu Kato said “I don’t put much importance on as to whether the [abc] conjecture itself has actually been proved or not, or, if so, how it has been done.” The point of the talk was that there are problems involving the way addition and multiplication in the integers interact that “traditional” mathematics find intractable, such as the abc conjecture, the twin primes conjecture, and the Goldbach conjecture, and that IUTT is designed to handle such problems. There are serious mathematicians involved with this, so I don’t think it can be dismissed out of hand.

For what it’s worth, Mochizuki has a new paper out with Tsujimura in which they announce settling several big conjectures in anabelian geometry. The bibliography doesn’t mention any of the IUTT papers and related ones, so it seems to be independent of it.

This is because mathematicians such as Peter Scholze have not submitted refutation papers while claiming that IUTT is logically inconsistent.

This news re-emphasizes to us the fact that their claims are only on a personal level, not as mathematicians. If IUTT were correct, the abc conjecture would have been solved as just a secondary problem.

This means that IUTT has the higher logical structure sufficient as a theory to evaluate problems in number theory.

In other words, the those incidents about IUTT that we remembered are a mathematician’s problems, not mathematical problems, because this announcement tell us the IUTT still has some potential to undo much of the existing work related to number theory.

Nakamoto,

For discussion of this, please submit comments to the newer blog post which is specifically about this. Scholze and Stix did write a paper. Their argument is not that IUTT is inconsistent, just that it is not capable of providing the tool needed for a proof of abc.