The mathematical community broadly does not accept Mochizuki's IUT proof of the abc conjecture.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. Decomposed into two named arguments. For: a new documentary claim on the 2018 Scholze-Stix conclusion, a new attribution claim on Scholze's zbMATH review (scored 0.2, left as stub), a new sociological claim on the composition of endorsements, and the existing claim that the 3.11-to-3.12 argument as written cannot be formalized (the LANA project's July 2026 conclusion). Against: the existing PRIMS publication claim, a new claim recording the named public affirmations, and a new inference claim that publication establishes acceptance (seeded low), which is the step the against argument fails on. Deliberately did not attach the existing claim "Mochizuki's rebuttals have not persuaded arithmetic geometers outside his circle" because it already lists this claim as a subclaim; attaching it here would create a cycle. Every new dependency was checked with the Matcher first; all came back novel. Assessment verified at confidence 0.9, credence 0.97. Web search (five queries, the cap) surfaced the 2026 LANA formalization developments, which materially strengthen the claim; the zbMATH review and the Nature web page could not be fetched (403 and paywall), so the review's content rests on secondary descriptions and the Nature text on the magazine PDF excerpt. Recorded three affirming instances (Nature/Kedlaya 2020, Woit 2020, Deep Forest newsletter) with readings; one provenance edge from Woit to Nature; source map written and marked immaterial. No denying instance was found in sources read; Fesenko's claim that many mathematicians have checked the theory would be the natural one to record on a later pass. Importance set to 0.4 (notable), contestation 0.35: the Extractor's prior was apt. Canonical form kept: fifteen words, neutral, the form the discourse uses. Marginal yield 0.15: a later pass could open the zbMATH review directly and record a defender's denying instance, but neither is likely to move the verdict.
Assessed Verified
verdict confidence 0.90 · credence 0.97
Shinichi Mochizuki posted his four inter-universal Teichmüller theory papers in 2012, claiming a proof of the abc conjecture, and the question of whether the wider mathematical community accepts that proof has had a stable answer since 2018. In that year Peter Scholze and Jakob Stix, after a week of discussions in Kyoto, concluded that the proof of Corollary 3.12 contains a serious gap that cannot be repaired. Number theorists who had spent years trying to follow the papers described the report as settling the matter for most of the field, and the abc conjecture has continued to be listed as open in reference works and to be treated as a hypothesis, rather than a theorem, in subsequent research. The strongest case for acceptance is institutional: the papers were refereed and published in Publications of RIMS in 2021, and a number of mathematicians, among them Ivan Fesenko, Yuichiro Hoshi, Go Yamashita and Chung Pang Mok, have publicly affirmed the proof. That case rests on the premise that refereed publication is what community acceptance consists of, and for these papers the usual link between the two broke down. The journal is edited at Mochizuki's own institute, the leading critics stated that publication changed nothing in their judgment, and Scholze's review of the published version for zbMATH maintains that the proof of Corollary 3.12 is incomplete. Public endorsements come almost entirely from RIMS colleagues and long-standing advocates; Kirti Joshi, the outside researcher most sympathetic to the theory's ideas, holds that the papers do not establish the corollary as written. The most recent development points the same way. The LANA project, a Lean formalization effort based at ZEN University in Japan and conducted in dialogue with Mochizuki, reported in July 2026 that after two years it had isolated an unproven compatibility at the passage from Theorem 3.11 to Corollary 3.12, that the argument as written could not be formalized, and that it continued to suspend judgment on whether the abc conjecture had been proved; Hoshi, one of the proof's original supporters, acknowledged that many project members feel "some insurmountable wall" at that step. What would change the picture is public confirmation by independent arithmetic geometers that they have followed a complete argument, whether through a successful formalization, through Joshi's programme, or through a revised account by Mochizuki that the LANA project and outside experts endorse.
Claim entered the graph