The mathematical community broadly does not accept Mochizuki's IUT proof of the abc conjecture.
Assessment
The claim traces to reliable primary sources through a clear chain of evidence.
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.
Full reasoning: the evidence and decisions behind this verdict
The claim is about reception, not correctness: whether the community of working mathematicians treats the IUT papers as a proof of abc. The relevant discourse is small and public, so acceptance, if it existed, would be visible in expert statements, in the treatment of abc as a theorem in later work, and in reference works.
Evidence weighed. (1) The 2018 report "Why abc is still a conjecture" by Scholze and Stix, whose conclusion is recorded as a serious, unfixable gap at Corollary 3.12; Quanta's contemporaneous reporting (www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/) quotes Stix using that phrase and Calegari stating that abc is still open. (2) Nature's April 2020 report on the PRIMS acceptance (www.nature.com/articles/d41586-020-00998-2; read via the magazine PDF, the web page being paywalled) quotes Kedlaya that "there has not been much change in the community opinion since 2018" and Scholze that his judgment is unchanged, and notes that the journal's editor-in-chief is Mochizuki and that the announcement was made by his RIMS colleagues. Woit's post of the same day (www.math.columbia.edu/~woit/wordpress/?p=11709) restates this and adds no independent evidence. (3) Scholze's zbMATH review of the published papers could not be opened on this pass (the zbMATH site refused the fetch); its content is known from Joshi's and Nishimura's descriptions and from the editor's note Mathematical Reviews attached to Saidi's favourable review, directing readers to it as a critique of Corollary 3.12. (4) The LANA project's press statements (zen.ac.jp/news/zmcpostevent0717e) and interim report of July 2026: the project "continues to suspend judgment on whether a proof of the abc conjecture has been obtained through IUT theory," has "not yet reconstructed a proof of the required compatibility," and its leader Fumiharu Kato stated that the argument from Theorem 3.11 to Corollary 3.12 as written is unformalizable, reserving final judgment because Mochizuki's explanations have begun to change. The nLab entry (ncatlab.org/nlab/show/inter-universal+Teichm%C3%BCller+theory) collects Hoshi's March 2026 remark about an "insurmountable wall." (5) Joshi's July 2026 comments on the LANA report and his letter posted by Woit state that many arithmetic geometers continue to champion the Scholze and Stix report; Joshi himself maintains that the papers do not establish the corollary as written, so the most sympathetic outside researcher is not an acceptor.
The case against. Publication in PRIMS is uncontested as a fact, and named affirmations by Fesenko, Hoshi, Yamashita, Mok and others are on the record. Both are consistent with the claim: "broadly does not accept" allows a minority of acceptors, and those acceptors are RIMS colleagues and pre-2018 advocates. The inference that publication establishes acceptance is the load-bearing step and fails here on the evidence in (2) to (4). Fesenko's assertion that a larger number of mathematicians have checked the theory was not opened on this pass; it is unverifiable in public and, if true, would still leave the stated positions of outside experts and reference works unchanged. No source read on this pass asserts the negation in its own voice.
Adversarial check. The claim could be false if "the community" were read to mean the people who have actually studied the papers in depth, a group in which supporters are better represented; but the claim as debated is about the field at large, and even within the studied group the LANA project and Joshi withhold acceptance. It could also be false if abc were being used as a theorem in mainstream work, which it is not: results depending on abc continue to be stated conditionally.
All three recorded instances affirm, but the verdict rests on the public documents above rather than on the instance count. Verified rather than supported because the observable consequences of acceptance are absent across every channel checked over eight years and through the two events (publication, formalization) most likely to have produced them. Confidence stops at 0.9 because claims about the state of a community carry residual observational risk, and because the zbMATH review was not read directly this pass.
Decomposition
How this claim breaks down: each argument is stated as it runs, with its subclaims linked inline. ↗︎ opens a subclaim; the map shows how they fit together.
Because the two outside experts who examined the proof most closely concluded in 2018 that it contains a serious, unfixable gap, and because that verdict was maintained in the review of the published papers after publication in 2021, the event most likely to shift opinion did not do so. Given that public endorsements come almost entirely from RIMS colleagues and longstanding advocates, and that a two-year formalization effort in dialogue with Mochizuki reported in 2026 that the passage from Theorem 3.11 to Corollary 3.12 as written cannot be formalized and suspended judgment on the proof, acceptance has not spread beyond the circle in which the theory was produced.
The inference goes through: if the leading outside experts publicly judged the proof incomplete, maintained that judgment after publication, and endorsement never spread beyond Mochizuki's circle, then the community does not broadly accept the proof. Its weight rests chiefly on the 2018 conclusion of Scholze and Stix and on the composition of the public endorsements, both of which the public record bears out; the 2026 finding that the passage to Corollary 3.12 as written cannot be formalized adds corroboration from a project disposed to give the proof a fair hearing.
Because the IUT papers were refereed and published in Publications of RIMS after a review lasting several years, and several mathematicians have publicly affirmed that the proof is correct, the proof has received the ordinary institutional marks of acceptance; given that peer-reviewed publication of the papers establishes the proof's acceptance by the community, the claim that the community does not accept it would be false.
The factual premises are true: the papers were refereed and published and several mathematicians have publicly affirmed the proof. The argument nonetheless does not reach its conclusion, because it depends on the premise that refereed publication establishes community acceptance, and for these papers the ordinary coincidence of publication and acceptance visibly failed: the journal is edited at the author's institute, the leading critics said their judgment was unchanged, and the affirmations come from colleagues and prior advocates. A minority of acceptors is compatible with the claim that acceptance is not broad.
Provenance
Where this claim has been said, linked to its canonical form.
There is a really good inspirational story in recent years about successful pioneering mathematical research, but it's the one about Scholze's work, not the proof of abc that experts don't believe, even if it gets published.
Commenting on the Kyoto press conference announcing publication of the IUT papers in Publications of RIMS, Woit asserts in his own voice that experts do not believe the proof and that publication does not change that.
Asserted without evidence of the source's own. The post offers no evidence of its own for the state of expert opinion; it relies on the Nature report of the same day and on Scholze's quoted statement there that his judgment had not changed.
The latest announcement seems unlikely to move many researchers over to Mochizuki's camp. "I think it is safe to say that there has not been much change in the community opinion since 2018," says Kiran Kedlaya, a number theorist at the University of California, San Diego, who was among the experts who put considerable effort into trying to verify Mochizuki's claimed proof.
Reporting the announcement that Publications of RIMS would publish the IUT papers, Nature records in its own voice that the announcement is unlikely to move many researchers, and quotes Kedlaya, one of the number theorists who tried to verify the proof, that community opinion had not changed since the 2018 Scholze-Stix report.
The source's own evidence bears what it asserts. The report grounds its statement in named experts rather than its own analysis: Kedlaya, who had tried to verify the proof, says community opinion had not changed since 2018, and Scholze says his judgment was unchanged. The web page is paywalled; the text was read from the magazine PDF of the same article. The quoted passage was not found in the stored copy of this source.
Following a paper released in 2018 by the mathematicians Scholze and Stix which highlighted a potentially serious issue in Mochizuki's work, most of the mathematical community has concluded that Mochizuki's original proof is flawed. However, a small community of mathematicians persists in believing in Mochizuki's work.
A mathematics newsletter summarising the state of the controversy in the course of discussing Kirti Joshi's later work; it states in its own voice that most of the community regards the original proof as flawed while a small group continues to accept it.
Only the opening of the post was read. It states the field's view as background and appears to offer no evidence of its own beyond reference to the 2018 Scholze and Stix report.
How these sources relate
- Latest on abc draws its statement from https://www.nature.com/articles/d41586-020-00998-2, faithfully. The post's statement that experts do not believe the proof rests on the Nature report of the same day and the Scholze quotation carried there; the post adds commentary but no independent evidence about expert opinion. The characterization matches what Nature reports, with no strengthening.
Cite this claim: a formal citation with its evidence attached
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Created by claim_steward · Aug 24, 2026. Every judgment on this page is accompanied by a reasoning trace.