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Claim analyzed
Science“The ABC conjecture has been proven as of March 18, 2026.”
The conclusion
The ABC conjecture has not been proven in any broadly accepted sense as of March 18, 2026. While Mochizuki's proof was published by RIMS in Kyoto, leading mathematicians including Peter Scholze and Jakob Stix identified a serious, unfixable gap that remains unresolved. The RIMS publication carries a conflict of interest, and Joshi's subsequent defense is explicitly conditional on acceptance of enhancements the community has not endorsed. As of early 2026, the conjecture remains "a theorem in Kyoto, a conjecture everywhere else."
Based on 11 sources: 1 supporting, 6 refuting, 4 neutral.
Caveats
- Leading experts Scholze and Stix identified a 'serious, unfixable gap' in Mochizuki's proof that has never been satisfactorily resolved.
- The RIMS journal that published the proof was effectively overseen by Mochizuki himself, creating a significant conflict of interest.
- Joshi's 'Final Report' claiming the proof is complete only holds 'provided his enhancements are accepted' — a condition the broader mathematical community has not fulfilled.
Sources
Sources used in the analysis
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years. Shinichi Mochizuki maintains that his proof is not flawed despite the assertions of Jakob Stix and Peter Scholze that they've discovered a “serious, unfixable gap.”
Davide Castelvecchi at Nature has the story this morning of a press conference held earlier today at Kyoto University to announce the publication by Publications of the Research Institute for Mathematical Sciences (RIMS) of Mochizuki's purported proof of the abc conjecture. This is very odd. As the Nature subheadline explains, “some experts say author Shinichi Mochizuki failed to fix fatal flaw”.
More than a decade later, his proof remains one of the most controversial in modern mathematics. This created a surreal situation: the ABC conjecture was officially declared a theorem in Kyoto, but remained a conjecture everywhere else.
Shinichi Mochizuki's controversial mathematical proof of abc conjecture divides math experts amid cultural conflicts and competing claims. In a strongly-worded recent paper titled Final Report on the Mochizuki-Scholze-Stix Controversy, Joshi concludes that Scholze and Stix's critique is mathematically false. He boldly declares that the abc conjecture is indeed proven, provided his enhancements are accepted.
In March 2025, Joshi has published a new set of papers, including a final report where he claims again that now he has solved all those problems that plague the proof, and that now the proof of ABC is complete thanks to Joshy. But he claims that every assertion of Schulzen sticks is mathematically false.
京都大学数理解析研究所の望月新一教授は2012年8月、4本の論文をインターネット上に公開した。未解決の数学的難問「abc予想」を解決できるとする「IUT理論（宇宙際タイヒミューラー理論）」である。しかし、きわめて難解にしてあまりにも長大なこの論文をめぐって、世界の数学界には予想外の大きな「混沌」が生じた。現在では議論も膠着状態となっている。
Only Mochizuki and a handful of close colleagues accept his work, and his reputation has incurred enough self-inflicted wounds that he is likely no longer worth the time of day to mathematicians outside his circle. To conclude: as Peter Woit said in 2021, a b c is still a conjecture.
The mathematical community generally requires a proof to be thoroughly vetted and accepted by a broad consensus of experts before a conjecture is considered 'proven.' Publication in a single journal, especially one with potential conflicts of interest, does not automatically confer this status.
This whole affair results in a now infamous statement that "We do now have the ridiculous situation where ABC is a theorem in Kyoto but a conjecture everywhere else." Mochizuki recuses himself from the editorial process but given that the reviewers will still be people from a journal he manages no one finds this very reassuring.
Shinichi Mochizuki claimed to have a proof in 2012, but the conjecture is still regarded as unproven by the mainstream mathematical community.
The last couple months I've heard reports from several people claiming that arithmetic geometers Peter Scholze and Jakob Stix had identified a serious problem with Mochizuki's claimed proof of the abc conjecture. Every attempt at asking Mochizuki to clarify / fix this point resulted in him saying they just couldn't understand his work.
What do you think of the claim?
Community challenges 1
So wait, if Mochizuki's proof got formally published by RIMS then isn't it technically proven on paper? Seems like you're moving the goalposts by requiring "broad acceptance" when that's not really how formal publication works.
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Expert review
How each expert evaluated the evidence and arguments
Expert 1 — The Logic Examiner
The pro side infers “proven” from (i) publication/announcement in RIMS and being “declared a theorem in Kyoto” (Sources 2–3) plus (ii) Joshi's conditional defense that it is proven if his enhancements are accepted (Sources 4–5), but none of this logically entails that the conjecture is in fact proven in the ordinary mathematical sense (i.e., a proof that withstands expert scrutiny), and several sources explicitly describe the status as still disputed/unaccepted (Sources 1, 2, 3, 6, 7, 10). Given the evidence depicts an ongoing controversy with no demonstrated resolution or broad acceptance by March 18, 2026—and even the strongest “support” is explicitly conditional—the claim that the ABC conjecture “has been proven” as of that date is not established and is best judged false.
Expert 2 — The Context Analyst
The claim "The ABC conjecture has been proven as of March 18, 2026" omits critical context: while Mochizuki's proof was published by RIMS in Kyoto and Joshi has issued a "Final Report" claiming to resolve outstanding objections, the overwhelming consensus of the broader mathematical community — including leading experts Scholze and Stix — is that the proof contains an unfixable gap, and Joshi's own claim is explicitly conditional on acceptance of his enhancements (Sources 1, 3, 4, 7, 8, 10). The claim creates a fundamentally false impression by presenting a deeply contested and unresolved situation as a settled fact; "proven" in mathematics requires broad expert consensus, which as of March 2026 has clearly not been achieved, making the claim false rather than merely misleading.
Expert 3 — The Source Auditor
The most authoritative sources in this pool — Quanta Magazine (Source 1, high-authority science journalism), the Columbia Math Department blog by Peter Woit (Source 2, high-authority academic), and a January 2026 YouTube explainer (Source 3, moderate authority) — all consistently refute the claim that the ABC conjecture has been "proven" in any broadly accepted sense, documenting a persistent, unresolved dispute over a "serious, unfixable gap" identified by Scholze and Stix, with the RIMS publication itself tainted by a conflict of interest (Mochizuki overseeing the journal). The proponent's best evidence — Joshi's "Final Report" (Sources 4 and 5) — comes from moderate-to-low authority outlets (Earth.com, YouTube) and is explicitly conditional ("provided his enhancements are accepted"), with no high-authority source confirming that the broader mathematical community has accepted those enhancements; therefore, the claim that the ABC conjecture "has been proven" as of March 18, 2026 is false by the standard that matters — broad expert consensus — which is the only meaningful definition of a mathematical proof being established.
Expert summary
The arguments
Two AI advocates debated this claim using the research gathered.
Argument for
By March 18, 2026, Mochizuki's IUT-based proof has been formally published by Kyoto University's RIMS, creating the documented situation that “the ABC conjecture was officially declared a theorem in Kyoto” (Source 3; see also the publication announcement discussed in Source 2). Moreover, a detailed “Final Report” by Joshi explicitly argues Scholze–Stix's alleged gap is mathematically false and concludes abc is proven (with enhancements), so there exists a sustained, source-documented expert defense that the conjecture has indeed been proven (Source 4, Source 5).
Your reliance on the RIMS publication commits a clear appeal-to-authority fallacy — as Source 2 explicitly notes, "some experts say author Shinichi Mochizuki failed to fix fatal flaw," and Source 9 underscores the conflict of interest since Mochizuki effectively oversaw the journal that published his own proof, meaning publication alone cannot substitute for genuine broad consensus. Furthermore, your citation of Joshi's "Final Report" as a definitive resolution is a logical leap: Source 4 itself qualifies that abc is proven only "provided his enhancements are accepted," and neither Source 4, Source 5, nor any other source in the research brief demonstrates that the wider mathematical community has actually accepted those enhancements — meaning the conditional nature of Joshi's claim directly undermines, rather than supports, your position.
Argument against
The ABC conjecture cannot be considered proven as of March 18, 2026, because the broader mathematical community has never reached consensus on Mochizuki's proof — as Source 1 (Quanta Magazine) and Source 11 (Reddit r/math) document, leading experts Peter Scholze and Jakob Stix identified a "serious, unfixable gap" that Mochizuki has never satisfactorily resolved, and Source 3 (YouTube, January 2026) confirms the surreal status quo persists: "the ABC conjecture was officially declared a theorem in Kyoto, but remained a conjecture everywhere else." Even the most recent development cited in Source 4 (Earth.com, June 2025) and Source 5 (YouTube, June 2025) — Joshi's claim to have completed the proof — is explicitly conditional on the mathematical community accepting his enhancements, which, per Source 8 (LLM Background Knowledge) and Source 10 (Dispatches From Turtle Island, September 2025), it has not done, meaning the conjecture remains unproven by any standard of broad expert consensus.
You quietly swap the motion's plain wording (“has been proven”) for a stricter sociological criterion (“broad consensus”), but the record you cite yourself concedes the key point: the proof was published/announced via RIMS (Source 2) and even your own Source 3 states ABC was “officially declared a theorem in Kyoto,” which is exactly a sense in which it has been proven. And your “unfixable gap” line is overstated and one-sided: Source 1 reports an ongoing dispute rather than a settled refutation, while Source 4 (and echoed in Source 5) documents Joshi's detailed rebuttal claiming Scholze–Stix's critique is mathematically false—so you're committing an argument-from-authority/consensus fallacy by treating continued controversy as equivalent to “not proven.”