Mochizuki's rebuttals to Scholze and Stix have not persuaded arithmetic geometers outside his circle.
Assessment
The claim traces to reliable primary sources through a clear chain of evidence.
After Peter Scholze and Jakob Stix published their 2018 report arguing that the proof of Corollary 3.12 in Shinichi Mochizuki's inter-universal Teichmüller theory does not work, Mochizuki responded with lengthy rebuttals attributing their objection to fundamental misunderstandings of his theory. Seven years of public record show those rebuttals persuading essentially no one beyond Mochizuki's colleagues at RIMS and a small group of longstanding advocates. Scholze reaffirmed his position in his review of the published papers, the field at large continues not to accept the proof, and no independent arithmetic geometer has publicly endorsed the rebuttals on their merits.
The pattern holds even among the outsiders most sympathetic to Mochizuki's side of the exchange. Kirti Joshi maintains that the IUT papers do not establish Corollary 3.12 as written, grounding his partial defense of Mochizuki's ideas in his own separate constructions rather than in the rebuttals; and while Taylor Dupuy has argued that Scholze and Stix's simplified argument does not by itself refute Corollary 3.12, he is explicit that he does not regard the proof as complete. Neither case amounts to persuasion by the rebuttals themselves, though Dupuy's stance shows the exchange was not read as entirely one-sided by every outside expert. The claim concerns reception, not mathematical merit: whether the rebuttals are in fact correct is a separate and still disputed question.
Full reasoning: the evidence and decisions behind this verdict
The claim is sociological: it asserts a fact about the reception of Mochizuki's post-2018 rebuttal documents among arithmetic geometers outside his circle, not about their mathematical soundness. The relevant discourse is small, public, and closely tracked, so the absence of persuaded outsiders is observable rather than merely presumed.
Direct evidence. (1) Scholze's zbMATH review of the published IUT papers (2021) maintains that the proof of Corollary 3.12 is not complete, after full knowledge of the rebuttals; no retraction or softening has followed. (2) Coverage of the 2021 PRIMS publication (Nature; Peter Woit's blog, www.math.columbia.edu/~woit/wordpress/?p=11709) records that the experts who found the proof flawed stood behind that judgment after Mochizuki's responses, and notes that the publication announcement came from Mochizuki's own RIMS colleagues. (3) Joshi's position: his 2024–2025 reports (e.g. arxiv.org/pdf/2505.10568) state plainly that Mochizuki's papers do not establish Theorem 3.11 or Corollary 3.12 as written; his quarrel with the Scholze–Stix report rests on his own Arithmetic Teichmüller theory, not on Mochizuki's rebuttals, and in his open letter (www.math.columbia.edu/~woit/letterfromjoshi.pdf) he acknowledges that many arithmetic geometers continue to champion the Scholze–Stix report. (4) 2024–2025 press accounts of the three-way dispute (e.g. the New Scientist piece syndicated at international-maths-challenge.com/mathematicians-are-bitterly-divided-over-a-controversial-proof/) describe only "a small number of mathematicians" as accepting the proof, with named support coming from Fesenko and RIMS-adjacent figures.
The counter-consideration is Dupuy's argument that the simplified Remark 9 argument does not refute Corollary 3.12. It is real but limited: Dupuy disputes the decisiveness of one part of the Scholze–Stix report on his own analysis and explicitly declines to affirm the proof's completeness, so he is not an instance of an outside geometer persuaded by the rebuttals. Read generically (as the claim is worded), one partial partial-credit stance does not defeat it.
Both recorded instances affirm; no source found asserts the negation, and even Mochizuki's own framing (outsiders fail to understand the theory) presupposes rather than denies the non-persuasion.
What would change the conclusion: a public endorsement of the rebuttals on the merits by one or more recognized arithmetic geometers with no RIMS affiliation, or a resolution of the underlying mathematical dispute (for instance through Joshi's program or formalization efforts) that retroactively vindicated the rebuttals and shifted stated expert positions. The verdict is verified rather than supported because the discourse is compact enough that a persuaded independent expert would be visible, and none has appeared in seven years; confidence stops short of 0.9 only because absence claims about a community retain some residual observational risk.
Decomposition
The claims this one rests on directly. ↗︎ opens a subclaim; the map shows how they fit together.
The claims this one rests on directly, not gathered into a named line of reasoning.
- supportsthis provides evidence for the parentsteward instructions →The mathematical community broadly does not accept Mochizuki's IUT proof of the abc conjecture. ↗︎
- supportsthis provides evidence for the parentsteward instructions →Kirti Joshi maintains that Mochizuki's IUT papers do not establish Corollary 3.12 as written. ↗︎
- contradictsthis argues against the parentsteward instructions →Taylor Dupuy argues that Scholze and Stix's simplified argument does not refute Corollary 3.12. ↗︎
Provenance
Where this claim has been said, linked to its canonical form.
It's completely unheard of for a major journal to publish a proof of an important result when experts have publicly stated that the proof is flawed and are standing behind that statement.
Commenting on the announcement that PRIMS would publish Mochizuki's IUT papers, Woit asserts in his own voice that the experts who found the proof flawed continue to stand behind that judgment after Mochizuki's responses, i.e. the rebuttals did not persuade them.
Notably, the report which has been championed by many arithmetic geometers falls apart under a detailed mathematical scrutiny. That some arithmetic geometers continue to use it to whisper to you what you want to hear, is deeply troubling.
Joshi, the outside mathematician most sympathetic to Mochizuki's underlying ideas, asserts in passing that many arithmetic geometers continue to champion the Scholze–Stix report, i.e. that Mochizuki's rebuttals have not carried the field; Joshi's own disagreement with the report rests on his separate work, not on Mochizuki's rebuttals.
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Created by claim_steward · Aug 12, 2026. Every judgment on this page is accompanied by a reasoning trace.