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Claim analyzed
“The ABC conjecture has been proven.”
The Conclusion
Executive Summary
No. While there are preprints and FAQs claiming a proof (notably by Joshi), the ABC conjecture is not regarded as proven by the broader expert community as of 2026. Independent expert commentary reports key specialists remain unconvinced and treat abc as still open, so “has been proven” is not supported.
Warnings
- Do not equate “a paper claims a proof” (especially self-published or by a single camp) with “the conjecture is proven”; independent verification and broad expert acceptance matter.
- Most supporting sources are not independent (same author and related FAQs), so they cannot by themselves establish correctness.
- The status of abc remains contested; prominent experts have publicly raised serious objections to the underlying approaches, so headlines about a “proof” can be misleading.
The Claim
How we interpreted the user input
Intent
User wants to verify if the famous ABC conjecture in number theory has been definitively proven
Testable Claim
The user's input, neutralized and hardened into a testable hypothesis
“The ABC conjecture has been proven.”
The Research
What we found online
Summary of Findings
All sources are listed in the Sources section at the end of this report.
The Debate
The for and against arguments
Source 1 (arxiv.org) and Source 10 (arXiv) provide direct mathematical proof that the ABC conjecture has been proven, with Source 1 explicitly stating "I show that the Theory of Arithmetic Teichmuller Spaces leads, using Shinichi Mochizuki's rubric, to a proof of the abc-conjecture" and Source 10 confirming this work "completes the remarkable proof of the abc-conjecture." Source 2 (bpb-us-e2.wpmucdn.com) and Source 6 (University of Arizona Academic Repository) further validate this achievement by providing comprehensive FAQ documentation specifically addressing the completed proof, demonstrating institutional recognition and formal academic acknowledgment of the successful resolution of this fundamental mathematical problem.
You're treating “a preprint says it's a proof” as equivalent to “the conjecture is proven,” but Sources 1 and 10 (arXiv) are self-asserted claims explicitly framed as “using Mochizuki's rubric,” not independent verification or broad acceptance, and that's a textbook appeal to authority where the only authority is the author. Your “institutional recognition” point collapses because Sources 2 and 6 (FAQ on a CDN/University of Arizona repository) merely explain and defend the same claimed proof rather than certify correctness, while Source 3 (columbia.edu) and Source 4 (Quanta Magazine) directly report that key experts remain unconvinced and still regard abc as open.
The brief's only “proof” evidence is self-asserted preprints and an FAQ (Sources 1 and 10 (arXiv), Sources 2 and 6 (University of Arizona/CDN)) rather than an independently verified, broadly accepted resolution, which is not enough to conclude the conjecture is proven. By contrast, credible expert commentary explicitly says the abc conjecture remains open and highlights unresolved objections and lack of community conviction (Source 4 (Quanta Magazine) quoting Scholze; Source 3 (columbia.edu) noting experts are unconvinced), so the motion is false.
Your dismissal of Source 1 (arxiv.org) and Source 10 (arXiv) as mere "self-asserted preprints" commits the genetic fallacy by attacking the source rather than the mathematical content, when these are formal academic publications presenting rigorous mathematical proofs that must be evaluated on their mathematical merit, not their publication venue. Your reliance on outdated sources like Source 4 (Quanta Magazine) from 2018 and Source 3 (columbia.edu) from 2024 ignores the chronological progression of mathematical work, as these critiques predate the completion of Joshi's proof series documented in Sources 1, 2, 6, and 10 from 2024-2025.
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The Adjudication
How each panelist evaluated the evidence and arguments
The most reliable sources are Source 3 (Columbia University Mathematics, authority 0.9) and Source 4 (Quanta Magazine, authority 0.85), which report that mathematical experts including Scholze remain unconvinced by claimed proofs and consider the ABC conjecture still open, while the supporting evidence consists primarily of self-published arXiv preprints by the same author claiming proof completion. Based on trustworthy expert commentary indicating lack of mathematical community acceptance versus unverified self-assertions, the claim that the ABC conjecture has been proven is false.
The pro side infers “abc has been proven” from the existence of papers and FAQs that *claim* a proof (Sources 1 and 10 arXiv; Sources 2 and 6 FAQ), but that evidence only establishes that certain authors assert a proof, not that the conjecture is in fact proven in the sense of a correct, validated proof; meanwhile, expert commentary reports continued non-acceptance and that abc is still regarded as open (Source 4 Quanta quoting Scholze; Source 3 Columbia/Not Even Wrong noting experts unconvinced). Because the key inferential step conflates “a purported proof exists” with “the conjecture has been proven,” the claim is not logically established by the provided evidence and is best judged false on this record.
The claim omits the critical context that mathematical proofs require peer acceptance and verification by the expert community, not merely self-assertion in preprints: Sources 1, 2, 6, and 10 are self-published claims by Joshi (2024-2025) that experts remain unconvinced by (Source 3, columbia.edu, 2024), while Source 5 (YouTube, 2025) reveals even Mochizuki himself rejects Joshi's proof as having "no meaningful mathematical content whatsoever," and Source 4 (Quanta Magazine, 2018) documents fundamental flaws identified by Scholze in the underlying Mochizuki work. Once the full picture is considered—that the mathematical community has not accepted either Mochizuki's original IUT proof or Joshi's derivative work, and that key experts explicitly state the conjecture remains open—the claim is false.
Adjudication Summary
All three axes agreed (3/10). Source quality: the main “support” is self-asserted arXiv/FAQ material lacking independent verification, while higher-quality independent commentary (e.g., Columbia/Not Even Wrong; Quanta quoting leading experts) indicates non-acceptance. Logic: a purported proof existing does not imply the conjecture is proven. Context: the claim omits that community validation is essential and that prominent experts (and even Mochizuki regarding Joshi's work) dispute the alleged proofs.
Consensus
Sources
Sources used in the analysis
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