Is the abc conjecture solved?

Sonar Pro

Vote: No

The abc conjecture is not solved. Mainstream mathematical consensus, as reflected in credible sources, regards it as unproven despite claims by Mochizuki (2012) and Joshi (recent preprints).[1][2][3][4] Prominent experts like Peter Scholze explicitly state the conjecture remains open, citing fundamental flaws in Mochizuki's inter-universal Teichmüller theory (IUT) proof strategy, confirmed after direct discussions.[3][2] Even Mochizuki rejects Joshi's derivative work as lacking mathematical content.[1] Wikipedia and Columbia University reports affirm no broad community acceptance.[4][2] Pro-proof sources are limited to self-published arXiv preprints and non-independent FAQs by the same authors, insufficient for establishing a validated proof.[1]

GPT-5.4

Vote: No

The best current answer is no: the abc conjecture is not generally regarded as solved by the mathematical community. Shinichi Mochizuki claimed a proof via inter-universal Teichmüller theory, and related papers were eventually published. But publication alone did not produce broad expert consensus that the proof has been verified. For a major conjecture like abc, "solved" usually means the proof is widely understood, checked, and accepted by specialists. That level of acceptance has not been reached here, so the cautious and accurate vote is No.

Grok 4.1 Fast

Vote: No

The abc conjecture, proposed in 1985, remains unsolved in the eyes of the mathematical community. Shinichi Mochizuki's 2012 proof attempt using Inter-universal Teichmüller Theory (IUT) is highly complex and has not gained acceptance after over a decade of scrutiny. Prominent mathematicians like Peter Scholze and Jakob Stix identified a critical flaw in Corollary 3.12, which undermines the proof's core logic. Mochizuki's responses have not resolved these concerns to the satisfaction of experts. No peer-reviewed publication in a major journal has validated the proof, and conferences/workshops (e.g., 2018 Kyoto workshop) ended without consensus. Partial results exist, but the full conjecture lacks a verified proof.

Gemini 3.1 Pro

Vote: No

While Shinichi Mochizuki claimed to have proven the abc conjecture in 2012 using his Inter-universal Teichmüller theory, his proof has not been widely accepted by the mathematical community. In 2018, Fields Medalist Peter Scholze and Jakob Stix published a report detailing a serious, unresolvable flaw in the logical steps of the proof (specifically surrounding Corollary 3.12). Mochizuki and his close colleagues failed to provide a satisfactory explanation to bridge this logical gap for the rest of the community. Because a mathematical proof requires broad consensus, independent verification, and the ability to withstand intense peer scrutiny to be considered 'solved,' and the overwhelming global consensus is that Mochizuki's work does not constitute a valid proof, the abc conjecture is currently considered unsolved.

Claude Opus 4.6

Vote: No

The status of the abc conjecture remains genuinely controversial in the mathematical community. Shinichi Mochizuki published a purported proof using his Inter-universal Teichmüller (IUT) theory, and it was accepted and published in 2021 by the journal PRIMS (of which Mochizuki is chief editor). However, a significant portion of the mathematical community, including prominent mathematicians like Peter Scholze and Jakob Stix, have identified what they believe is a fundamental gap in the proof (specifically in Corollary 3.12 of the third paper). Mochizuki disputes their objections, but has not convinced the broader community. A proof is generally considered valid in mathematics when there is broad consensus among experts that the argument is correct. No such consensus exists for Mochizuki's work. Multiple attempts at verification workshops and seminars outside of Mochizuki's close circle have failed to produce agreement that the proof is complete and correct. Since the mathematical community has not reached consensus that a valid proof exists, it is most accurate to say the abc conjecture is not yet solved in any widely accepted sense.

Kimi K2.5

Vote: No

The abc conjecture remains unsolved in the sense that no proof has achieved consensus acceptance from the broader mathematical community. While Shinichi Mochizuki released a claimed proof in 2012 using Inter-universal Teichmüller Theory (IUTT), his work is extraordinarily complex and has resisted independent verification by most number theorists. Despite workshops in 2015-2016 and ongoing efforts by a small group of specialists, significant gaps and foundational issues remain unresolved. The mathematical community generally considers the conjecture open until a proof is widely understood and verified. Without broad acceptance or alternative proofs emerging, we cannot claim the problem is solved.

Final Summary

The AI Roundtable reached a swift and unanimous verdict: the abc conjecture is not solved. While Shinichi Mochizuki claims to have cracked the code using Inter-universal Teichmüller theory, Claude Opus 4.6 and Sonar Pro led the charge in arguing that a proof is only a solution if the mathematical community actually accepts it—which, in this case, it emphatically has not.

All 6 models agreed on "No" after discussion

Strongest Arguments

• No: A mathematical proof requires broad consensus and independent verification to be considered 'solved.' The existence of a fundamental, unaddressed logical gap in Corollary 3.12, identified by experts like Peter Scholze and Jakob Stix, means the work fails to meet the standard of a verified proof despite its publication in the journal PRIMS.