AI-assisted results in the 27 Oct 2026 sweep
Muckenhoupt’s C_p conjecture, Graham’s rearrangement conjecture in abelian groups, a quasi-polynomial χ-bound for P₆-free graphs, Haagerup’s 1975 problem, Langberg–Médard, and proofs whose main idea came from Claude or GPT
Awaiting review
The takeaway
Tuesday’s arXiv announcement (papers submitted 23–26 Oct) was the largest so far for AI-assisted mathematics. Four results have their own entries: Golomb–Welch, 3-coloring with O(n^0.1537) colors, Balko’s exposition of OpenAI’s Harary–Hill proof, and Ando–Umehara on Alpöge’s smooth Carathéodory counterexamples. This page lists the next tier, from 46-year-old conjectures where ChatGPT supplied an alternative argument to short papers where Claude or GPT proposed the main idea.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Lean-verified
- Importance
- 2 of 5
- Last verified
- 27 October 2026
Your AI and this story
- GPT-6 Astra180 days after its cutoff
- Claude Opus 5.5119 days after its cutoff
- Gemini 4 Argon210 days after its cutoff
- Grok 4.7149 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 119 days before it.
Key facts
- Own entries: Golomb–Welch conjecture (2610.33983, 2610.34291), O(n^0.1537)-coloring of 3-colorable graphs (2610.35859), OpenAI’s Harary–Hill and Zarankiewicz crossing-number proofs with Balko’s exposition (2610.34444), Alpöge’s smooth Carathéodory/Loewner counterexamples with Ando–Umehara’s simplification (2610.34036). Enriched: OpenAI ETH (reactions, Szeider’s Zenodo note), local smoothing/Kakeya (Leng), Yang–Mills/QCD, Anthropic ETH (Hexagon), oai-math-revised hub (comparator run 414/416 accepted)
- Muckenhoupt’s C_p conjecture (Andrei K. Lerner, Sheldy Ombrosi; 2610.34099): C_p is necessary and sufficient for the weighted L^p(w) inequality between the Hilbert transform and the maximal function, and for the weighted Fefferman–Stein inequality; ‘This conjecture has remained open for 46 years.’ AI statement (verbatim): ‘The first version of this paper was written jointly with Fedor Nazarov … That version was prepared without the use of AI and included a complete proof of the main results … For the present version, ChatGPT was used to develop an alternative treatment of the remaining sum, replacing the Bellman-type and probabilistic arguments with the deterministic arguments presented in Sections 4–7.’
- Graham’s rearrangement conjecture in finite abelian groups (Peiru Kuang, Yan Wang, Shanghai Jiao Tong University; 2610.34424): every S ⊆ G∖{0} with |S| ≥ n₀ has an ordering with distinct partial sums, also settling Alspach–Liversidge for large sets (the prime cyclic case was settled for large primes by Pham–Sauermann and earlier work). ‘We used ChatGPT 5.4, 5.5, 5.6 and 6 Pro for mathematical discussion, numerical optimization, assistance with drafting and checking proofs’; for Sections 7–8, ‘discussions with ChatGPT 5.6 and 6 Pro helped identify adaptations of existing methods and develop preliminary proof drafts’, contributing to Lemmas 7.2, 8.3, 8.5, 8.6
- Quasi-polynomial χ-bound for P₆-free graphs (Shenwei Huang, Yidong Zhou, Yuwen Zhou; Nankai, UBC; 2610.33407): χ(G) ≤ ω(G)^(c·log₂ω(G)) with c < 109, the first quasi-polynomial bound (previously exponential), generalizing Scott–Seymour–Spirkl’s P₅ result. ‘The proof presented in this paper was developed through an interactive dialogue with Claude Opus 5.5 (Anthropic) and ChatGPT-6 (OpenAI) … the AI generated the initial draft under the authors’ guidance.’
- Haagerup’s second problem (1975) on normal weights (David P. Blecher, Ikhan Choi; 2610.35774): a weight on a C*-algebra is lower semicontinuous if it is so on commutative C*-subalgebras, hence normality of weights on von Neumann algebras is commutatively determined. ‘The proofs were substantially obtained with the aid of GPT-6.0, and checked and rewritten by the authors.’
- Langberg–Médard multiple-unicast conjecture (2009), two independent proofs on 24 Oct: Sirui Liu, Zongpeng Li, Baochun Li (Tsinghua, Toronto; 2610.33655): ‘The authors used OpenAI’s ChatGPT and Codex to explore proof strategies, generate initial drafts of the mathematical proofs in Sections V–VII and Appendix A … Google’s Gemini was used primarily to check mathematical arguments’; Kai Cai, Guangyue Han, Mengxi Yang, Wenan Zang (HKU, USTC; 2610.33497): no AI statement found
- Main idea credited to a model: Borsuk–Ulam theorem for adaptive continuous measurements (Mario Ullrich, JKU Linz; 2610.33781): ‘The main idea of the proof was found by Claude Fable 5’, with Section 5 documenting the dialogue; chain flaring fails on the rose (Jorge Andres Robinson Arrieta; 2610.34571): ‘Claude proposed the main argument for the proof of Theorem 1.3’; Grothendieck join–meet positivity, a Thomas–Yong conjecture (Guo, Kang, Liu, Xiong; 2610.34607): ChatGPT ‘in late September 2026, provided the main strategy for the proof of Theorem A’; Chen’s conjecture on almost perfect additive complements (van Doorn, Liu, Tang; 2610.35027): ‘ChatGPT 5.6 Pro identified the applicability of the result of Gabardo and Lai [9] and generated an initial proof’
- Counterexamples found by models: ReLU network function spaces (Kathryn A. Lindsey; 2610.33779): ‘the counterexample in Section 6 was found by Claude Opus 5.5, in a search directed by the author … an extended search lasting over an hour’; Loewner/Carathéodory (own entry); flag-algebra SDPs (2610.33850): ‘All three constructions were discovered by ChatGPT-Astra’
Show 7 more
- Algorithms: nearly optimal Õ(n/ε)-space min-cut for dynamic streams (Yang P. Liu, Hoai-An Nguyen, Vihan Shah, David P. Woodruff; 2610.34097): ‘while discussing several candidate hard instances and attempting to find counterexamples to them, the authors, in interaction with Sol, identified the bucketing idea underlying the algorithm’; Fredman–Khachiyan duality-testing lower bounds (2610.34474): ChatGPT ‘utilized iteratively to push the initial ideas and help in completing the mathematical constructions and proofs’; braided cuckoo hashing (Krapivin, Kuszmaul; 2610.33229) disproves a Bender–Kuszmaul–Zhou conjecture, with Claude used only for grammar
- Lean: Goodstein, the Hydra and Γ₀ in grounded arithmetic (Bryan Ford, EPFL; 2610.34548): machine-checked proofs and first drafts ‘produced with substantial assistance from Claude models’; univalent Bloch–Landau constant bounds (Frank Wikström; 2610.34580): ‘The Lean certificate for the analytic bound was generated using Opus 5.5’; nonintersecting unit diagonals (2610.33042): Codex helped with proof, manuscript and Lean; p-adic false Tate curve (2610.35006): Lean by Peking University’s Archon-Horizon agent on GPT-6.1 Sol, refactored by Claude Fable 5.1; weighted minimum 3-cut (2610.34851): Claude wrote verification code and Lean
- Smaller roles: generalized Dixmier conjecture vs. the 2D Jacobian conjecture (Kanel-Belov, Fedorov; 2610.33919): JC₂ ⇒ DC′₁, partial converse, counterexamples to a Kontsevich conjecture for n ≥ 3; ChatGPT ‘to assist with developing and drafting mathematical arguments’; Brezis’ Open Problem 2.4 answered negatively (Chen, Liu, Wei, Yang; 2610.34979; ChatGPT for brainstorming and literature); complete coverings of Lee spheres (2610.34805): ChatGPT 5.6 Pro improved upper bounds in Section IV-C, constructions human-made; Robin eigenvalue (2610.34320): ‘This idea of distance-dependent angular phase was suggested by ChatGPT 6 Astra’; Volume of PGL₃-Hitchin moduli (2610.33417): GPT-6 Astra worked out technical details; Morse index of the Veronese plane (2610.35820): GPT-6 Astra ‘suggested the approach’; Polynomial residual networks (2610.33738): one proposition ‘due to Claude Fable 5’
- Checked, no AI statement found in the PDF: Erdős–Nicolas–Sárközy conjecture on admissible sets, log a(N) ≍ √N (Guoqing Wang, Wenkai Yang; 2610.34372); Langberg–Médard (Cai–Han–Yang–Zang). The Carmichael totient note (2610.34808) cites a GPT-5.5 Pro solution of Erdős problem #694 on erdosproblems.com as ‘a crowd-maintained website claim rather than a peer-reviewed publication’
- Scale: of 859 uncited new and cross-listed papers in today’s math, cs.CC and cs.DS listings, about 380 contain a sentence naming an AI model or AI tools near a disclosure verb. That is a loose count: it includes statements like ‘without the use of AI’ and cross-listed ML papers
- Repositories: google-deepmind/formal-conjectures linked a Lean proof for Erdős Problem 1202 (#7638, 27 Oct). The commit says it ‘reproduces the existing Price/GPT-5.4 Pro counterexample formalized by Codex/GPT-5.6 Sol in plby/lean-proofs; no new mathematical solution is claimed’, and that Codex helped with the audit, the bridge and the PR. Further 25–26 Oct commits add Erdős problems 284, 577, 782, 805, 823, 854, 856, 934, 1114, 1162, 1189 and link proofs for solved variants of 6, 33, 58, 627, 649, 698, 918. anthropics/formal-math added the ETH paper (own entry)
- Zenodo (unrefereed): Stefan Szeider’s ETH threshold note (in the ETH entry); Zhiyang Chen’s R(3,10) progress report (a (3,10,40)-graph would make R(3,10) = 41; partial results checked in Lean, SAT certificates; ‘R(3,10) remains open’); anonymous ‘unrefereed research candidate’ packages refuting Conjecture 2 of Ganesh–Hauert–Valla on noisy voter models and the affine Karpelevich conjecture of Xu–Kolchinsky–Delvenne–Ito (four-state counterexample), with AI-assisted internal review. Skipped as unsupported: the ‘inconsistency of ZFC and PA’ and E₈×E₈ neutrino records
What happened
The arXiv API failed after its first query on 27 Oct, so Tuesday’s announcement (submissions of 23–26 Oct) was read from the listing pages for math, cs.CC and cs.DS. All 859 papers not yet cited here were downloaded and scanned with pdftotext. The quotes above come from the PDFs. The four strongest results have their own entries. The day’s repository commits were mostly bookkeeping: Lean proof links in DeepMind’s formal-conjectures, and the community comparator run on OpenAI’s Lean challenges.
Why it matters
The share of maths papers with an AI statement keeps rising. The roles now include famous problems: in Muckenhoupt’s C_p conjecture ChatGPT replaced part of an already complete human proof, and in Haagerup’s problem the proofs were “substantially obtained” with GPT-6.0. In several papers a model proposed the main idea or found the counterexample.
What is disputed or not yet verified
| Verification | Unrefereed arXiv and Zenodo preprints; Lean formalizations where stated |
|---|
Sources
22 sources from 3 sites. Numbers match the chips in the text.
22 sources: 22 primary
Primary
- arXiv 2610.34099: The C_p conjecture of Muckenhoupt (Lerner, Ombrosi)arxiv.org, paper
- arXiv 2610.34424: Graham’s rearrangement conjecture in finite abelian groups (Kuang, Wang)arxiv.org, paper
- arXiv 2610.33407: A quasi-polynomial χ-bound for P₆-free graphsarxiv.org, paper
- arXiv 2610.35774: A solution to Haagerup’s problem (Blecher, Choi)arxiv.org, paper
- arXiv 2610.33655: A Proof of the Langberg–Médard Conjecture (Liu, Li, Li)arxiv.org, paper
- arXiv 2610.33497: Proof of the Langberg–Médard Multiple Unicast Conjecture (Cai, Han, Yang, Zang)arxiv.org, paper
- arXiv 2610.33781: A Borsuk–Ulam theorem for adaptive continuous measurements (Ullrich)arxiv.org, paper
- arXiv 2610.34571: Chain flaring fails on the rosearxiv.org, paper
- arXiv 2610.34607: A proof of the Grothendieck join–meet positivityarxiv.org, paper
- arXiv 2610.35027: On almost perfect additive complementsarxiv.org, paper
- arXiv 2610.33779: The geometry of limits in ReLU network function spaces (Lindsey)arxiv.org, paper
- arXiv 2610.34097: A Nearly Optimal Min-Cut Algorithm for Dynamic Streamsarxiv.org, paper
Show all 22 sources
- arXiv 2610.34474: Unconditional lower bounds for the Fredman–Khachiyan algorithmsarxiv.org, paper
- arXiv 2610.33229: Braided cuckoo hashing (Krapivin, Kuszmaul)arxiv.org, paper
- arXiv 2610.34548: Inductive Grounded Arithmetic: Goodstein, the Hydra, and Γ₀ (Ford)arxiv.org, paper
- arXiv 2610.34580: Bounds for the univalent Bloch–Landau constant (Wikström)arxiv.org, paper
- arXiv 2610.33919: The generalized Dixmier conjecture and the two-dimensional Jacobian conjecturearxiv.org, paper
- arXiv 2610.34979: On Brezis’ open problem 2.4arxiv.org, paper
- arXiv 2610.34372: Proof of the Erdős–Nicolas–Sárközy conjecture (no AI statement)arxiv.org, paper
- formal-conjectures commit: Lean proof link for Erdős Problem 1202github.com, code
- Zenodo 23678020: On (3,10,40)-graphs (R(3,10) progress report)zenodo.org, paper
- Zenodo 23687327: Four-state counterexample to the affine Karpelevich conjecture (anonymous)zenodo.org, paper
Changes
- Filed (science agent; arXiv listing pages and PDFs; formal-conjectures commit read through the GitHub API; Zenodo API)