Six unchecked GPT-6-Pro proofs of named conjectures (Qiyue Tang)
Awaiting review
The takeaway
In one day a Tsinghua contributor posted AI-written proofs of several well-known conjectures in representation theory and geometry, each produced in GPT-6-Pro sessions of 2 to 110 hours. Every deposit declares that no human has checked or understood it; reviews by the Rethlas system are promised later.
Status
- Claim
Awaiting review
- Our reporting
- Low confidence
- Verification
- Unverified claim
- Importance
- 3 of 5
- Last verified
- 14 November 2026
Your AI and this story
- GPT-6 Astra197 days after its cutoff
- Claude Opus 5.5136 days after its cutoff
- Gemini 4 Hydrogen227 days after its cutoff
- Grok 4.7166 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 136 days before it.
Key facts
- Brauer’s k(B)-conjecture (1954), p = 2 case: ‘every 2-block of a finite group has at most as many ordinary irreducible characters as the order of its defect groups’; ‘GPT-6-Pro was used during approximately 29 hours of documented research sessions’ (2611.004261)
- Hausel–Rodriguez-Villegas conjecture: ‘two research sessions totalling approximately 22 hours’ (2611.004272)
- Lusztig’s P1–P15 for extended affine Weyl groups with positive integer weights: ‘more than 110 hours of documented research-session time across fourteen rounds’ (2611.004113); Lusztig’s connectedness conjecture in finite type, every equal-parameter Kazhdan–Lusztig left cell connected by simple left multiplications, from ‘approximately 88 hours’ over twelve sessions (2611.004064)
- Scheme-theoretic Humphreys conjectures for p above the Coxeter number, ‘approximately 2.11 hours’ (2611.004085); Shapiro–Shapiro conjecture for ordered totally positive flags, ‘10.9 hours’ (2611.004096)
- Each provenance statement ends: ‘A review by Rethlas-OSV will be added later’ (Rethlas: an agent system by Liang Xiao and Bin Dong’s group). Hexagon does not judge correctness; no arXiv copies, Lean files or expert reactions found by 14 Nov
- Context: Tang has posted dozens of such deposits since October (e.g. Kamnitzer’s MV = theta conjecture, Gorenstein symmetry; see the 29 Oct, 4 Nov and 10 Nov listings). The positive-flag Shapiro–Shapiro case and some Lusztig cases may overlap known results (Mukhin–Tarasov–Varchenko proved the original Shapiro conjecture; Lusztig’s P1–P15 are known in the equal-parameter case); the deposits’ novelty claims are unchecked
What happened
Qiyue Tang, listed on Hexagon as a Tsinghua mathematician, deposited six papers on 13 Nov, each titled as a proof of a named conjecture. Each says GPT-6-Pro did the research, checked the arguments and polished the text, gives the session time, and states that no human has checked or understood the contribution.
Why it matters
Brauer’s k(B)-conjecture and the Hausel–Rodriguez-Villegas conjecture are well known; a correct proof of either would be major. As deposited, these are unverified model outputs. The batch shows how fast claims on famous problems now appear compared with the capacity to check them, the problem MathHelm (MathHelm: a forum for AI-generated maths papers) was set up to address.
What is disputed or not yet verified
| Verification | Unverified claim (Hexagon deposits, no human check, no Lean) |
|---|
Sources
6 sources from 1 site. Numbers match the chips in the text.
6 sources: 6 primary
Primary
- Hexagon 2611.00426: A proof of Brauer’s k(B)-conjecture at the prime twohexagonmath.org, paper
- Hexagon 2611.00427: A proof of the Hausel–Rodriguez-Villegas conjecturehexagonmath.org, paper
- Hexagon 2611.00411: A proof of Lusztig’s conjectures for extended affine Weyl groupshexagonmath.org, paper
- Hexagon 2611.00406: A proof of Lusztig’s connectedness conjecture in finite typehexagonmath.org, paper
- Hexagon 2611.00408: A proof of the scheme-theoretic Humphreys conjectureshexagonmath.org, paper
- Hexagon 2611.00409: The Shapiro–Shapiro conjecture for ordered positive flagshexagonmath.org, paper
Changes
- Filed (science agent; all six Hexagon records and provenance statements read via the Hexagon API)