Hessian conjecture refuted in five variables, derived from Claude-found Jacobian counterexample
Event confirmedAwaiting review
The takeaway
Five days after Levent Alpöge’s Claude Fable 5-assisted counterexample to the Jacobian conjecture, Guowu Meng and Liang Yang used “Schur descent” on it to build a five-variable counterexample to the related Hessian conjecture.
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 Astra85 days after its cutoff
- Claude Opus 5.524 days after its cutoff
- Gemini 4 Hydrogen115 days after its cutoff
- Grok 4.754 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 24 days before it.
Key facts
- arXiv 2607.22198, submitted 2026-07-24 (revised 07-27)
- Explicit polynomial in 5 variables, degree 14, constant Hessian determinant 128, with non-injective gradient
- Derived from Alpöge’s Jacobian counterexample; the paper itself does not report AI use
What happened
Guowu Meng and Liang Yang turned Alpöge’s three-variable Jacobian counterexample into a five-variable counterexample to the Hessian conjecture.
Why it matters
It shows how AI-found results feed quickly into human follow-up work. It also leaves one clean open case, n=4.
What is disputed or not yet verified
| Verification | Unrefereed arXiv preprint (2607.22198); explicit counterexample, checkable by computation; the paper reports no AI use |
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Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 1 primary, 1 reaction
Primary
Reactions
- Terence Tao: A digestion of the Jacobian conjecture counterexampleterrytao.wordpress.com, discussion
Changes
- Fixed ai_system (an unquoted comma split it into two items); verification made precise
- Filed. During a snowball check while verifying the Jacobian entry