Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI’s ‘100 open problems’ claim
Awaiting review
Importance: major (4 of 5)The takeaway
On 22 Sep 2026 Francesco Deangelis (University of Münster) posted a claimed proof of the planar Mumford–Shah conjecture (1989), a central open problem in the calculus of variations and image segmentation.
Status
- Claim
Awaiting review
- Our reporting
- Low confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 Astra145 days after its cutoff
- Claude Opus 5.584 days after its cutoff
- Gemini 4 Hydrogen175 days after its cutoff
- Grok 4.7114 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 84 days before it.
Key facts
- arXiv 2609.26732 (22 Sep 2026): ‘On September 9, 2026, I obtained a proof of the Mumford–Shah conjecture, formulated in 1989, using ChatGPT Astra’
- Timeline in the author’s note: 5 Sep, Astra in Work mode ran 6 hours without a complete proof; 6 Sep, it proved the author’s Dirichlet-boundary conjecture in 1 h 20 min, building on his unpublished April 2026 work; 9 Sep, given that result, it produced a complete proof after 2 h 30 min (37 pages); 11 Sep, a shorter version, which is the one posted
- Author’s caveat: ‘This prompted me to make the current AI-generated draft publicly available now, to document the chronology of this work. I will continue checking the mathematical details’
- Claimed method: classify planar generalized global minimizers with a second-variation argument (two perpendicular translations of a compact crack portion, a Hodge identity and holomorphic rigidity). The known equivalence between that classification and interior regularity then gives the conjecture
- Status: unrefereed, not formalised, and not publicly checked by independent experts as of 30 Sep 2026
What happened
Deangelis, who worked on Mumford–Shah regularity in his PhD, gave ChatGPT Astra his thesis, reference books and unpublished notes. First it proved a boundary-regularity conjecture of his. Then, given that result, it produced a full claimed proof of the interior conjecture. He posted the model’s shortened manuscript almost unchanged, with a note on its provenance.
Why it matters
If correct, it would settle one of the best-known open problems in the calculus of variations. The case also shows OpenAI’s unverified “100 open problems” announcement leading independent researchers to rush their own AI-generated claims onto arXiv before checking them.
What is disputed or not yet verified
| Verification | Unverified claim, no expert review: preprint by the prompting author, who says his own check is ongoing; not formalised |
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Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
Changes
- Fixed ai_system (unquoted comma); verification wording aligned with the catalogue convention
- Filed