---
id: "2026-09-22-mumford-shah-conjecture-astra-claim"
url: "https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2026-09-22"
date_precision: day
category: science
importance: 4
confidence: low
status: [Awaiting review]
verification: Preprint only
sources: 1
editor: human editor
human_review: null
version: "2026-10-19"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-09-22-mumford-shah-conjecture-astra-claim/

# Mathematician posts an unchecked ChatGPT Astra proof of the planar Mumford–Shah conjecture (1989), citing OpenAI's '100 open problems' claim

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. He says ChatGPT Astra produced it on 9 Sep. He calls it an 'AI-generated draft' that he is still checking. He released it early to document priority after OpenAI's 21 Sep claim that an internal model had solved 100+ open problems.

## 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without a complete proof; 6 Sep, it proved the author's Dirichlet-boundary conjecture in 1 h 20 min, building on his unpublished April 2026 work; 9 Sep, given that result, it produced a complete proof after 2 h 30 min (37 pages); 11 Sep, a shorter version, which is the one posted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Deangelis, who worked on Mumford–Shah regularity in his PhD, gave ChatGPT Astra his thesis, reference books and unpublished notes.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

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 145 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 84 days after its cutoff
- Gemini 4 Hydrogen (training cutoff March 2026): 175 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 114 days after its cutoff

## Sources

1. [arXiv 2609.26732: Solution of the Mumford–Shah conjecture (Deangelis)](https://arxiv.org/abs/2609.26732) (arxiv.org, paper)

## Changes

- 2026-10-19: Fixed ai_system (unquoted comma); verification wording aligned with the catalogue convention
- 2026-09-30 (filed): Created

## Related

- 2026-09-30: [Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help](https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/index.md)
- 2026-09-21: [OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)](https://postcutoff.com/e/2026-09-21-openai-100-open-problems-claim/index.md)
- 2026-09-03: [OpenAI releases GPT-6 Astra, its first GPT-6 model](https://postcutoff.com/e/2026-09-03-gpt-6-astra/index.md)