White's Conjecture on Matroids
White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank binary matroid constitutes a counterexample.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Matroid theory
- Posed by
- Neil White
- Year posed
- 1980
- Years open
- 46y
- Solved
- 2026-07-02
- Model
- ChatGPT-5.5 Pro, Claude Opus 4.8
- Vendor
- OpenAI; Anthropic
- Collaborators
- Matt Larson
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 40 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The author prompted ChatGPT-5.5 Pro to check White's conjecture and it claimed to prove the result for ranks and . After further prompting to check for random matroids of ranks , , , and , it found a matroid isomorphic to the given counterexample. ChatGPT-5.5 Pro and Claude Opus 4.8 were used for proofreading and generating the figures.
Verification
arXiv preprint with explicit binary matroid construction; not yet peer-reviewed.
Sources
Submitted by HiddenPanther560 on