Not evaluated
Counterexample to Hadwiger's conjecture
The gist
OpenAI claims a counterexample to Hadwiger's conjecture, announced on October 6, 2026, in a manuscript dated September 23, 2026.
DiscoverIA status on October 11, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-hadwiger-counterexample-r1
@misc{discoveria-oai-hadwiger-counterexample-r1,
author = {{DiscoverIA}},
title = {Counterexample to Hadwiger's conjecture},
howpublished = {DiscoverIA registry, entry oai-hadwiger-counterexample},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-hadwiger-counterexample#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 10 s reading time, estimated
What it changes
If this counterexample held, Hadwiger's conjecture would be refuted. It belongs to combinatorics and graph theory.
What remains unclear
OpenAI supplies the Lean (a language in which a computer checks every step of a proof); no independent verification has been found.
In the glossary : Conjecture, Counterexample
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.compage read word for word
Method
The result rests on a preprint dated September 23, 2026 and on Lean supplied by the claimant: formalization.yaml:37, configuration HadwigerCounterexample. The cited title, “A counterexample to Hadwiger's conjecture”, comes from formalization.yaml in the openai/math repository. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from github.com (page read, quotation checked word for word).
Limits
The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (combinatorics / graph theory)
- Independent check
- none found
- Checked by
- claimant
- Sources
- 1 : 1 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 371 of 372, by family number
- Not evaluated : De Giorgi's conjecture in dimension eight (family 375)
- Not evaluated : Universal computation in forced Navier–Stokes flows (family 376)
- Not evaluated : Interior C^(1,α) regularity for infinity-harmonic functions (family 377)
- Not evaluated : Counterexample to Hadwiger's conjecture
- Withdrawn : Three manuscripts withdrawn after a sign error (Weil classes, Kuga–Satake K3, rational Hodge)
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