Not evaluated
A counterexample to Kurosh's division-ring problem (family 201)
The gist
In its release of October 6, 2026, OpenAI claims a counterexample to Kurosh's division-ring problem (manuscript dated September 23, 2026).
DiscoverIA status on October 12, 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 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-201-counterexample-kuroshs-division-ring-problem-r1
@misc{discoveria-oai-fam-201-counterexample-kuroshs-division-ring-problem-r1,
author = {{DiscoverIA}},
title = {A counterexample to Kurosh's division-ring problem (family 201)},
howpublished = {DiscoverIA registry, entry oai-fam-201-counterexample-kuroshs-division-ring-problem},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-201-counterexample-kuroshs-division-ring-problem#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript held, it would provide a case of this kind for the statement targeted by Kurosh's problem. That problem concerns division rings, systems in which one can add, multiply and divide by any non-zero element. The subject belongs to algebra.
What remains unclear
No third-party assessment is recorded, and OpenAI provides no Lean (a language in which a computer checks every step of a proof) for this family. The sources read do not state the exact statement the manuscript would target.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
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.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · A-Counterexample-to…link only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “A Counterexample to Kurosh’s Division-Ring Problem”, dated September 23, 2026, the only one of family 201. It is filed under the section “Algebra” of overview.tex; history.md reports no revision. The internal model that produced it has not been released. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Algebra)
- In openai/math
- family 201, section “Algebra”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
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 195 of 372, by family number
- Not evaluated : A counterexample to the little finitistic-dimension conjecture (family 198)
- Not evaluated : Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama (family 199)
- Not evaluated : Eisenbud–Green–Harris and lex-plus-powers in characteristic zero (family 200)
- Not evaluated : A counterexample to Kurosh's division-ring problem (family 201)
- Not evaluated : The blockwise Alperin weight conjecture (family 202)
- Not evaluated : Donovan's conjecture over fields and discrete valuation rings (family 203)
- Not evaluated : Tensor saturation for even spin groups (family 204)
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