Not evaluated
Hilbert's tenth problem over Q (family 004)
The gist
On October 6, 2026, OpenAI published a manuscript on Hilbert’s tenth problem over Q, from an unreleased internal model.
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-fam-004-hilbert-10-q-r1
@misc{discoveria-oai-fam-004-hilbert-10-q-r1,
author = {{DiscoverIA}},
title = {Hilbert's tenth problem over Q (family 004)},
howpublished = {DiscoverIA registry, entry oai-fam-004-hilbert-10-q},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-004-hilbert-10-q#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Hilbert’s tenth problem asks whether a general method exists that decides, for any polynomial equation, whether it has integer solutions. The variant over Q, the set of rational numbers (fractions), concerns rational solutions; if the manuscript were correct, it would provide a result on this question.
What remains unclear
The sources read do not state the result the manuscript claims. No Lean (a language in which a computer checks every step of a proof) has been identified, though this is an estimate, and no independent assessment is recorded.
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 · consulted on Oct 20, 2026 ·
We give a negative answer to Hilbert's tenth problem over the rational numbers
Method
OpenAI publishes a manuscript (preprint) for family 004, listed in CONTENTS.md of the openai/math repository. The absence of Lean rests on a search-engine snippet from a third-party blog (cellcog.ai) that writes “Not yet”. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026; source read on October 20, 2026 from github.com (page read, quotation checked word for word: “We give a negative answer to Hilbert's tenth problem over the rational numbers”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (logic / number theory)
- Checked by
- no verifier identified
- Sources
- 1 : 1 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
OpenAI publication page not accessible (403 error, page rendered with JavaScript); PDF preprint not opened.
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 4 of 372, by family number
- Not evaluated : Milne's rationality conjecture (family 001)
- Not evaluated : Full BSD formula for Selmer corank 0 or 1 (family 002)
- Not evaluated : Quasi-Riemann hypothesis: zero-free half-plane Re(s) > 7/8 (family 003)
- Not evaluated : Hilbert's tenth problem over Q (family 004)
- Not evaluated : Irrationality of Catalan's constant (family 005)
- Not evaluated : Goldfeld's conjecture (family 006)
- Not evaluated : Two-point Chowla and the corrected binary Elliott conjecture (family 007)
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