The gist
OpenAI (GPT-5.2 Pro) and Harmonic (Aristotle) claim a solution to Erdős problem #728, announced in January 2026 at the latest on January 4, 2026, written up in formal form. Status not yet evaluated.
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-erdos-728-gpt52-aristotle-2026-01-r1
@misc{discoveria-erdos-728-gpt52-aristotle-2026-01-r1,
author = {{DiscoverIA}},
title = {Erdős #728 by GPT-5.2 Pro and Aristotle, formally written up},
howpublished = {DiscoverIA registry, entry erdos-728-gpt52-aristotle-2026-01},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-728-gpt52-aristotle-2026-01#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the solution holds, it would be an example of a division of labour: a language model proposes the reasoning and a proof tool checks its logical consistency. It would concern an open number theory question posed by Erdős.
What remains unclear
The logical-consistency certification comes from Aristotle, Harmonic's own tool, and Harmonic is one of the claimants. A human review is not specified, and the mention of an arXiv text comes from Quanta Magazine.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · quantamagazine.org
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 through an AI summary (level 2 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 sourcequantamagazine.orgpage read through an AI summary
Method
DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from quantamagazine.org (page read through a model summary, quotation not rechecked).
Limits
The status source was read through a model summary; its quotation was not rechecked. DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI GPT-5.2 Pro ; Harmonic (Aristotle)
announced on Jan 2026 - Nature
- new result
- Field
- Mathematics (number theory)
- Checked by
- Aristotle (Harmonic's tool); human review not specified
- Sources
- 1 : 1 through an AI summary
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
An observation is added; none is ever erased.
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