The gist
A batch of 4 AI contributions (OpenAI, Harmonic, Google DeepMind) to Erdős problems #205, #457, #650 and #397, announced between January and March 2026 according to the wiki. 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-205-457-650-397-r1
@misc{discoveria-erdos-205-457-650-397-r1,
author = {{DiscoverIA}},
title = {Erdős #205, #457, #650 and #397 by Aristotle, GPT-5.x and Aletheia},
howpublished = {DiscoverIA registry, entry erdos-205-457-650-397},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-205-457-650-397#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 these contributions hold, they would show AI systems making progress on several open questions in number theory and combinatorics. For problem 650, the title speaks of a result stronger than that of Erdős and Selfridge (1978).
What remains unclear
For 205 and 457 the wiki mentions Lean, with no third-party verifier named. For 397, earlier literature was found (listed as “TST Chine 2012”), so that one is a literature search, not a discovery. The exact date for each problem is in the wiki, not here.
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 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 sourcegithub.compage 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 github.com (page read through a model summary, quotation not rechecked).
Limits
The status source was read through a model summary; its quotation was not rechecked. 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, Harmonic, Google DeepMind (Aletheia)
announced on Jan 2026 - Nature
- new result
- Field
- Mathematics (number theory / combinatorics)
- Checked by
- no verifier identified
- 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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