Not evaluated
Erdős problem #397: full solution with a Lean proof according to the wiki (Aristotle, GPT-5.2 Pro)
The gist
According to the teorth/erdosproblems wiki on AI and Erdős problems, Aristotle and GPT-5.2 Pro reportedly obtained a full solution to problem #397 (announced on January 10, 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-erdos-397-aristotle-gpt-5-2-pro-1b-r1
@misc{discoveria-erdos-397-aristotle-gpt-5-2-pro-1b-r1,
author = {{DiscoverIA}},
title = {Erdős problem #397: full solution with a Lean proof according to the wiki (Aristotle, GPT-5.2 Pro)},
howpublished = {DiscoverIA registry, entry erdos-397-aristotle-gpt-5-2-pro-1b},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-397-aristotle-gpt-5-2-pro-1b#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Problem #397 belongs to number theory and binomial coefficients (which count the ways to choose some objects from others, order not mattering). If the solution held, it would settle this problem in full. The wiki does, however, point to comparable literature, China TST competition (2012), found after the fact on January 14, 2026 and marked as similar (“Yes”).
What remains unclear
The wiki points to a proof in Lean (a language in which a computer checks every step of a proof) without naming a third-party verifier, and no independent verification is on record. The sources read do not say what the solution contains.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · wiki
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Wiki frozen
- 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.
Dated archive: status recorded on the wiki frozen on Jun 30, 2026
Sources
- Main sourcegithub.com · wikipage read word for word · consulted on Oct 12, 2026
- Reference listerdosproblems.comlink only, reading not recorded
- Corroborationterrytao.wordpress.compage read word for word · consulted on Oct 17, 2026 ·
We have created a github repository to coordinate this process
- Repositorygithub.com · CONTRIBUTING.mdpage read word for word · consulted on Oct 17, 2026 ·
this status is an unofficial crowdsourced classification of the problem
Method
Source: the “AI contributions to Erdős problems” wiki of the teorth/erdosproblems repository (a repository presented by Terence Tao in his blog post of August 31, 2025); frozen on June 30, 2026 (commit c8ad430, “freeze”) and read on October 12, 2026 in the git repository. Category 1(b), “AI alongside literature” (AI in parallel with the literature (a comparable result found afterwards); no significant human involvement). Humans named by the wiki: none; AI systems: Aristotle, GPT-5.2 Pro. Date given by the wiki: January 10, 2026. Exact text: “Full solution (Lean)”; green flag (“full resolution”, according to the wiki's legend). The wiki flags a Lean proof without naming a third-party checker. Comparable literature found afterwards: China TST competition (2012), on January 14, 2026; similar according to the wiki: “Yes”. Status of the problem in the teorth/erdosproblems community database (data/problems.yaml, unofficial classification, snapshot of October 12, 2026 with no commit identified, current state, not that of June 2026): disproved, answered in the negative (informal_status=disproved); a solution has been formalised in Lean (formal_status=Lean). This status concerns the problem, not this contribution. Problem page not read by DiscoverIA: https://www.erdosproblems.com/397. The DiscoverIA registry also holds an entry that groups several problems, this one included; the two entries may overlap. DiscoverIA status: not evaluated (only the wiki's classification exists). Recorded on October 12, 2026.
Limits
DiscoverIA has not checked this contribution itself. 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
- Aristotle, GPT-5.2 Pro, according to the AI-Erdős wiki
announced on Jan 10, 2026 - Nature
- new result
- Field
- Mathematics (Erdős problem #397 (number theory ; binomial coefficients))
- Wiki category
- AI alongside literature (IA parallèle à la littérature (comparable découverte après coup)
- Wiki verdict
- « Full solution (Lean) » : 🟢 résolution complète (légende du wiki)
- Checked by
- no verifier identified
- Sources
- 4 : 3 read word for word, 1 link only
- 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
AI contributions to Erdős problems (wiki by T. Tao, frozen on June 30, 2026) · entry 156 of 521, by problem number
- Not evaluated : Erdős problem #396: OEIS sequence computed according to the wiki (Claude Opus 4.6, Gemini 3.1 Deep Think, GPT-5.4 Pro)
- Not evaluated : Erdős problem #396: related result according to the wiki (GPT-5.4 Pro, GPT-5.4 Thinking)
- Not evaluated : Erdős problem #397: full solution according to the wiki (Aletheia)
- Not evaluated : Erdős problem #397: full solution with a Lean proof according to the wiki (Aristotle, GPT-5.2 Pro)
- Not evaluated : Erdős problem #397: full solution found in the literature according to the wiki (ChatGPT Deep research)
- Not evaluated : Erdős problem #399: formalisation by Codex (proof: Barfield (2025))
- Not evaluated : Erdős problem #400: candidate partial result according to the wiki (GPT)
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