Not evaluated
Erdős problem #649: formalisation by Aristotle, GPT (proof: Tong; Sampaio)
The gist
According to the teorth/erdosproblems wiki on AI and Erdős problems, Aristotle and GPT reportedly formalised the proof “Tong; Sampaio” of problem #649 (formalisation dated by the wiki from February 7 to June 1, 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-649-aristotle-gpt-2b-r1
@misc{discoveria-erdos-649-aristotle-gpt-2b-r1,
author = {{DiscoverIA}},
title = {Erdős problem #649: formalisation by Aristotle, GPT (proof: Tong; Sampaio)},
howpublished = {DiscoverIA registry, entry erdos-649-aristotle-gpt-2b},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. Formalisation of a known result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-649-aristotle-gpt-2b#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The wiki sees a formalisation here: if it held, the proof “Tong; Sampaio” would have a version that a computer can check, with no new result. Problem #649 belongs to number theory.
What remains unclear
The wiki does not name the formal language of this formalisation, and the sources read name no verifier. A verification published after the wiki's freeze would not appear there.
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 2(b), “Formalization” (secondary contribution). Humans named by the wiki: none; AI systems: Aristotle, GPT. Dates given by the wiki: “7 Feb-1 Jun, 2026”. Exact text: “Formalization”. Proof to formalise: Tong; Sampaio; wiki flag on this proof: green (“full resolution”, according to the wiki's legend); the wiki does not name the formal language on this line. Literature cited by the wiki: none. 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/649. DiscoverIA status: not evaluated (only the wiki's classification exists). Recorded on October 12, 2026.
Limits
Nature: formalisation (an already known result translated into a language a machine can check), not a discovery. DiscoverIA has not checked this contribution itself.
Key facts
- Claimed by
- Aristotle, GPT, according to the AI-Erdős wiki
announced on Feb 7, 2026 - Nature
- formalisation of a known result
- Field
- Mathematics (Erdős problem #649 (number theory))
- Wiki category
- Formalization (contribution secondaire : formalisation)
- Proof formalised
- Tong; Sampaio's
- 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 256 of 521, by problem number
- Not evaluated : Erdős problem #646: formalisation by Aristotle (proof: Berend (1997))
- Withdrawn : Erdős problem #647: proof judged incorrect by the wiki (ChatGPT Deep research, DeepSeek DeepThink, Gemini)
- Not evaluated : Erdős problem #648: formalisation by Aristotle (proof: Cambie (2025))
- Not evaluated : Erdős problem #649: formalisation by Aristotle, GPT (proof: Tong; Sampaio)
- Not evaluated : Erdős problem #650: numerical optimization according to the wiki (AlphaEvolve)
- Not evaluated : Erdős problem #650: formalisation by Aristotle (proof: He, Li and Tang (2026))
- Not evaluated : Erdős problem #650: full solution found in the literature according to the wiki (ChatGPT Deep research)
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