Not evaluated
Erdős problem #26: formalisation by Aristotle (proof: Ruzsa)
The gist
According to the teorth/erdosproblems wiki on AI and Erdős problems, Aristotle reportedly formalised the proof by Ruzsa on problem #26 (formalisation announced on December 28, 2025).
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-26-aristotle-2b-r1
@misc{discoveria-erdos-26-aristotle-2b-r1,
author = {{DiscoverIA}},
title = {Erdős problem #26: formalisation by Aristotle (proof: Ruzsa)},
howpublished = {DiscoverIA registry, entry erdos-26-aristotle-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-26-aristotle-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, it would allow the proof it targets, that of Ruzsa, to be checked by computer. Problem #26 belongs to number theory, around divisors.
What remains unclear
The wiki does not name the formal language (one in which a computer checks every step of a proof) used on this line. The sources read do not say whether anyone has checked the formalisation, or whether the formalised statement matches that of the problem.
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 system: Aristotle. Date given by the wiki: December 28, 2025. Exact text: “Formalization”. Proof to formalise: Ruzsa; 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/26. 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, according to the AI-Erdős wiki
announced on Dec 28, 2025 - Nature
- formalisation of a known result
- Field
- Mathematics (Erdős problem #26 (number theory ; divisors))
- Wiki category
- Formalization (contribution secondaire : formalisation)
- Proof formalised
- Ruzsa'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 9 of 521, by problem number
- Not evaluated : Erdős problem #21: partial result with a Lean proof according to the wiki (Aristotle, GPT-5.5 Pro)
- Not evaluated : Erdős problem #24: formalisation by Aristotle (proof: Grzesik (2012))
- Not evaluated : Erdős problem #25: partial result according to the wiki (GPT-5.4 Pro)
- Not evaluated : Erdős problem #26: formalisation by Aristotle (proof: Ruzsa)
- Not evaluated : Erdős problem #26: solution to a stronger problem according to the wiki (DeepMind prover agent)
- Not evaluated : Erdős problem #31: formalisation by Aristotle and GPT (proof: Lorentz (1954), Wouter van Doorn (2025))
- Not evaluated : Erdős problem #34: formalisation by Aristotle (proof: Konieczny (2015))
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