Nov 23, 2025 Not evaluated

Erdős problem #645: formalisation by Aristotle, GPT (proof: Brown and Landman (1999))

The gist

Aristotle and GPT reportedly formalised the proof by Brown and Landman (1999) of problem #645 (formalisation announced on November 23, 2025), according to the teorth/erdosproblems wiki on AI and Erdős problems.

DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.

Status detailsDetails

AI draft, not reviewedWhat has not been reviewed?

Text written by an AI (DiscoverIA pipeline), on Oct 17, 2026. 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.

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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

DiscoverIA. (2026, October 12). Erdős problem #645: formalisation by Aristotle, GPT (proof: Brown and Landman (1999)) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/erdos-645-aristotle-gpt-2b#releve-1

BibTeX @misc, key discoveria-erdos-645-aristotle-gpt-2b-r1

@misc{discoveria-erdos-645-aristotle-gpt-2b-r1,
  author       = {{DiscoverIA}},
  title        = {Erdős problem #645: formalisation by Aristotle, GPT (proof: Brown and Landman (1999))},
  howpublished = {DiscoverIA registry, entry erdos-645-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-645-aristotle-gpt-2b#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/erdos-645-aristotle-gpt-2b#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

To formalise a proof is to rewrite it in a language that a computer can check step by step. The wiki sees a secondary contribution of formalisation: if it held, the proof by Brown and Landman (1999), which the wiki marks “complete resolution”, could be checked in that way.

What remains unclear

The wiki does not name the formal language on this line, and the sources read do not say whether anyone has checked this formalisation. A verification published after the wiki was frozen would not appear in it.

For experts

Sources, method, key facts, status history, report an error

Status

Not evaluated

Recorded on Oct 12, 2026 · github.com · wiki

Step 1 of 4 on the scale: not evaluated. Next step: under review.

Nov 23, 2025Announced
Jun 30, 2026Wiki frozen
Oct 12, 2026Recordednot 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

Full history

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. Date given by the wiki: November 23, 2025. Exact text: “Formalization”. Proof to formalise: Brown and Landman (1999); 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): proved, answered in the affirmative (informal_status=proved); 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/645. 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 Nov 23, 2025
Nature: formalisation of a known result
Field: Mathematics (Erdős problem #645 (number theory ; additive combinatorics ; ramsey theory ; arithmetic progressions))
Wiki category: Formalization (contribution secondaire : formalisation)
Proof formalised: Brown and Landman's
Checked by: no verifier identified
Sources: 4 : 3 read word for word, 1 link only
Part of: AI contributions to Erdős problems (wiki by T. Tao, frozen on June 30, 2026)
This entry: AI draft, not reviewed

Status history

Only one observation so far.

01Oct 12, 2026
First observation:Not evaluatedCurrent status
Source: github.comread word for word

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 251 of 521, by problem number

See all 521 entries

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