Jun 22, 2026 Not evaluated

Erdős problem #1054: partial result with a Lean proof according to the wiki (Claude Opus 4.8, GPT-5.5 Pro, Principia Math)

The gist

The “AI contributions to Erdős problems” wiki lists, dated June 22 and 23, 2026, work by Claude Opus 4.8, GPT-5.5 Pro and Principia Math on Erdős problem #1054, marked “Partial result (Lean)”.

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 13, 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 #1054: partial result with a Lean proof according to the wiki (Claude Opus 4.8, GPT-5.5 Pro, Principia Math) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a#releve-1

BibTeX @misc, key discoveria-erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a-r1

@misc{discoveria-erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a-r1,
  author       = {{DiscoverIA}},
  title        = {Erdős problem #1054: partial result with a Lean proof according to the wiki (Claude Opus 4.8, GPT-5.5 Pro, Principia Math)},
  howpublished = {DiscoverIA registry, entry erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/erdos-1054-claude-opus-4-8-gpt-5-5-pro-principia-math-1a#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

If this result held, it would advance Erdős problem #1054, a number theory question about divisors; the wiki describes it as partial. In the October 12, 2026 reading, erdosproblems.com still listed the problem as open.

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 checker, and no third-party assessment is recorded. The sources read do not say what the partial result covers exactly.

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.

Jun 22, 2026Announced
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

Proofs: Preuve Lean indiquée par le wiki, vérificateur tiers non nommé

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(a), “AI standalone” (AI alone; no comparable literature known; no significant human involvement). Humans named by the wiki: none; AI systems: Claude Opus 4.8, GPT-5.5 Pro, Principia Math. Dates given by the wiki: “22-23 Jun, 2026”. Exact text: “Partial result (Lean)”; yellow flag (“partial progress”, according to the wiki's legend). The wiki flags a Lean proof without naming a third-party checker. 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): open (informal_status=open); no formalised solution known (formal_status=unformalized). This status concerns the problem, not this contribution. Problem page not read by DiscoverIA: https://www.erdosproblems.com/1054. 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: Claude Opus 4.8, GPT-5.5 Pro, Principia Math, according to the AI-Erdős wiki
announced on Jun 22, 2026
Nature: new result
Field: Mathematics (Erdős problem #1054 (number theory ; divisors))
Wiki category: AI standalone (IA seule ; littérature comparable inconnue ; implication humaine non significative)
Wiki verdict: « Partial result (Lean) » : 🟡 progrès partiel (légende du wiki)
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 448 of 521, by problem number

See all 521 entries

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