Aug 9, 2025 Not evaluated

Erdős problem #686: various partial results according to the wiki (AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro)

The gist

According to the teorth/erdosproblems wiki on AI and Erdős problems, humans with several AI models reportedly obtained various partial results on problem #686 (dated by the wiki from August 9, 2025 to March 15, 2026).

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 #686: various partial results according to the wiki (AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d#releve-1

BibTeX @misc, key discoveria-erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d-r1

@misc{discoveria-erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d-r1,
  author       = {{DiscoverIA}},
  title        = {Erdős problem #686: various partial results according to the wiki (AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro)},
  howpublished = {DiscoverIA registry, entry erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/erdos-686-alphaproof-claude-gemini-deep-think-gpt-5-2-1d#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

Problem #686 belongs to number theory. If the results held, they would deal with the problem only in part. The wiki places the entry among AI collaborating with humans, with significant human involvement.

What remains unclear

The sources read do not say what these various partial results cover, what part each human and each AI played, or whether anyone has checked them. A check 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.

Aug 9, 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 1(d), “AI collaborating with humans” (significant human involvement). Humans named by the wiki: Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc, a human contributor; AI systems: AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro. Terence Tao, named here as a contributor, also presented the repository in his blog post of August 31, 2025. Dates given by the wiki: “9 Aug, 2025-15 Mar, 2026”. Exact text: “Various partial results”; yellow flag (“partial progress”, according to the wiki's legend). 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/686. DiscoverIA status: not evaluated (only the wiki's classification exists). Recorded on October 12, 2026.

Limits

DiscoverIA has not checked this contribution itself.

Key facts

Claimed by: Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc, a human contributor with AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro, according to the AI-Erdős wiki (Name replaced by a role)
announced on Aug 9, 2025
Nature: new result
Field: Mathematics (Erdős problem #686 (number theory))
Wiki category: AI collaborating with humans (IA en collaboration avec des humains ; implication humaine significative)
Wiki verdict: « Various partial results » : 🟡 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 278 of 521, by problem number

See all 521 entries

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