Not evaluated
Erdős problem #659: full solution according to the wiki (Gemini 3)
The gist
According to the teorth/erdosproblems wiki on AI and Erdős problems, Benjamin Grayzel, with Gemini 3, reportedly obtained a full solution to Erdős problem #659 (announcement of January 13, 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-659-gemini-3-1d-r1
@misc{discoveria-erdos-659-gemini-3-1d-r1,
author = {{DiscoverIA}},
title = {Erdős problem #659: full solution according to the wiki (Gemini 3)},
howpublished = {DiscoverIA registry, entry erdos-659-gemini-3-1d},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-659-gemini-3-1d#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Problem #659 belongs to geometry, under the heading “distances”. If the full solution held, the problem would be dealt with in full.
What remains unclear
The sources read do not say what the solution consists of, what part Benjamin Grayzel and Gemini 3 each played, or whether anyone has checked it. 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 1(d), “AI collaborating with humans” (significant human involvement). Humans named by the wiki: Benjamin Grayzel; AI system: Gemini 3. Date given by the wiki: January 13, 2026. Exact text: “Full solution”; green flag (“full resolution”, 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): 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/659. 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
- Benjamin Grayzel with Gemini 3, according to the AI-Erdős wiki
announced on Jan 13, 2026 - Nature
- new result
- Field
- Mathematics (Erdős problem #659 (geometry ; distances))
- Wiki category
- AI collaborating with humans (IA en collaboration avec des humains ; implication humaine significative)
- Wiki verdict
- « Full solution » : 🟢 résolution complète (légende du wiki)
- 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 267 of 521, by problem number
- Not evaluated : Erdős problem #658: formalisation by Aristotle (proof: Solymosi (2004))
- Not evaluated : Erdős problem #659: full solution according to the wiki (Aletheia)
- Not evaluated : Erdős problem #659: formalisation by Aristotle (proof: Gemini and Grayzel (2026))
- Not evaluated : Erdős problem #659: full solution according to the wiki (Gemini 3)
- Not evaluated : Erdős problem #659: partial results, upgradeable to a full solution, found in the literature according to the wiki (Gemini Deep Research)
- Not evaluated : Erdős problem #666: formalisation by Aristotle (proof: Chung (1992), Brouwer, Dejter, and Thomassen (1993))
- Not evaluated : Erdős problem #671: candidate full solution with a Lean proof according to the wiki (Codex, GPT-5.5 Pro)
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