Erdős #333: first “autonomous” LLM solution claimed, already solved by Erdős and Newman in 1977
Status
Withdrawn
Recorded on · quantamagazine.org
Outside the verification path
- Announced
- Recordedwithdrawn
What this status means
Source reading : Source read through an AI summary (level 2 of 3)
Withdrawn or abandoned by its author, or marked incorrect by the reference source.
The gist
Kevin Barreto, with Liam Price, announced on 25 December 2025 the first “autonomous” solution of an Erdős problem (#333) by an LLM, already solved by Erdős and Newman in 1977.
Cite this entry
A single status snapshot since Oct 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-erdos-333-barreto-2025-12-25-r1
@misc{discoveria-erdos-333-barreto-2025-12-25-r1,
author = {{DiscoverIA}},
title = {Erdős #333: first “autonomous” LLM solution claimed, already solved by Erdős and Newman in 1977},
howpublished = {DiscoverIA registry, entry erdos-333-barreto-2025-12-25},
note = {Status « Withdrawn », snapshot 1, recorded on October 11, 2026. new result},
year = {2026},
url = {https://discoveria.ai/en/fiche/erdos-333-barreto-2025-12-25/#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: Antoine Olivier, Oct 18, 2026Report an error
What has not been reviewed?
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
Key facts
- Claimed by
- Not shown (withdrawn entry)
announced on Dec 25, 2025 - Nature
- new result
- Field
- Mathematics (number theory / combinatorics)
- Checked by
- unnamed third party (forum user)
- Sources (domains)
- 3 : 2 read word for word, 1 links only
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
To understand
Analogy
It is like thinking you have opened a new path through a forest, then discovering that a marked trail has run there for a long time.
What it changes
Since the status is “withdrawn”, this entry does not show that an LLM solved an open question by itself. It is a reminder that a question listed as open may already have a published answer, which makes checking the literature essential.
What remains unclear
The AI contributions wiki gives two rows for this problem: a complete Lean solution (Claude Opus 4.5, GPT-5.2 Pro), whose equivalent already existed in the literature, and an incorrect proof claimed by GPT-5.2 Pro. The earlier solution was pointed out by a forum user who is not named.
3 sources.
For experts
Sources(domains)
- primairequantamagazine.orglink only, reading not recorded
- articleerdosproblems.compage read word for word · consulted on Oct 18, 2026 ·
Theorem 2 of [ErNe77] already implies a negative answer to this problem
- listegithub.compage read word for word · consulted on Oct 18, 2026 ·
| [[333]](https://www.erdosproblems.com/333) | Claude Opus 4.5, GPT-5.2 Pro | 25 Dec, 2025 | 🟢 Full solution (Lean) | 🟢 Erdős and Newman (1977)
Method
According to erdosproblems.com/333, Theorem 2 of [ErNe77], the paper by Erdős and Newman, already implies a negative answer to the question. The wiki lists the case in section 1(b), among AI solutions for which comparable literature exists. Status “withdrawn” recorded on 11 October 2026 from quantamagazine.org (page read through a model summary, quotation not rechecked).
Limits
The status source was read through a model summary; its quotation was not rechecked.
It is like thinking you have opened a new path through a forest, then discovering that a marked trail has run there for a long time.
Status history
Only one observation so far.
- 01
First observation:WithdrawnCurrent status
claim abandoned by its author after an earlier solution was found
Source: quantamagazine.orgread through an AI summary
An observation is added; none is ever erased.
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