Erdős #90 unit-distance conjecture disproved by an internal OpenAI model
Status
The gist
An internal OpenAI model disproved Erdős's unit-distance conjecture (problem #90), and nine mathematicians published a verified version on 20 May 2026.
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-90-unit-distance-r1
@misc{discoveria-erdos-90-unit-distance-r1,
author = {{DiscoverIA}},
title = {Erdős #90 unit-distance conjecture disproved by an internal OpenAI model},
howpublished = {DiscoverIA registry, entry erdos-90-unit-distance},
note = {Status « Peer reviewed », snapshot 1, recorded on October 11, 2026. new result},
year = {2026},
url = {https://discoveria.ai/en/fiche/erdos-90-unit-distance/#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 13, 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
- OpenAI (modèle interne)
announced on May 20, 2026 - Nature
- new result
- Field
- Mathematics (discrete geometry / combinatorics)
- Checked by
- 9 named mathematicians (simplified “human-verified” version)
- Sources (domains)
- 2 : 1 read word for word, 1 links only
- This entry
- Reviewed by Antoine Olivier, Oct 13, 2026
To understand
Analogy
Like a rule supposed to hold in every case: a single case that contradicts it is enough to show that it is false.
What it changes
To disprove a conjecture is to prove that it does not hold. This discrete geometry question posed by Erdős, about how many pairs of points can be exactly the same distance apart, therefore has a negative answer, and the review by named mathematicians gives the result firmer support than the announcement alone.
What remains unclear
The documented check covers a short, simplified version of the counterexample, published by these reviewers. No publication in a peer-reviewed journal has been found.
2 sources.
For experts
Sources(domains)
- primairearxiv.orglink only, reading not recorded
- corroborationerdosproblems.compage read word for word ·
disproved by an internal model at OpenAI
Method
Alon, Bloom, Gowers, Litt, Sawin, Shankar, Tsimerman, Wang and Wood publish a "digested, human-verified" version on arXiv (2605.20695); the sources read do not describe how the counterexample is built. OpenAI's original text was not reopened for this record. Status “peer reviewed” recorded on 11 October 2026 from arxiv.org (page read, quotation checked word for word).
Limits
The status may change if a new source is published; the dated history stays visible.
Like a rule supposed to hold in every case: a single case that contradicts it is enough to show that it is false.
Status history
Only one observation so far.
- 01
First observation:Peer reviewedCurrent status
review by experts named in a preprint; no peer-reviewed journal publication found
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
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