The gist
Google DeepMind claimed on March 30, 2026, according to the AI contributions wiki, a Lean solution to Erdős problem #125 in its lower-density formulation.
DiscoverIA status on October 11, 2026: not evaluated, meaning no third-party evaluation found.
Text written by an AI, reviewed by Antoine Olivier,
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-125-deepmind-r1
@misc{discoveria-erdos-125-deepmind-r1,
author = {{DiscoverIA}},
title = {Erdős #125: complete Lean solution claimed by a DeepMind prover agent},
howpublished = {DiscoverIA registry, entry erdos-125-deepmind},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/erdos-125-deepmind#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The question asks whether a certain set of integers has positive lower density, that is, whether it always fills at least a fixed share of the integers. According to erdosproblems.com, DeepMind's argument shows that this density is zero; if the proof holds, an AI agent would have settled this form of the question on its own, with a proof in Lean, a language in which software checks every step.
What remains unclear
The Lean file is supplied by DeepMind itself, which is not the same as an independent check, and no outside verifier is named. The original source also asked whether the upper density is positive, and erdosproblems.com does not say that this form is settled.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read through an AI summary (level 2 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.
Sources
- Main sourcegithub.compage read through an AI summary
- Papererdosproblems.compage read word for word · consulted on Oct 18, 2026 ·
DeepMind later improved this argument to prove that the lower density has to be $0$
Method
The AI contributions wiki lists for #125 a complete Lean solution by DeepMind's prover agent, dated March 30, 2026. On erdosproblems.com, the question addressed is the [Er97] one; an argument found by DeepMind, then improved, proves there that the lower density is zero. Status “not evaluated” recorded on October 11, 2026 from github.com (page read through a model summary, quotation not rechecked).
Limits
The status source was read through a model summary; its quotation was not rechecked. A Lean proof supplied by the claimant does not count as formal verification by a third party. DiscoverIA has recorded no independent evaluation as of this date.
Key facts
- Claimed by
- Google DeepMind
announced on Mar 30, 2026 - Nature
- new result
- Field
- Mathematics (number theory)
- Checked by
- no verifier identified
- Sources
- 2 : 1 read word for word, 1 through an AI summary
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
Status history
Only one observation so far.
An observation is added; none is ever erased.
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.