Peer reviewed
9 of 353 open Erdős problems solved in Lean, according to DeepMind
AlphaProof Nexus (Google DeepMind, Science): 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean, according to the authors
The gist
Google DeepMind published its AlphaProof Nexus study in Science on October 8, 2026: the authors report 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean.
DiscoverIA status on October 13, 2026: peer reviewed, meaning published in a journal or reviewed by named experts.
Text written by an AI, reviewed by Antoine Olivier,
Cite this entry
The status has changed 2 times since Oct 11, 2026: a citation always points to a dated snapshot. Cite an earlier snapshot
Cite snapshot 3, Oct 13, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-alphaproof-nexus-science-2026-10-08-r3
@misc{discoveria-alphaproof-nexus-science-2026-10-08-r3,
author = {{DiscoverIA}},
title = {AlphaProof Nexus (Google DeepMind, Science): 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean, according to the authors},
howpublished = {DiscoverIA registry, entry alphaproof-nexus-science-2026-10-08},
note = {Status “Peer reviewed”, snapshot 3, recorded on October 13, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/alphaproof-nexus-science-2026-10-08#releve-3},
urldate = {2026-10-13}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A peer-reviewed article states that an AI system solved mathematical problems that were still open, with proofs written in Lean, a language in which a computer checks every step of a proof. The study first appeared as an arXiv preprint on May 21, 2026.
What remains unclear
The Science reviewers are anonymous and no named third party has rerun the published Lean proofs yet. The figures are the authors' own. For comparison, the OEIS Open benchmark (arXiv 2608.11941) reports 147 of 492 conjectures solved by general-purpose language models.
Read the papers
Advancing mathematics research with AI-driven formal proof search
Advancing Mathematics Research with AI-Driven Formal Proof Search
What it establishes : The authors present AlphaProof Nexus, an agent that searches for proofs in Lean, and evaluate it at scale on open problems; after each success, experts on the team checked that the Lean statement was faithful.
Where to start : The abstract, then Table 1 (Section 3), which lists the 9 Erdős problems solved; the same section covers the 44 OEIS conjectures and analyses the failures. The version published in Science has a differently worded abstract with the same figures.
Written by an AI · reviewed by a human
For experts
Sources, method, key facts, status history, report an error
Status
Peer reviewed
Recorded on · api.crossref.org
Step 3 of 4 on the scale: peer reviewed. Next step: formally verified.
What this status means
Source reading : Source read word for word (level 3 of 3)
Published in a journal or reviewed by named experts.
Sources
- Main sourcedoi.orglink only, reading not recorded
- Status sourceapi.crossref.orgpage read word for word · consulted on Oct 13, 2026 ·
Advancing mathematics research with AI-driven formal proof search
- Paperarxiv.org · 2605.22763page read word for word · consulted on Oct 18, 2026 ·
Our most capable agent autonomously resolved 9 of 353 open Erdős problems
- Paperarxiv.org · 2605.22763v2page read word for word · consulted on Oct 13, 2026 ·
we developed a framework, AlphaProof Nexus, for LLM-aided proof generation
- Lean proofgithub.compage read word for word · consulted on Oct 13, 2026 ·
Lean math proofs generated by AlphaProof Nexus and accompanying natural language prose proofs.
- Claimant's statementdigg.compage read through an AI summary · consulted on Oct 11, 2026
- Paperquantamagazine.orgpage read through an AI summary · consulted on Oct 11, 2026
Method
The arXiv preprint 2605.22763 (version 1 of May 21, 2026, version 2 of June 8, 2026) and the Science article (DOI 10.1126/science.aej2213) share the same title and the same 21 authors. The Lean proofs and their natural-language write-ups are published in the google-deepmind/alphaproof-nexus-results repository. Status “peer reviewed” recorded on October 13, 2026 from api.crossref.org (page read, quotation checked word for word). History: 3 dated observations, oldest first.
Limits
A Lean proof supplied by the claimant does not count as formal verification by a third party.
Key facts
- Claimed by
- Google DeepMind (AlphaProof Nexus; 21 authors, one of them from Aarhus University)
announced on Oct 8, 2026 - Nature
- new result
- Field
- Mathematics (mathematics / formal proof)
- Checked by
- Science peer review (anonymous reviewers)
- Sources
- 7 : 4 read word for word, 2 through an AI summary, 1 link only
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
Status history
Most recent first; each observation is numbered in the order it was recorded.
- 03
Not evaluatedbecomesPeer reviewedCurrent status
peer-reviewed journal article: received 2026-05-27, accepted 2026-08-17, published 2026-10-08 (Science 394(6820):234-239); anonymous reviewers; public Lean proofs not re-run by a…
Read the full reason
peer-reviewed journal article: received 2026-05-27, accepted 2026-08-17, published 2026-10-08 (Science 394(6820):234-239); anonymous reviewers; public Lean proofs not re-run by a named third party
Source: api.crossref.orgread word for word
- 02
Status confirmed:Not evaluated
observation of the arXiv preprint 2605.22763 (v1 of 2026-05-21)
Source: quantamagazine.orgread through an AI summary
An observation is added; none is ever erased.
Cite an earlier snapshot
These snapshots no longer give the current status. Cite them only to date a past state.
Cite snapshot 2, Oct 11, 2026
Not evaluated status superseded on Oct 13, 2026
observation of the arXiv preprint 2605.22763 (v1 of 2026-05-21)
APA citation with the dated link
BibTeX @misc, key discoveria-alphaproof-nexus-science-2026-10-08-r2
@misc{discoveria-alphaproof-nexus-science-2026-10-08-r2,
author = {{DiscoverIA}},
title = {AlphaProof Nexus (Google DeepMind, Science): 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean, according to the authors},
howpublished = {DiscoverIA registry, entry alphaproof-nexus-science-2026-10-08},
note = {Status “Not evaluated”, snapshot 2, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/alphaproof-nexus-science-2026-10-08#releve-2},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
Cite snapshot 1, Oct 11, 2026
Not evaluated status superseded on Oct 13, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-alphaproof-nexus-science-2026-10-08-r1
@misc{discoveria-alphaproof-nexus-science-2026-10-08-r1,
author = {{DiscoverIA}},
title = {AlphaProof Nexus (Google DeepMind, Science): 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean, according to the authors},
howpublished = {DiscoverIA registry, entry alphaproof-nexus-science-2026-10-08},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/alphaproof-nexus-science-2026-10-08#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
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