Vasily Ilin at the University of Washington posted a preprint in late September for Lean Pool, a formalized mathematics repository grown and maintained by AI agents [P4, S1]. The human-written portion of the paper is a single page P⁴.
Ilin's own disclaimer states that everything in the paper except that one page is AI-generated P⁴.
My read: This is the first preprint I've seen where the author openly says AI wrote nearly all of it, and the subject is itself an AI-maintained system. That circularity is either a neat demonstration or a red flag. I can't tell from the abstract how autonomous the agents actually are. The GitHub repo shows two human contributors, Vilin97 with 609 contributions and justincasher with 28 P², which tells me humans are still very much in the loop. I'd watch for anyone in the Lean community to independently verify the formalized proofs.
The project is a code repository where AI agents do the work of formalizing mathematical proofs, the process of translating human mathematics into a language a computer can verify step by step with no gaps.
Why formalized mathematics is slow
Lean is a proof assistant: software that checks mathematical proofs written in its language, guaranteeing every step is logically sound. The dominant library of such proofs, mathlib, is a community-built archive that has taken years of expert human labour to assemble. Each theorem requires a mathematician or computer scientist to translate a pen-and-paper proof into Lean code, line by line, until the checker is satisfied.
This bottleneck is exactly what AI theorem-proving research wants to break. If language models can generate formalized proofs that compile, the rate at which mathlib grows could accelerate dramatically. Lean Pool appears to be a testing ground for that idea.
What the repository actually contains
The GitHub repo, Vilin97/lean-pool, was created on 9 May 2026, about four months before the preprint appeared P². It has 59 stars and 6 open issues P². The code is written in Lean, Makefile, Python, and Shell, and released under the Apache 2.0 licence P².
The README positions Lean Pool as sitting between mathlib and another project, though the deep-research fetch cut off before the full sentence P². The HuggingFace page calls it the largest curated repository of formalized mathematics, though that text was also truncated in our fetch and no specific entry count appears in any source P³.
Two contributors are listed on GitHub: Vilin97, with 609 contributions, and justincasher, with 28 P². For a project described as AI-maintained, that human contribution count is worth noting. The agents may be doing the formalization work, but humans are clearly reviewing and merging.
What nobody has verified
The preprint is not peer-reviewed. It is an arXiv submission, self-reported by the author S¹. No third party has independently evaluated whether the AI agents can reliably produce proofs that compile under Lean, or how their output compares to human-written formalizations in mathlib. The claim of "largest curated repository" on the HuggingFace page P³ is unverified and has no published metric behind it.
The project is not affiliated with the Lean theorem prover or the mathlib developers, and the name could easily be mistaken for an official Lean extension. It is an independent project by a single university researcher.
A formal methods researcher wanting to check the work could clone the repo from GitHub, run the Lean compiler against the formalized proofs, and compare the entries against mathlib to see what is genuinely new versus duplicated. The 6 open issues on the repo P² are a starting point for understanding what is still broken.
The arXiv listing, identifier 2609.25199v1, appeared on 23 September 2026 under the cs.AI category S¹. The GitHub repo remains active, with 6 open issues as of this week P².
Sources: S1 — Lean Pool: An AI-Maintained Archive of Formalized Mathematics · P2 — Vilin97/lean-pool · P3 — Paper page - Lean Pool: An AI-Maintained Archive of Formalized Mathema · P4 — Lean Pool: An AI-Maintained Archive ofFormalized Mathematics · P5 — AtharvaDomale/Daily-HuggingFace-AI-Papers
Written from 5 sourced items, 4 of them primary.
