Lean Pool: An AI-Maintained Archive of Formalized Mathematics
Vasily Ilin
University of Washington
Published September 21, 2026 · on the feed September 23, 2026 · ▲ 27 · arXiv 2609.25199
The abstract
Lean Pool is a repository of formalized mathematics. It is grown, maintained and optimized by AI agents.
The Brief
1:16A short podcast summary of the paper. Written and voiced by AI.
Transcript
Lean Pool. An AI-Maintained Archive of Formalized Mathematics. By Vasily Ilin, from the University of Washington. Published on the twenty-first of September. Its code repository is worked out: about seventy-five source files, with a readme and a licence.
Lean Pool is a repository of formalized mathematics.
It is an archive. Its contents are mathematics written in formalized form, gathered in one place as a repository.
What sets it apart is who does the work. The repository is grown, maintained and optimized by AI agents. Growing it means adding to it. Maintaining it means keeping what is already there in order. Optimizing it means improving what exists. All three jobs, on this description, are carried out by agents rather than by people.
It is for anyone who needs an archive of formalized mathematics, and for anyone interested in what AI agents can do when they are put in charge of looking after one. Both audiences meet in the same repository: one comes for the mathematics, the other for the way it is kept.
The title sums up the whole idea in a phrase: an AI-maintained archive of formalized mathematics. The repository exists, it holds formalized mathematics, and AI agents grow it, maintain it and optimize it.
Paper Quest · 7 chapters · about 33 min
Play this paper
Learn it by doing: make the calls the authors made, guess the result before you see it, and defend it in a viva graded on your own words. Chapter 1 is right here.
Chapter 1 🧩 · The problem
Every quest starts with a wall. Here it is a mountain of checked proofs that nobody can keep alive.
AI systems now produce mathematical arguments faster than mathematicians can read them. A proof assistant can check them, but its standard maths library lacks much research-level mathematics and grows only slowly, because every addition passes strict human review.
The road ahead
- 1 · The problem ~7 min AI writes proofs faster than people can check them, and the places where checked proofs could live are too slow or fall apart.
- 2 · What came before ~3 min
- 3 · The key idea ~9 min Pool finished formalizations into one shared archive, let the kernel and automated reviewers guard it, and let AI agents keep it working.
- 4 · Choose your own research ~3 min
- 5 · How it works ~3 min
- 6 · Field test ~3 min
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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