Lean Pool: an AI-maintained archive of Lean formalizations grows past 3 million lines
On Sept 21, 2026 Vasily Ilin posted arXiv 2609.25199 describing Lean Pool, a repository of formalized mathematics "grown, maintained and optimized by AI agents". It collects Lean 4 projects that do not fit Mathlib, keeps them compiling across Lean upgrades, and optimizes and repairs them with agents. At writing it held 211 projects and about 3.2M lines of Lean; by Sept 30 the GitHub README listed 253 projects and about 4.8M lines. Reviews run on GPT-6 Astra through a Codex worker.
Key facts
- Paper: arXiv 2609.25199 (v1 Sept 21, 2026), sole author Vasily Ilin; 52 pages; per the paper, only about a page is human-written and the rest was produced almost entirely by AI
- At writing: 211 pooled projects, 3,228,485 lines of Lean, 193,862 declarations, 837 registered main results, 18 commit contributors; Lean version bumped six times
- GitHub README (checked Sept 30, 2026): 253 projects, 4,786,161 lines of Lean, 2 open challenges; Apache-2.0
- Acceptance gates: deterministic linters, no `sorry`, warning-free builds, plus an LLM review by GPT-6 Astra (xhigh effort) via a privately run Codex worker and advisory Greptile reviews
- Positioned between Mathlib and one-off formalization projects: a maintained formal counterpart to arXiv that keeps attribution per project
What happened
With AI systems producing large Lean formalizations in 2026, many projects end up as unmaintained one-off repositories that stop compiling when Lean or Mathlib changes. Lean Pool gathers them into one repository and uses agents to discover projects, upgrade dependencies, fix breakage and optimize proofs.
Why it matters
It is an early example of mathematical infrastructure run mostly by AI agents, with humans as maintainers and contributors. The quick growth (about 3.2M lines in the paper, about 4.8M in the README by Sept 30) reflects how much formal mathematics AI systems now produce.
Changelog
- 2026-09-30: created (resolves the leads.md line on Lean Pool)
Related events
- Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claims ★★★
- Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue) ★★★★
Sources (3)
- paperarXiv 2609.25199: Lean Pool: An AI-Maintained Archive of Formalized Mathematics
- codeGitHub: Vilin97/lean-pool
- docsLean Pool index
id: 2026-09-21-lean-pool-ai-maintained-formal-math-archive · updated 2026-09-30 · open in the interactive timeline