Lean Pool: An AI-Maintained Archive of Formalized Mathematics

arXiv:2609.25199 · cs.AI · Submitted 2026-09-21 · Read on arXiv

cs.AI

Submitted: 2026-09-21

Updated: 2026-09-21

Comments: 52 pages, 6 figures. Includes a catalogue of imported projects

Code: https://github.com/ShengtongZhang-alt/BN

Project page: https://vilin97.github.io/lean-pool

License: http://creativecommons.org/licenses/by/4.0/

The gist: Lean Pool is a repository of formalized mathematics.

Terminology

• Benchmark — 12× in this paper · explained in 2 episodes
• Verification — 11× in this paper · explained in 2 episodes
• AI Agents — 8× in this paper · explained in 2 episodes
• Provenance — 7× in this paper · explained in 4 episodes
• Axioms — 6× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Hypergraph — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Embeddings — 2× in this paper · explained in 2 episodes
• Generative AI — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Formal Verification — 1× in this paper · explained in 2 episodes
• KV cache — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes

Abstract

Sources

• First Proof
• Semantic Search over 9 Million Mathematical Theorems
• Primitive sets and von Mangoldt chains: Erd\H{o}s Problem #1196 and beyond
• ABC implies that Ramanujan's tau function misses almost all primes
• On the paucity of lattice triangles
• Formalizing Mason-Stothers Theorem and its Corollaries in Lean 4
• A formal proof of the Ramanujan--Nagell theorem in Lean 4
• Edge-decompositions of graphs with high minimum degree
• Bounds on the exceptional set in the $abc$ conjecture
• A complete formalization of Fermat's Last Theorem for regular primes in Lean
• Chebyshev quotients, Demazure multiplicities, and Dyck-path models
• Propositional Dynamic Logic has Craig Interpolation: a tableau-based proof
• The Wedderburn-Artin Theorem
• Formalizing computability theory via partial recursive functions
• Thakur's hypotheses on power sums of $\mathbb{F}_q[t]$
• Dead ends in square-free digit walks
• Almost all primes are partially regular
• Fel's Conjecture on Syzygies of Numerical Semigroups

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