Mathlib

Mathlib is the Lean mathematics library referenced in 137. 对洪乐潼的4小时访谈：AI for Math、把数学变成Lean、数学天书中的证明、直觉、被创造与被发现的. The source presents it as the formalized knowledge base that lets systems such as Axiom Prover reuse existing definitions, lemmas, and proof infrastructure instead of starting every theorem from scratch.

Source Position

• Mathlib is part of the AI For Math substrate because AI provers need a formal library, not only natural-language mathematical training data.
• Hong says some research areas have less Lean infrastructure, which makes distribution shift and new-field benchmarks harder.
• The source treats Mathlib maintenance and expansion as a collaborative-math problem: human mathematicians, formalizers, and AI systems all contribute to the usable proof base.

Connections

• Lean Theorem Prover — proof assistant ecosystem Mathlib belongs to in the source.
• Auto-Formalization and Interactive Theorem Proving — processes that add to and use the library.
• Axiom, Axiom Prover, and AI Mathematician — systems that depend on formalized mathematical knowledge.