Lean Theorem Prover

Lean Theorem Prover is the formal proof language and checker discussed 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 treats Lean as a code-like language for writing mathematical definitions, statements, and proofs that can be checked by a machine.

Source Position

• Lean matters because a proof is not only persuasive prose; it can become an executable artifact that reports errors when definitions, tactics, or proof steps fail.
• Hong distinguishes Interactive Theorem Proving from older fully automatic theorem proving: current systems still use a proof assistant, but AI can take over more of the tactic-writing and search role.
• The episode says Lean is also a bottleneck because data is limited, syntax and state are fragile, and verification speed can constrain system design.
• Auto-Formalization is difficult because informal math papers must be translated into Lean definitions, theorem statements, and proof structures before AI can reliably work with them.

Connections

• Mathlib — Lean’s mathematics library in the episode’s account.
• Axiom, Axiom Prover, and AI For Math — company and system built around Lean-style formal proof.
• Formal Verification, Formal Specification, and AI Coding Verification — software and systems branch where Lean-like proof can matter.