Terence Tao’s AI-Assisted Formal Proof Workflow: Claude Code Meets Lean 4

Terence Tao’s recent demonstration of AI-assisted formal proofs using Anthropic’s Claude Code and Lean 4 has sparked interest across mathematics and AI programming circles. The core value isn’t AI proving theorems independently; instead, it’s AI helping mathematicians translate informal proof ideas into machine-verifiable Lean code—cutting down the tedious, time-consuming parts of formalization.

To understand the partnership: Lean 4 is an interactive theorem prover that requires every proof step to be explicitly verifiable by its compiler, while Claude Code acts as an AI programming agent. It doesn’t "know" math proofs but can read project contexts, search Lean’s mathlib for relevant lemmas, generate code snippets, and iterate based on Lean’s error feedback until the code compiles. This combination mitigates AI hallucinations by using Lean’s strict verification as a safety net.

Setting up the workflow is accessible to most developers: no high-end GPU is needed since Claude Code runs on Anthropic’s cloud. First, install Lean 4 via elan (the Lean version manager) and its VS Code extension for real-time verification. Next, install Claude Code globally using npm with npm install -g @anthropic-ai/claude-code. Create a Lean project with a lakefile to include mathlib dependencies, then launch Claude Code in the project directory to ensure it can access the Lean context.

A simple test case illustrates the process: take the proposition "for any natural number n, n +0 =n" in Main.lean with a sorry placeholder. Claude Code can locate the placeholder, generate the necessary Lean proof steps (using tactics like rw Nat.add_zero), and verify the code with lake env lean Main.lean to ensure no errors.

This workflow empowers mathematicians to focus on high-level reasoning rather than mechanical code writing. It’s a significant step toward making formal proofs more accessible, as the AI handles the repetitive tasks of checking mathlib and structuring verifiable code.

Sources

• CSDN Blog Post: "Terence Tao Uses Claude Code for AI-Assisted Formal Proofs in Lean" by weixin_27966471 (https://blog.csdn.net/weixin_27966471/article/details/164250919)