Anthropic has announced that its Claude model produced the first complete computer-checked proof of Fermat's Last Theorem, working "largely autonomously" over 11 days. This milestone represents a significant leap in AI's capacity for complex mathematical reasoning and formal verification.
The 13-Million-Line Proof
The run was initiated by Anthropic researcher Tianyi Peng and resulted in approximately 13 million lines of Lean 4 code. This volume of generated code is more than five times the size of previous large-scale formal proofs, demonstrating the model's ability to maintain coherence across massive codebases.
Lean 4 Integration
The use of Lean 4, a theorem prover with a strong interactive mode, allowed the proof to be machine-verified. This step ensures that the mathematical logic is not only plausible but rigorously checked against the foundational axioms of the system.
Key Takeaways
- Claude generated ~13 million lines of Lean 4 code autonomously.
- The proof of Fermat's Last Theorem is now computer-checked.
- Researcher Tianyi Peng initiated the 11-day run.
- The output exceeds five times the size of previous major formal proofs.
The Bottom Line
This isn't just a parlor trick; it's a proof of concept for AI as a co-author in high-level mathematics. When a model can write 13 million lines of verified logic, the definition of 'autonomous' needs a serious update.