The open problem dates back to 2014 from Dan Anderson; the breakthrough preprint was released on arXiv in early April 2026.

Researchers observed that the AI completed the task faster than any human could, underscoring its potential to accelerate mathematical discovery and verification.

Human involvement can still speed up research when a mathematician guides Archon, showing that core reasoning may be automated while humans provide strategic direction.

The achievement signals substantial automation in mathematical research, reducing repetitive and rigorous tasks while preserving proof accuracy, with human guidance able to further accelerate the process.

The system tackled a commutative algebra conjecture posed by Dan Anderson, solving and verifying it after about 80 hours of computation using restricted documents it could not obtain autonomously.

The work is presented in a preliminary arXiv paper and has not yet undergone peer review.

Led by a team at Peking University, the project appeared on arXiv as an open-access preprint, with peer review still pending.

This development follows the rise of Chinese AI models and major tech players, boosting China’s visibility in the field and sharpening competition with the United States.

The AI framework combines a natural-language reasoning agent (Rethlas) with a formalisation agent (Archon) and uses Lean 4 to convert proofs into machine-checkable statements.

A workflow mirrors mathematical practice: Rethlas searches strategies, Archon translates potential proofs into interactive theorem-prover projects, and Lean 4 stores the formalized theorems and definitions.

The approach employs a dual-agent system: an informal reasoning agent to explore strategies and draft proofs, and a formal verification agent to translate them into rigorous, machine-checkable proofs.

A Peking University team developed an AI system that autonomously solved and verified a decade-old open problem in commutative algebra with minimal human intervention.