A research team based in China says its artificial intelligence system has done something no AI has publicly done before: independently solved an open problem in pure mathematics that had stumped human researchers for roughly a decade. The claim, laid out in an April 2025 arXiv preprint, describes a two-agent framework that generated a proof strategy for an unsolved conjecture in commutative algebra, then translated that strategy into a machine-checkable proof using the Lean 4 theorem prover. If the result survives expert scrutiny, it would represent a landmark moment in AI-assisted research and a signal that China’s AI-for-math programs are producing results at the frontier of the field.
How the system works
The framework pairs two AI agents with distinct roles. The first, referred to in the preprint as Rethlas, operates in natural language, reasoning through the problem much the way a human mathematician would: forming conjectures, sketching proof strategies, and iterating when an approach fails. The second, referred to as Archon, takes those informal arguments and converts them into formal proofs written in Lean 4, a widely used interactive theorem prover maintained by the open-source community and adopted by mathematicians worldwide. Both agent names originate solely from the preprint and have not been independently verified or referenced elsewhere.
According to the preprint, titled “Automated Conjecture Resolution with Formal Verification,” the pipeline runs end-to-end without human intervention. Rethlas proposes a line of attack, Archon attempts to formalize it, and if the formalization fails, the system loops back to refine its reasoning. The authors say this cycle ultimately produced a complete, verified proof of a conjecture in commutative algebra that had been open since roughly 2015. The preprint attributes the original problem to U.S.-based mathematicians, but it does not name the conjecture’s authors or provide a detailed publication history, and that provenance has not been independently confirmed through mathematical institutions or the researchers who allegedly posed the question.
What Lean 4 verification does and does not prove
Lean 4 is a powerful tool. When a proof “type-checks” in Lean, it means every logical step follows correctly from the axioms and definitions encoded in the system. That is a stronger guarantee than most human-written proofs receive before peer review, where referees check arguments by hand and can miss subtle errors.
But formal verification has a well-known limitation: it confirms that the proof is internally valid, not that the formalization accurately captures the original mathematical problem. Translating a conjecture from its natural-language statement into Lean’s formal language involves choices about definitions, encodings, and scope. If any of those choices subtly diverge from what the original problem intended, the proof may be correct on its own terms but not actually resolve the conjecture as mathematicians understand it.
This is the gap that independent experts will need to close. Mathematicians familiar with the original conjecture will have to inspect both the informal reasoning and the Lean 4 code to confirm they match. As of May 2026, no third-party audit of the proof code has been publicly reported, and the preprint has not undergone formal peer review. Both of those steps are standard and typically take weeks to months for claims of this magnitude.
Two China-based projects, one research direction
The Rethlas-Archon preprint is not an isolated effort. A separate China-based team recently published a peer-reviewed paper in Nature Machine Intelligence describing TongGeometry, an AI system that autonomously generates and solves Olympiad-level geometry problems using guided tree search and formal verification. TongGeometry operates in a different mathematical domain and targets competition problems rather than open research questions, but it shares a core design philosophy: close the loop between creative problem-solving and rigorous proof-checking, with minimal human involvement.
The two projects come from different teams and use different technical approaches, so treating them as a single coordinated program would overstate the evidence. Together, though, they illustrate a shared research direction: building AI systems designed not merely to assist mathematicians but to operate with a degree of autonomy in generating and verifying results. Only these two projects have been publicly documented with this specific ambition from China-based groups, so characterizing the trend more broadly than the available evidence supports would be premature. For comparison, Western labs are pursuing related goals; Google DeepMind’s AlphaProof system in 2024 solved International Mathematical Olympiad problems at a silver-medal level using a reinforcement-learning approach paired with Lean 4.
Where the Rethlas-Archon claim differs from AlphaProof and TongGeometry is in its target. Both of those systems have demonstrated strength on competition problems, which are difficult but have known solutions. Solving an open research problem, one where no human has yet found an answer, would be a qualitative step forward.
Why the mathematics community’s response will be decisive
Claims that an AI has solved a famous unsolved problem tend to travel fast, often faster than the careful, methodical process mathematicians use to confirm or refute new results. The history of mathematics includes numerous instances where announced breakthroughs required significant corrections or turned out to rest on flawed assumptions. Formal verification reduces but does not eliminate that risk.
The strongest near-term evidence will come from the Lean 4 code itself, assuming the authors release it publicly. Any mathematician or computer scientist with access to a Lean 4 environment can run the proof and confirm it type-checks. That step would verify internal consistency. The harder question, whether the formalization faithfully represents the original conjecture, requires domain expertise and will likely play out through discussions in algebraic research communities, on forums, and eventually through journal peer review.
For now, the most defensible reading is this: a Chinese research team has produced a formally verified proof of what it describes as a decade-old open problem in commutative algebra, using an AI pipeline that required no human mathematical input. The methodology is credible, the verification tool is respected, and the ambition is real. Whether the result holds up as a genuine resolution of the conjecture it targets is a question only the mathematics community can answer, and that process is just beginning.
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*This article was researched with the help of AI, with human editors creating the final content.
