AI cracks decades-old math problem

A math proof is not just an answer. It is a chain of steps that has to survive hostile inspection. That is why this story matters. A team at Peking University says its AI system did something stronger than “got the right idea” — it solved an open algebra problem and then turned the argument into a machine-checked proof in Lean 4. The problem was Anderson’s conjecture, posed in 2014, and the team posted the work in April 2026. (arxiv.org)(news.sciencenet.cn)tative algebra, a branch of math that studies rings — algebraic objects that help mathematicians describe local structure and deformation. In plain English, the conjecture asked whether every weakly quasi-complete ring must also be quasi-complete. The team says the answer is no, and built a counterexample proving that the implication fails. (github.com) ### Why is (arxiv.org)erent from exam problems. An olympiad question has a known solution. An open problem does not. The system was not just pattern-matching toward a teacher’s answer key. It had to search the literature, find a route that might work, and produce an argument that could be checked line by line. That is much closer to research. (arxiv.org) ### What actually did the AI do? The setup used t(github.com)looks more like how humans sketch ideas. Archon handled formal verification — translating the proof into Lean 4, breaking it into subgoals, refining the argument, and synthesizing proof steps that a proof assistant could verify. Think of it as one system proposing the path and another forcing every bridge on that path to hold weight. (arxiv.org 1)(arxiv.org 2)eresting part is retrieval. The team says Rethlas used a search system called Matlas to scan a huge body of mathematical statements and connect Anderson’s conjecture to results that did not look obviously related at first glance. That led it to a counterexample strategy. So the breakthrough was not just raw language generation. It was search plus reasoning plus verification, all chained together. (news.sciencenet.cn) much? Because AI can sound convincing while being wrong. A formal proof assistant does not care whether the prose feels elegant. Every step has to type-check. The Peking team says Archon generated about 19,000 lines of Lean 4 code and even had to reroute around gaps in existing formal math libraries by finding equivalent paths. That is the difference between “the model says it proved it” and “the proof compiles.” (news.sciencenet.cn)AI has done serious math? No — but it is a different level of seriousness. Systems like AlphaGeometry and AlphaProof already showed that AI could hit olympiad-level performance, even reaching medal-level results on IMO-style problems. But those are still benchmarked contests. This new result is being framed as end-to-end conjecture resolution with formal verification on a research problem, which is a more ambitious claim. (nature.com)e result does not mean AI can now do frontier mathematics on demand. The paper presents a specific success case, and open problems vary wildly in difficulty. Even here, the system leaned on substantial search infrastructure and formal tools built over years. So this is not “math solved.” It is more like the first convincing glimpse of a new workflow. (arxiv.org) ### Bottom line? The real news is not that a chatbot (nature.com) found a new argument for a live math problem and locked that argument into machine-checkable form. If that holds up, the most important shift is trust. AI math is moving from impressive-looking answers toward proofs that can actually be verified. (arxiv.org)