A Chinese artificial intelligence system has solved a decade-old mathematical problem without any human intervention, according to a new study. The algebra conjecture was first posed in 2014 by American mathematician Dan Anderson, who died in 2022.
The AI, developed by a team at Peking University, processed decades of mathematical literature to crack the problem and verify its own findings. The researchers said the system, which uses a reasoning framework called Rethlas, completed the task within 80 hours of runtime.
“Using this framework, we successfully solved an open problem in commutative algebra and automatically formalised the proof with essentially no human intervention,” the team wrote in a study posted on the arXiv repository. The work has not yet been peer-reviewed.
The AI system can perform mathematical tasks faster than any human, including work that normally requires collaboration between experts in different fields. The researchers noted that while other AI systems can solve maths problems, they typically require significant human supervision.
“Mathematical proofs demand complete rigour, yet even expert-written proofs may contain subtle flaws and proofs produced by LLMs, which are prone to hallucination, are far less reliable,” the scientists wrote. Their framework integrates a natural language reasoning agent with a formalisation agent to autonomously tackle and verify research-level mathematics.
The researchers said the work “provides a concrete example of how mathematical research can be substantially automated using AI”. They added that the paradigm could reduce human effort in mathematical research, though a mathematician could speed up the process by guiding the system.
