Human-AI team reports proof for a decades-old chaos puzzle

Mathematicians in China have reported a computer-checked proof of the three-dimensional case of the Ghys conjecture, a problem first posed in 1995. The team combined expert judgement with an AI model to develop the argument.

The conjecture connects chaos and geometry. Broadly, it asks whether a particular kind of chaotic motion forces the mathematical space in which it occurs to have a highly regular structure. The reported proof concerns the three-dimensional case, rather than settling the conjecture in full.

Led by Great Bay University professor Xu Disheng, the researchers worked with Shanghai Artificial Intelligence Laboratory’s Shusheng-S2 model. Across seven rounds of reasoning, the model explored multiple routes and generated detailed arguments. Researchers identified promising ideas, rejected dead ends and guided the next round of exploration.

A separate Peking University team translated the paper’s four main theorems into computer-checkable form. The proofs passed Lean, a system that checks mathematical reasoning step by step. Experts also confirmed that the formal statements matched those in the paper.

The research has been posted as a preprint on arXiv, and the verification code is publicly available, allowing others to examine the work.