An AI helped crack a 30-year-old maths puzzle.
In 1995 Étienne Ghys guessed that chaotic systems with a rigid complex geometry can only live on very simple shapes. The three-dimensional case stayed open for over thirty years.
Mathematicians Disheng Xu and Jiesong Zhang have now proved it, working with Shanghai AI Lab's model Intern-S2. The AI wrote about a thousand pages of candidate arguments. The humans picked the winning route.
Then a machine checked it: the four main theorems were verified in the Lean proof checker, about 550,000 lines of code written by up to 100 AI agents.
The caveats: it is a preprint, three theorems assume one classic 1969 result, and higher dimensions are still open.
Our take: AI widens the search, people supply the judgement. So who had the idea?
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1October 19, 2026 3K
