The lead
Claude Fable produces a verified counterexample to the 85-year-old Jacobian Conjecture
The Jacobian Conjecture is one of the best-known open problems in algebraic geometry. A machine-found, hand-checkable counterexample would be a landmark for AI-assisted math, though the informal announcement means it is not yet peer reviewed.
The model output a low-degree polynomial map on C^3 with a constant Jacobian determinant of -2 that is not injective (three inputs map to one output), which if it holds refutes a conjecture open since 1939. Readers independently reproduced the algebra in SymPy and Wolfram Alpha and started a Lean formalization, but it was announced on social media, so mathematicians are still scrutinizing it.
CONVOYour sharpest 'where is AI actually today' story for senior conversations this week: a model handed mathematicians a checkable answer to an 85-year problem and humans verified it in an afternoon. Lead with the caveat that it broke on Twitter, not in a journal.