An AI just broke an 87-year-old maths problem, in a tweet sent during the World Cup final
On Sunday evening, as Spain and Argentina played out the World Cup final, the mathematician Levent Alpöge posted a short message on X. The Jacobian conjecture, he wrote, is false. He thanked a friend for asking about it, and another friend, “fable,” for working during the match.
That second friend was Fable 5, Anthropic’s latest AI model. Together they had produced a counterexample to a problem that had resisted mathematicians for 87 years. It was 216 characters long.
What was actually broken
The Jacobian conjecture was set out by Ott-Heinrich Keller in 1939. In rough terms, it says that a certain kind of polynomial map, one whose Jacobian determinant is a non-zero constant, must be reversible with a neat polynomial inverse.
It became one of the field’s most stubborn open problems. Stephen Smale put it on his famous 1998 list of challenges for the 21st century. New Scientist...
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