> AI’s solution to 87-year-old riddle takes mathematicians by surprise. I want to know how many Brownbacks this cost.

Mathematicians have been trying to prove the Jacobian conjecture for nearly a century, but now the Claude Fable 5 AI has apparently found a counterexample that disproves it
By Matthew Sparkes
20 July 2026

Levent Alpöge announced the solution on X
levent via Twitter

A mathematician has cracked an 87-year-old conundrum with the help of AI and announced the solution unceremoniously in a tweet. The finding is the most difficult mathematical problem yet solved by AI, say experts.

Levent Alpöge at Harvard University wrote on X on 19 July that the Jacobian conjecture – which academics have spent decades trying to prove was true – is actually false, giving a tiny, 216-character counterexample as proof.
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A golden age of maths is dawning and mathematicians are freaking out

The Jacobian conjecture – which suggests that a certain type of mathematical function would also work in reverse – was formally set out by Ott-Heinrich Keller in 1939. It was also on an influential list of 18 fiendishly difficult problems for mathematicians to tackle in the 21st century drawn up by Stephen Smale in 1998.

https://www.newscientist.com/article/25 … -surprise/

More serious treatment:

https://en.wikipedia.org/wiki/Jacobian_conjecture