AIBRIEF
Levent Alpöge, a mathematician at AI lab Anthropic, posted a one line possible counterexample to the Jacobian conjecture — a long standing open problem about whether certain polynomial functions can always be cleanly reversed — on X during the
A working mathematician at the AI lab Anthropic has put forward a possible counterexample to the Jacobian conjecture, an 87-year-old open problem in algebraic geometry, and the math community is now doing the public work of checking it.
Levent Alpöge posted the candidate on X this week, crediting Claude for working the problem during the World Cup final. A conjecture is an unproven idea many mathematicians believe to be true; a counterexample is a single instance that would prove it false, which is the reason the post drew attention.
The Jacobian conjecture asks whether certain polynomial functions can always be cleanly reversed. If Alpöge's candidate is correct, the conjecture is false. The casualness of the delivery is itself part of the story: the result arrived as a single X post, with no preprint, no journal, and no press release.
Within days, Sébastien Bubeck published a public analysis on his blog treating the claim as worth taking seriously. The Singularity Hub writeup and a Conversation pickup carry the same framing, but neither is the original signal; the post is.
The Jacobian conjecture has a history of proposed counterexamples that did not survive scrutiny, and this one is still being checked. No one has yet declared the conjecture dead.