An Anthropic Researcher Says Fable Just Helped Him Disprove The 85-year-old Jacobian Conjecture

An Anthropic researcher says he and Claude Fable 5 have disproved the 85-year-old Jacobian conjecture. Levent Alpoge, a number theorist who works at Anthropic and previously held a Junior Fellowship at Harvard's Society of Fellows, announced it on X on Sunday night. He posted a single explicit polynomial map with a note thanking "my close friend akhil for asking about it" and "my other close friend fable for working during the world cup final." Buried in the tweet was a counterexample to the Jacobian conjecture, a question about polynomial equations that has been open since 1939. The function takes three numbers (x, y, z) and outputs three new numbers built entirely from sums and products of the inputs. Its Jacobian determinant works out to a constant, -2, nonzero everywhere. But the function sends three genuinely different starting points to the exact same output, showing it is not invertible. This single collision is enough to sink the conjecture. The reaction from mathematicians online was immediate. A Stanford professor summed up the significance in a post, walking through exactly why the example works and noting a further, almost cinematic coincidence buried in the problem's history.