User levent, posting via the handle @__alpoge__, announced that the Jacobian Conjecture is false. According to the post, the discovery was made with assistance from Akhil and the AI model Claude Fable, which performed the work during the world cup final.

The provided counterexample is a polynomial map from C^3 to C^3 defined by the expression ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z). This mapping has a Jacobian determinant of -2. It maps the points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0). The announcement has generated significant attention on Hacker News, receiving 776 points and 484 comments as of July 20, 2026.

User levent, posting via the handle @__alpoge__, announced that the Jacobian Conjecture is false. According to the post, the discovery was made with assistance from Akhil and the AI model Claude Fable, which performed the work during the world cup final.

The provided counterexample is a polynomial map from C^3 to C^3 defined by the expression ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z). This mapping has a Jacobian determinant of -2. It maps the points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0). The announcement has generated significant attention on Hacker News, receiving 776 points and 484 comments as of July 20, 2026.