Terence Tao explains an AI-assisted three-dimensional counterexample to the long-standing Jacobian conjecture

Terence Tao outlines a reported counterexample to the Jacobian conjecture, showing that in three or more complex dimensions a polynomial map can have a nonzero constant Jacobian yet fail to be invertible. The post presents the example explicitly and notes that the conjecture remains open in two dimensions while being straightforward in one dimension.

If validated, the result would overturn a major assumption in algebraic geometry and reshape work on polynomial maps and local-to-global invertibility. The claimed role of AI-assisted discovery also points to a growing trend in which machine systems help generate or verify breakthroughs in advanced mathematics.