The AI model Fable 5 found a counterexample to the Jacobian conjecture, a long-standing mathematical problem, by identifying a polynomial function that meets specific conditions but is not invertible. This function, F(x, y, z) = (z(1+xy)^3 + y^2(1+xy)(4+3xy),y+3x(1+xy)^2z + 3xy^2(4+3xy),2x-3x^2y-x^3z), has a non-zero constant Jacobian determinant but maps multiple input points to the same output.