P(x,y) =
Q(x,y) =
J =
det(J) =
Drużkowski
Why the 1939 conjecture fell in 2026 — drag a polynomial map and feel its Jacobian field
The 1939 Jacobian Conjecture held in 2D but fell in 3D. Levent Alpöge posted this exact polynomial map on July 19, 2026 — it has constant Jacobian 1 yet is not invertible.
A 2×2×2 cube becomes tangled under Alpöge's map — the conjecture fails above dimension 2.