2 published verifications about Jacobian Conjecture Jacobian Conjecture ×
“The Jacobian conjecture is false.”
An explicit three-dimensional counterexample falsifies the general Jacobian conjecture. The result is supported by a rigorous construction, independent Lean 4 verification, and expert analysis. The two-dimensional case remains open, but that does not preserve a conjecture universally quantified across dimensions.
“The Jacobian conjecture is true.”
The evidence does not support treating the Jacobian conjecture as a solved theorem. Authoritative mathematical sources describe it as still open and unproven, and purported proofs cited in weaker sources have not achieved accepted verification. Results about real or generalized variants also do not establish the classical conjecture as settled.