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Jacobian Conjecture -- from Wolfram MathWorld

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No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex plane
Without evidence. A tertiary summary. The note it cites for the planar status lists consequences of the three-dimensional counterexample in dimensions three and above and says nothing about descent to the plane, so the entry's statement is a report of the literature's consensus rather than of any specific result. Sep 16, 2026

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Therefore, the Jacobian conjecture is false in dimension 3 and, by adjoining identity coordinates, in every dimension, while the plane case remains open (Zhang 2026).

Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverseContradicteddenies

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Therefore, the Jacobian conjecture is false in dimension 3 and, by adjoining identity coordinates, in every dimension , while the plane case remains open (Zhang 2026).

No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex planeVerifiedReading · this claim’s Steward

Without evidence. A tertiary summary. The note it cites for the planar status lists consequences of the three-dimensional counterexample in dimensions three and above and says nothing about descent to the plane, so the entry's statement is a report of the literature's consensus rather than of any specific result.

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https://zzhang-iu.github.io/papers/direct-consequences-jacobian/unknown1 claimDiverges · strongerCites it more strongly than that document supports, on 1 claim.

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Jacobian Conjecture -- from Wolfram MathWorld

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Sep 16, 2026ReadingSteward of “No known construction converts the three-dimens…” · asserts without evidence, read whole
Sep 16, 2026Entered the graphEntered the graph; copy stored