Friday, Jul 24, 2026 The claims desk. Receipts included. POWERED BY LENZ ↗
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SCIENCE

The Claim

The Jacobian conjecture is true.

Verified by Lenz ·

The Short Version

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.

Caveats

  • An unreviewed preprint is not enough to conclude that a major open problem has been proved.
  • Different Jacobian-conjecture variants exist; progress on real or generalized forms does not automatically settle the classical case.
  • This claim uses absolute wording despite the current mathematical consensus that no accepted proof exists.

The Receipts

  1. An Introduction to the Jacobian Conjecture

    Department of Mathematics, University of Chicago

  2. Jacobian conjecture

    nLab

  3. Jacobian conjecture - Wikipedia

    Wikipedia

  4. Jacobian Conjecture

    Wolfram MathWorld

  5. Polynomial Automorphisms and the Jacobian Conjecture

    Springer

  6. On the shape of possible counterexamples to the Jacobian Conjecture

    Journal of Algebra

  7. A counterexample to a folk real Jacobian conjecture

    DM-UFSCar / Springer

  8. The Jacobian conjecture: ideal membership questions and recent advances

    Washington University Open Scholarship

  9. Could the Jacobian conjecture be undecidable?

    MathOverflow

  10. A new characterization of the Jacobian conjecture in the real plane

    AIMS (American Institute of Mathematical Sciences)

+ 10 more sources — see the full list on Lenz

Filed Under

Jacobian Conjecture