# Jacobian conjecture

A statement in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: wikipedia:JacobianConjecture
- Collection: Wikipedia
- Page: https://qed.bot/s/wikipedia-jacobianconjecture
- Formal record: mixed
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Wikipedia/JacobianConjecture.lean

## AI claims

### Claude Fable 5, 19 Jul 2026

An explicit polynomial map in three variables with constant Jacobian determinant −2 that sends distinct points to the same image, disproving the Jacobian conjecture in every dimension above two. The two-variable case remains open.

- Outcome: full
- Autonomy A2: Directed. The system produced the result while building on literature or framing supplied to it.
- Evidence V2: Artifact reported. A proof or a constructed object is published, but nobody independent of its authors has rebuilt it.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Levent Alpöge
- Source: Wikipedia, Jacobian conjecture, https://en.wikipedia.org/wiki/Jacobian_conjecture
- Source: Formal Conjectures, the counterexample and the disproof in Lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Wikipedia/JacobianConjecture.lean
- Source: Terence Tao, A digestion of the Jacobian conjecture counterexample, https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/
- Source: The Conversation, why a tiny social media post has mathematicians rethinking AI, https://theconversation.com/hello-there-the-jacobian-conjecture-is-false-thanx-why-a-tiny-social-media-post-has-mathematicians-rethinking-ai-283883

## Formal statements

- FormalConjectures/Wikipedia/JacobianConjecture.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Wikipedia/JacobianConjecture.lean

Cite as: qed.bot, "Jacobian conjecture", https://qed.bot/s/wikipedia-jacobianconjecture, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/