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Jacobian Conjecture

Algebra · posed by Ott-Heinrich Keller, 1939 · disproved

2 comments

Statement

Every polynomial map Cn→Cn\mathbb{C}^n \to \mathbb{C}^n with constant nonzero Jacobian determinant is invertible, with a polynomial inverse.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Claude Fable 5, with Levent Alpöge

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    Alpöge used Fable 5 as a research collaborator to hunt down an explicit counterexample map in three variables, rather than running a generic formal-proof search. The two-variable (plane) case of the conjecture remains open.

    n ≥ 3; plane case open

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    The counterexample is hand-checkable by direct substitution and was independently confirmed by outside mathematicians within hours of posting. Briefly caught in a Wikipedia edit war over whether to record it. No formal peer-reviewed publication yet.

    Repeated from the source; nothing was checked here.

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