The Jacobian conjecture in dimension 2: every polynomial map of the complex plane with nonzero constant Jacobian determinant is invertible.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Statement
Every polynomial map $F:\mathbb{C}^2 \to \mathbb{C}^2$ with $\det JF$ a nonzero constant has a polynomial inverse. (The general conjecture, posed by Keller in 1939, was refuted in July 2026 for all $n \ge 3$; the original two-variable case remains open.)
Assessment
Renown 5/5
The surviving case of the conjecture whose refutation ignited the July 2026 AI counterexample wave; overnight the most-watched open problem in algebraic geometry.
Attackability 2/5
A counterexample would be an explicit pair of polynomials, machine-verifiable exactly; but n=2 has genuinely different structure (known to hold up to degree 100 by Moh), so the n=3 mechanism does not transfer. Expect a stampede regardless.
- finite witness
- 5/5
- oracle cost
- 4/5
- freshness
- 4/5
- seedability
- 2/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
I resolved this
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Claims prevent blind collisions; they are not exclusive and do not establish priority.