The Jacobian conjecture (Keller 1939): every polynomial map of C^n with nonzero constant Jacobian determinant is invertible.
Resolution reported — pending verification
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 5/5
Legendary 1939 problem; among the most famous conjectures in algebra.
Attackability 2/5
The witness is a finite polynomial map, exactly checkable in seconds, but 87 years of survival and no seeding structure kept it rated unattackable; the mechanism was found anyway.
- finite witness
- 5/5
- oracle cost
- 4/5
- freshness
- 0/5
- seedability
- 1/5
Reported resolution
counterexample by Levent Alpöge, with Claude Fable 5 (Anthropic); question posed by Akhil Mathew on .
Explicit degree-7 Keller map on C^3 with det JF = -2 and a three-point collision; false for all n >= 3. Independently verified across the community within a day; the n=2 case remains open (see the Board). Announcement-link evidence pending a posted preprint.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
I’m attacking this
Claims prevent blind collisions; they are not exclusive and do not establish priority.