trailThe Hessian conjecture is false in dimension five
Explicit five-variable witness· for
Meng and Yang's five-variable degree-14 polynomial has constant Hessian determinant 128 and a non-injective gradient map
atomic
Descent from the verified Jacobian counterexample· for
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
atomic
A counterexample to the Jacobian conjecture in three variables was announced in July 2026 and independently verified
In the 2026 Jacobian-counterexample construction, the complement of the ramification divisor and hyperplane preimage in P¹×P² is isomorphic to affine three-space.
The 2026 Jacobian conjecture counterexample has been formally verified in a proof assistant
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The Hessian conjecture is false in dimension five
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