A Simplified View of the Jacobian Conjecture

A new mathematical result by Levent Alpöge, developed with AI assistance (Anthropic's Fable/Claude), disproves the century-old Jacobian Conjecture by providing a concrete 3D counterexample. The conjecture asked whether a smooth, non-collapsing polynomial deformation of infinite space must always be globally invertible. The counterexample is a 3D polynomial function with a constant, nonzero Jacobian determinant (meaning no local pinching or tearing) that nonetheless maps two different inputs to the same output — proving the conjecture false. The disproof is verifiable with basic algebra and calculus, even though finding the right counterexample took nearly 100 years. Notably, the 2D version of the conjecture remains unsolved.

Source: https://towardsdatascience.com/a-simplified-view-of-the-jacobian-conjecture. 8sync News only summarizes and links out; content copyright belongs to the authors and original sources.