A digestion of the Jacobian conjecture counterexample
The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows. Conjecture 1 (Jacobian Conjecture) Let $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
AI Summary
A recent result using Fable AI has produced a counterexample to the Jacobian conjecture in three dimensions (and thus higher dimensions), showing it is false. The conjecture, which states that a polynomial map with non-zero constant Jacobian must be globally invertible, remains open only in two dimensions. The explicit example is a degree-seven polynomial map in three variables whose Jacobian is constant despite the map not being invertible.