tl;dr: The Jacobian conjecture—that a polynomial map with constant non-zero Jacobian must be globally invertible—was recently disproven in three dimensions using an AI-assisted construction, with an explicit degree-7 counterexample. Terence Tao provides a geometric digestion of this result, showing the counterexample arises from the multiplication map sending (linear, quadratic) polynomial pairs to their cubic product, restricted to a cleverly chosen affine slice. The key "miracle" is that this three-dimensional slice turns out to be polynomially isomorphic to affine 3-space, despite being cut out by cubic and quadratic equations.