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Came up with a way to generate an infinite family of counterexamples, via Fable + GPT 5.6 Sol
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
To my math-y friends: hasn't the ability of math models to do the kind of thing behind the Jacobian conjecture counterexample been kind of "obvious" for a while? @noahdgoodman @KuninDaniel @SuryaGanguli I'm not exactly a frontier user, but I've used math models to find annoying multi-variable calculus/algebraic geometry counterxamples to avoid wrong conjectures (eg. https://arxiv.org/pdf/2607.08561 sec A.10.5., coincidentally also about Jacobians). Haven't many of you kind of done similar things? Automated tools are really good at checking a simple set of conditions pretty exhaustively, and avoiding infinite check sets with clever reasoning about restrictions; humans find this kind of work boring / annoying. So isn't what's interesting / notable about the jacobian conjecture situation that no one had the patience to look for such counterexamples without automated tools, but were instead willing to put a lot of effort into complex theory-building work while (futilely) trying to prove it??