Jacobian Conjecture Disproved!

While you were watching the World Cup, Levent Alpoge was tasking Fable to disprove the Jacobean Conjecture, by finding the first known counterexample to it.

This sounded very exciting to me so I wanted to find out what the hell it meant, really.

So I prompted up an explainer. In the process, I think I may have been one of the first to discover there is an infinite family of such counterexamples. Specifically, in $C^3$, for every $n \ge 3$ , you can find a mapping from $C^3$ to $C^3$ where there are $n$ preimages for the same image. I can prove this fact. And 12 hours ago no one believed there was even one such counterexample. Neat!