Jacobian conjecture — AI-claimed counterexample explained via maps

It looks like he's trolling. Yeah, yeah. Hello there. The Jacobian conjecture is false. Thanks. And T-H-A-N-X-A-I figured out this crazy math problem. It's almost a hundred years old. It seems like it's a very big deal. Yes. And it's very understandable. We have to first understand functional maps, which in physics language, we like to call coordinate transformations. A map in this mathematical sense is when all of the points in your original space get mapped to a new space. In this case, a 2D plane being mapped to another 2D plane. A square is taken into a parallelogram. The Jacobian is the ratio between the new area and the old area. Which can also scale from 2D. Yes. You can have volumes, for example. The reason why it's called a map is from this concept of like maps of the earth. You can think about the Mercator projection. Areas near the poles get larger. That's why Africa looks small and Greenland looks the size of Africa. Because the Jacobian near Greenland is much larger than the Jacobian near Africa. But there's other projections where they try to preserve the Jacobian everywhere. But then that's going to distort the shape in some sense. Now here we've got an example where the determinant is a non-zero constant. Meaning no matter where I am in my map, the ratio of the areas is actually exactly the same. That little green area becomes a parallelogram. If I were to take that area and put it up top, the parallelogram might get more squished. It might have a different…