Verifying the result by hand

1:22:09coordinate is some seven degree polomial that has that mixes x y and z. The new y-coordinate is another I think seven degree polomial and then the the the z coordinate is not a seven degree polinomial. It's a little bit simpler but you you I've got this map where x x y and z goes to a new x new y new z. >> I calculated the derivatives which are on the left. So that becomes a matrix which you see on the top right. And then I did a little bit of cheating because I decided I didn't want to multiply all those polomials. Okay. I I I wanted to see if I could still do it if I still got it. And I went got halfway and I'm like [laughter] I still got it. So then so then I went on wolf frame alpha and I

1:22:49just multiplied all of those polomials to calculate the determinant and the determinant is -2 >> and then I went ahead and plugged in those two numbers. >> So fascinating >> and they went to the same number 1/4 0 0 >> there you go I did it on a single piece of paper plus okay a little bit of wolf frame alpha right it would have involved another piece of paper for me to do it but I I was already you can see the crossing out. I was like starting to make mistakes. I was like, let's >> This is so interesting because, you know, and I think this is why it had the, you know, it comes back to your point earlier about why it's easier to disprove >> uh than to prove because especially given the structure of this open problem

1:23:32and the nature of the disproof if that's the right naming. >> The counter example. >> The count sorry, the counter example. Um you it does not it anyone can do it and see that it is true. Going back to our point about mathematics. >> Yeah. >> And the objective nature of it. Yeah. >> Structure. >> Yeah. Exactly. I I did it. Anyone can do it. Right. This is something that algorithmically there's no AI here. Right. >> Right. It's just it's an algorithmic process of taking derivatives taking the determinant of the Jacobian. There you go. Boom. >> The there's a constant determinant and two points point to the same thing. So I can't go backwards. >> I can't go backwards. And it's not invertible. Which means the chacobian

1:24:12conjecture fundamentally not a real thing. >> It's not a real thing. Right? >> It's not a real thing. And it's a it's a counter example in degree um well it's in degree seven but it's in three dimensions right which means for all higher dimensions it's also not true because I can just take like uh consider the trivial map where I take a function of four dimensions >> um let's say xyz and t is our fourth dimension in allah relativity um x y and z do what that function was doing and t just points to t right so the time doesn't change that is going to have the the same Jacobian determinant and the

1:24:54things are going to point to the same point in 3D space and the time doesn't change right I can do that for n equals 5 n equals 6 any dimension greater than three now so this is disproved all dimensions greater than three >> right so the it's only true in two >> yeah now it's like now it's an open question >> oh right because we don't know