Source: https://thejenkinscomic.wordpress.com/2026/07/21/world-cup-result/
For reference: https://en.wikipedia.org/wiki/Jacobian_conjecture
On July 19, 2026, the mathematician and Anthropic employee Levent Alpรถge presented an explicit counterexample in three-dimensional space, discovered using Claude Fable 5, Anthropic's large language model, which disproves the n {\displaystyle n}-variable conjecture for n > 2 {\displaystyle n>2}.[19][20][21] The counterexample had far-reaching consequences and provided insight into why many previous approaches to proving the conjecture had failed
I also found this reddit comment, offering an explanation / context: https://www.reddit.com/r/explainlikeimfive/comments/1v2k0tr/eli5_what_is_jacobian_conjecture/oyvsul6/
Best ELI5 for the Jacobian Conjecture is maps and Greenland.
If you zoom all the way out on Google Maps, Greenland looks huge. But if you look on a globe, it's not that big. That's because when you represent the surface of our spherical globe as a flat 2D surface, stuff gets warped and transformed.
You can represent the transformation from a sphere to a 2D plane as a polynomial function transformation. Any time you do a polynomial transformation, you can find something called the Jacobian Determinate that represents how much the equation warps the results. So for each map projection above you would get a constant determinate as the warp is consistent across the transformation.
The conjecture was that, if the Determinate ("warp factor") was not zero, there was always a reverse polynomial function to undo the transformation. Basically, if you can go from asphere to Mercator map projection you can also go from Mercator to a sphere. And you could use the same transformation and undo functions to map Mara or Jupiter or any planet not just Earth.
Conjectures like this are not proven rules, but they are considered true because you can't prove them false. Well, someone found a polynomial transformation that has a constant Jacobian Determinate but does not have a polynomial reverse. ~~Not that you can't undo the transformation, but that the "undo" function doesn't qualify as a polynomial. It requires other math methods~~ Edit: The equation that proves the Conjecture false can't be undone. And since we have an example of the conjecture being wrong, that means the whole thing is wrong.
