A digestion of the Jacobian conjecture counterexample

> While this is an extremely quick verification, the construction presented in this fashion appears like a massive miracle. The polynomial {F} has degree seven, so a priori the Jacobian {\mathrm{det} DF} ought to be a polynomial in three variables of degree as large as {3 \times 6 = 18}, so the fact that all non-constant coefficients of this polynomial vanish looks like a massive cancellation involving {\binom{18+3}{3}-1 = 1329} coefficients, which is much larger than the {\binom{7+3}{3} = 120} degrees of freedom for a generic degree seven polynomial of three variables. So finding such a polynomial looks highly unlikely to be located by brute force.

Sounds like the most interesting part would be learning what approaches the LLM did use to see if that's reusable elsewhere. I'm guessing that's what the rest of the article is about? Because I also couldn't follow the maths any more.

The introduction to this piece was easy to follow, but as soon as he got into recapitulating it with algebra he lost me (because I'm bad at math). But he includes the GPT5 prompts for his conversation, which are easier to follow:

https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed...

Okay. So what does this overturn, intuitively? Can we no longer assume that functions are differentiable at certain points, or something?

Related:

Claude Fable produced a counterexample to the Jacobian Conjecture

https://news.ycombinator.com/item?id=48973869

Human mathematicians are being outcounterexampled

https://news.ycombinator.com/item?id=48983382

  Fable, explain the counterexample to the Jacobian conjecture intuitively. Make no mistakes.