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Notes -
Litt is almost certainly correct that "Fields Medal" is overselling it, but I think "very impressive" is still underselling it. This was roughly a top-50 open problem in mathematics, one famous for attracting flawed "proofs". A restricted version of the conjecture had been open for nearly a century before being proven. The full conjecture was open for over 80 years. One of the most successful 21st century number theorists had his math career derailed by spending his PhD on the Jacobian conjecture with unimpressive results.
I think my biggest reason for epistemic caution here is that this wasn't a case of "AI disproving the Jacobian conjecture", it's a case of "AI led by a Princeton math PhD disproving the Jacobian conjecture", and I haven't yet seen which half of that team was responsible for which ideas in the derivation. From a quick glance at Alpöge's dissertation and senior thesis, I guess he seems to be more of an Algebraic-geometry guy than an algebraic-Geometry guy, but he still seems to be comfortable with the sorts of algebraic geometry tools that were likely used to derive his example. It's possible that Fable did most of the heavy lifting and Alpöge's critical contribution was "being an Anthropic employee with unlimited Fable access", but it might not be a total coincidence that he's not a number theorist or a topologist or something.
Steve Smale (a Fields Medal winner) listed it as #16, and I'm not finding other famous lists definitively disagreeing. That still doesn't mean its solution ranks as #16, of course - at this point people were expecting a proof requiring brilliant new mathematical techniques, whereas the general ideas leading to the counterexample appear to fit in a tweet - but it does mean that it was a problem that some of the best minds in the world were considering, over the course of decades.
Just learned his PhD advisor was Manjul Bhargava, a Fields Medal winner for algebraic geometry work. Bhargava's work also seems to be more interested in geometry with number fields other than with boring old ℂ, though.
Apparently GPT reverse-engineered the ideas in that tweet above after looking at the counterexample's equations? Again, the guy prompting it is an algebraic geometer, but he still had to prompt it.
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