It would be great if an LLM could settle the Collatz conjecture next, god knows how many man-years have been burned on that by unsuspecting victims.
Many people believed the same about the Jacobian Conjecture.
Again, this is all non sequitur, because the context was a statement that most mathematicians believe the CC to be true, in which case there would be no "clean up".
... Or would it? The Jacobian counterexample seems like an especially simple, near-trivial integer-coefficient polynomial, but I haven't seen any thorough analysis of how "hard" it would have been to find by brute force, and I haven't seen Claude's reasoning.
Pretty hard. I asked Fable and it gave an estimate of 10^46 candidates in the counterexample's "reference class", and that's assuming you know how many distinct terms there are (as opposed to searching all polynomials of degree 7/6/4 for the three coordinates, which it estimates at 10^334).
"waste their time trying to prove it" is the MBA approach, where you should spit out results and articles.
Outside the MBA-thinking box, attacking hard problems, even unsuccessfully, is the way to gain deeper insight into various results and tools that you can later apply to other problems, i.e. no waste of time at all, unless you go to the extremes (like spending years on a single problem and nothing else).
Ergo: > “This is a really dangerous problem. People become obsessed with it and it really is impossible,” said Jeffrey Lagarias, a mathematician at the University of Michigan and an expert on the Collatz conjecture.
and
> “Collatz is a notoriously difficult problem — so much so that mathematicians tend to preface every discussion of it with a warning not to waste time working on it,” said Joshua Cooper of the University of South Carolina in an email.
(from https://www.quantamagazine.org/mathematician-proves-huge-res... )