My take on Jacobian conjecture:
(1) Very bullish for near-term impact of AI on math. Probably lots more of these coming soon.
(2) If you think of the main goal of math research as “solving well-known open problems” (and IMO many people do think this, and it’s a defensible view): it’s a huge deal
(3) from the POV of doing good science: of interest because it resolves a natural Q, but plausibly not generative beyond that.
Personally I am most excited about (1), but (perhaps idiosyncratically) I don’t care much about this conjecture.
Assuming this is correct, it is for me the first example of an LLM solving a problem not in my area that was nevertheless big enough that I had very definitely heard of it. Again it's a counterexample, so not in "end of mathematics" territory, but still pretty amazing.
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)