>> The model was perfectly capable of verifying its correctness.
It's an LLM. It can't do that.
It's an LLM. It can't do that.
A bunch of people on the original thread about the Conjecture were like "we need to wait and see if real mathematicians verify this proof it's probably just LLM psychosis", because they don't understand that the counterexample is a trivial calculation. Checking it isn't hard; any AP calc student can do it quickly. It's finding the counterexample that's the challenge.
It's as if someone presented a SHA-2 collision, which anyone could just feed to `openssl sha256` to see, and then naysayers were like "we need to wait for independent verification because the LLM can't know if that collision was real".
I don't know. Are you doing the thing were you're arguing against something you don't like that the other person never said?
Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.
Besides which you have no idea whether that's how the Jacobian conjecture counterexample was verified. Nobody does because no details were released.