AI Disproves Jacobian Conjecture (87 year old math problem)
(www.youtube.com)
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All it has to do is find a single example where the conjecture is false.
Sure, but if it's that easy, why wouldn't humans and simple computer programming not have found it?
Finding the counter example is difficult, verifying it is easy.
You can't brute force a counter example because the problem space of "all polynomial functions" is too large. A simple program isn't enough. You need to be clever.
But if it's difficult, why should we assume that the vaunted Mythos did it? I mean, I'm not even saying that it's impossible, only that we should take a wait and see approach than a hype train.
What level of proof would convince you that claude did it, and that it wasn't secretly done by a person?
You can infact brute force the problem space to find a counter example, it's called getting lucky. You cannot search the entire space to prove there are no counter-examples.
Because there are nearly infinite possibilities? It could be just a matter of trying a ton of stuff and eventually finding the needle in the haystack.
Disclaimer: I am not at all familiar with this particular proof, just proofs in general.
I'm not really seeing the advantage of AI there. If I wanted to generate a ton of possibilities, I'd write a script - not tell the most expensive AI to do it.
Disclaimer: I'm a total mathematical illiterate.
Tell me you've never written code without telling me you've never written code.
And, quite possibly, add "done math" to that statement as well.
Everything is obvious once it's already been found.