AI Disproves Jacobian Conjecture (87 year old math problem)
(www.youtube.com)
You're viewing a single comment thread. View all comments, or full comment thread.
Comments (16)
sorted by:
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?
Well look at the work the "old school mathematician" who used Claude to do it has done.
He probably had the right idea and told Claude what to do. Try combinations on this and find one that's a counterexample. He's working at Anthropic so it may actually be against his personal interest to claim it was really his idea and Claude just made him faster.
When you look at how well they copy a picture they have full access to the whole time it's kind of hard to imagine them coming up a Mona Lisa of math all on their own.
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.