AI Disproves Jacobian Conjecture (87 year old math problem)
(www.youtube.com)
Comments (18)
sorted by:
I'll believe it when it's confirmed by actual mathematics specialists.
There was massive AI fraud recently by a student at MIT, who claimed all sorts of patents that never existed, and then created a fake website in a company's name.
You will get fraud like this when valuations of up to 1 trillion are at stake.
It's a mathematical claim. It's not something you can confidence game, it's verifiable.
Sure. I'd still rather hear from specialists than from random Twitter users saying OMG DID YOU HEAR WHAT AI DID TODAY?
I know I'm very obnoxious, and I apologize, but I find the AI hype very obnoxious too.
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?
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.
Someone not taking credit for it would be enough. I'd actually expect it the other way around, that if Claude found something that a human would try to take credit for it (assuming no affiliation with the company).
I'm just taking a wait-and-see approach. If leading mathematicians confirm, who am I to say they're wrong?
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.
This is true.
Everything is obvious once it's already been found.
All you have to do is find a function that does not have an inverse, and has a non-zero Det(). The way used by the paper was to find a function which was not one-to-one, while haveing a constant determinant.
Pretty much any math or physics undergrad should be able to work the counter example by the end of their second year.
Someone tried to post it to Wikipedia. It got removed even though basicmath can now disprove it :
https://x.com/gergomoricz/status/2079338795132916084