AI Disproves Jacobian Conjecture (87 year old math problem)
(www.youtube.com)
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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.