Seems like that anyone can now prove math conjecture. Maybe someone already prove some math problem and is not even aware of it.
On the one-hand side, it's really impressive how LLMs drive mathematics forward, and this pace is only accelerating very quickly.<p>At the same time, most of the proofs I've looked at appear super messy and chaotic to me (while still being correct of course, so it doesn't matter). LLMs do not care about "elegance" the way human beings do, which is a big advantage. LLMs for mathematics is such a great fit on many levels. Can't wait for a significant breakthrough, prove P=NP and all hell breaks loose.
> <i>LLMs do not care about "elegance" the way human beings do, which is a big advantage.</i><p>It's just a matter of time before you can post train it for elegance too. Mathematical proofs in particular can be formally verified automatically which is a big advantage.
<i>> most of the proofs I've looked at appear super messy and chaotic to me (while still being correct of course, so it doesn't matter)</i><p>How do you know they're correct if they're super messy and chaotic?
Sure they care about elegance, or at least brevity. Minimizing tokens out, or generally "token efficiency," is part of the objective function for these systems. It doesn't mean they are perfect at it though.
> Minimizing tokens out, or generally "token efficiency," is part of the objective function for these systems.<p>First time I heard that, and I doubt it. Don’t customers pay for output tokens? If so, why would a company specifically spend time training their LLM to generate fewer?
You clearly haven't used Claude to generate code or documentation.
Please, what does that mean for Maxwell equations? For electromagnetism?<p>(Wikipedia redirects Maxwell's conjecture to Maxwell equations).
The Maxwell conjecture is a toy problem. The existence or nonexistence of a bound on the number of equilibrium points in an electrostatic arrangement of point charges doesn’t change much. I say that as an EE but not a specialist in electromagnetism.
<i>> what does that mean for Maxwell equations?</i><p>Nothing. They're still just as valid as they were before.<p><i>> For electromagnetism?</i><p>In practical terms, nothing significant. It's not going to change how anyone builds devices that use electromagnetism.
Ok, who gets the credit?<p>Does this work like a bug bounty program, where OpenAI pays you if you find a nice application for ChatGPT?
No but the Clay Mathematics Institute will give you $1,000,000 if you solve one of the 6 remaining Millennium Prize Problems, and if you solve certain Erdos problems you can get $10-10,000.
This is so inelegant I can't tell if it's accurate or not. ...On the other hand, I can't solve it myself.
Looks like the figures are cut off?