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The Maxwell Conjecture Is False (GPT 5.6 Sol)

arxiv.org

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Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#21

Post by _jayhack_ »

pdonis wrote: post #15
beernet wrote: post #5

On the one-hand side, it's really impressive how LLMs drive mathematics forward, and this pace is only accelerating very quickly. 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…

> 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) How do you know they're correct if they're super messy and chaotic?

formal verifiability e.g. vi Lean

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#23

Post by muglug »

echelon wrote: post #20
chorsestudios wrote: post #13

Earlier quoted context omitted.

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.

Even if you use AI tools?

Yes. But you’ll spend more in tokens than you’ll get back from prize money.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#24

Post by gjskngnf »

JPLeRouzic wrote: post #14

Please, what does that mean for Maxwell equations? For electromagnetism? (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.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#25

Post by d_burfoot »

Tip for smart science-y young people: think about a career in experimental physics. Experimental data is the complement of theoretical power. Since theory can be provided cheaply by LLMs, experimental ability is now the bottleneck for progress in physics.

I expect to see frontier labs or startups hiring experimentalists to provide data for LLMs to analyze, pushing towards breakthroughs in areas like room-temperature superconductors and fusion.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#26

Post by jmalicki »

HawtAds wrote: post #19
beernet wrote: post #5

On the one-hand side, it's really impressive how LLMs drive mathematics forward, and this pace is only accelerating very quickly. 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…

> LLMs do not care about "elegance" the way human beings do, which is a big advantage. 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've actually been involved in annotation projects doing RLHF to train LLMs to do exactly that. It's not a matter of time, it's already happening - it's just seemingly lower priority than "profitable" projects like post-training LLMs to replace white collar workers.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#28

Post by tcp_handshaker »

jmalicki wrote: post #26
HawtAds wrote: post #19

Earlier quoted context omitted.

> LLMs do not care about "elegance" the way human beings do, which is a big advantage. 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've actually been involved in annotation projects doing RLHF to train LLMs to do exactly that. It's not a matter of time, it's already happening - it's just seemingly lower priority than "profitable" projects like post-training LLMs to replace white collar workers.

>> post-training LLMs to replace white collar workers.

And I look forward to a single example where this happened....

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#29

Post by mellosouls »

Not to denigrate the moment (AI ingress into theory which this is a part of) or the result here, but these headlines are perhaps overstating the importance - some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important.

Maxwell's name being invoked here for instance implies a hundred year old foundational problem like Fermat, but it's just a recent conjecture that was inspired by reflections from the great man on his work.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#30

Post by js8 »

beernet wrote: post #5

On the one-hand side, it's really impressive how LLMs drive mathematics forward, and this pace is only accelerating very quickly. 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…

I agree, counterexample to P!=NP would be great. I tried but it's a mess.
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