The Maxwell Conjecture Is False (GPT 5.6 Sol) • Hacker News Board

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

#11

Post by Someone » Fri, Jul 31, 2026, 2:30 PM UTC

dcsommer wrote: post #6

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…

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.

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?

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

#12

Post by yreg » Fri, Jul 31, 2026, 2:38 PM UTC

Someone wrote: post #11

dcsommer wrote: post #6

Earlier quoted context omitted.

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. 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?

So they can charge more per token and decrease the pressure on their infra.

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

#13

Post by chorsestudios » Fri, Jul 31, 2026, 2:38 PM UTC

amelius wrote: post #9

Ok, who gets the credit? 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.

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

#14

Post by JPLeRouzic » Fri, Jul 31, 2026, 2:43 PM UTC

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

(Wikipedia redirects Maxwell's conjecture to Maxwell equations).

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

#15

Post by pdonis » Fri, Jul 31, 2026, 2:45 PM UTC

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?

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

#16

Post by KPGv2 » Fri, Jul 31, 2026, 2:47 PM UTC

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?

I've driven back roads in Ireland. Super messy and chaotic. I was still able to use a map to get to my destination.

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

#17

Post by pdonis » Fri, Jul 31, 2026, 2:48 PM UTC

JPLeRouzic wrote: post #14

Please, what does that mean for Maxwell equations? For electromagnetism? (Wikipedia redirects Maxwell's conjecture to Maxwell equations).

> what does that mean for Maxwell equations?

Nothing. They're still just as valid as they were before.

> For electromagnetism?

In practical terms, nothing significant. It's not going to change how anyone builds devices that use electromagnetism.

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

#18

Post by KPGv2 » Fri, Jul 31, 2026, 2:48 PM UTC

nelox wrote: post #10

senorrib wrote: post #7

Earlier quoted context omitted.

You clearly haven't used Claude to generate code or documentation.

"First rule in government spending: why build one when you can have two at twice the price" - S.R. Hadden

Personally, I've found city roads to be more reliable than the private roads where I live.

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

#19

Post by HawtAds » Fri, Jul 31, 2026, 2:50 PM UTC

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.

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

#20

Post by echelon » Fri, Jul 31, 2026, 2:51 PM UTC

chorsestudios wrote: post #13

amelius wrote: post #9

Ok, who gets the credit? 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.

Even if you use AI tools?