The Maxwell Conjecture Is False (GPT 5.6 Sol)

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.

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

#6

Post by dcsommer » Fri, Jul 31, 2026, 2:15 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…

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.

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

#7

Post by senorrib » Fri, Jul 31, 2026, 2:17 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.

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

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

#8

Post by josefritzishere » Fri, Jul 31, 2026, 2:18 PM UTC

This is so inelegant I can't tell if it's accurate or not. ...On the other hand, I can't solve it myself.

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

#9

Post by amelius » Fri, Jul 31, 2026, 2:18 PM UTC

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?

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

#10

Post by nelox » Fri, Jul 31, 2026, 2:22 PM UTC

senorrib wrote: post #7

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.

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

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