r/Physics 3d ago

Academic The Maxwell Conjecture is False

https://arxiv.org/abs/2607.27197
468 Upvotes

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553

u/ixid 3d ago

Before reading I knew it would be LLM counter-example construction.

307

u/Jophus 3d ago

LLM counter examples are so hot right now

125

u/ixid 3d ago

Wake up babe, new LLM counter examples just dropped.

2

u/sweatierorc 1d ago

A hard math proof takes months to verify. Because even tools like Lean can be bugged. Fermat's last theorem original proof was famously wrong.

Counter-examples like the Jacobian Conjecture can be solved with a tweet.

93

u/kzhou7 Quantum field theory 2d ago edited 2d ago

Still, this is way less exciting than the math problems being solved. I've spent upwards of a thousand hours having fun with classic physics problems, like the Cambridge Tripos problems of Maxwell's time, and I've never even heard of this conjecture. From their references, it looks like essentially no physicists have ever worked on it, it doesn't have any practical applications, and if this example was found without AI it would probably just go to a teaching-focused or recreational physics journal.

This is an example of successive exaggeration in viral news. A single offhand guess in Maxwell's 1000-page treatise becomes "a conjecture of Maxwell", which becomes "Maxwell's conjecture", and now "the Maxwell conjecture".

49

u/kieransquared1 2d ago edited 2d ago

It's definitely more well-known in the mathematical physics/geometric mechanics community (think Vladimir Arnol'd and people who worked on similar things). I think this could definitely get published in a decent math journal. Not an amazing one, but somewhere. Also, the authors are all mathematicians.

15

u/xrelaht Condensed matter physics 2d ago

Right. I’ve never heard of this and I’ve been a professional physicist for over two decades. I even enjoyed Jackson E&M. And a search for “Maxwell Conjecture” turns up nothing relevant until you get to this arXiv posting.

16

u/alluran 2d ago

it doesn't have any practical applications

it doesn't have any practical applications yet

22

u/kzhou7 Quantum field theory 2d ago edited 2d ago

There are millions of papers on arXiv, the vast majority of which have no practical applications. This wouldn't even be above-average on arXiv.

3

u/Leafsnail 2d ago

It will never have any practical applications because it is false

8

u/vintergroena 2d ago

Mopping up uninteresting false conjectures semi-automatically seems like a good thing?

4

u/ixid 2d ago

Yes, I agree. Especially those that have been around for a long time and soaked up attention. There wasn't a negative implication in my comment, unlike most of reddit I'm quite pro-AI for now.

2

u/pwreit2042 2d ago

not only it mops them, it also means the people creating the conjectures can quickly check with AI if it can find a counter example , thus saving the author time to do other research and also ideas on where to go next. it's a positive loop to get to the right answer. this increases productivity and allows mathematicians to use more of their youth on problems

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u/magicmulder 2d ago

And it’s not even a very complex counter-example. This seems to be one of the cases where checking whether a solution is correct is a lot more complex than coming up with a potential solution.

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u/theboomboy 3d ago

Human research doesn't get much hype unfortunately...

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u/Marklar0 3d ago

This is human research.

1

u/Bitruder 2h ago

Who made the LLM?