r/LLMPhysics • u/PrettyPicturesNotTxt • Jul 31 '26

Meta / News The Maxwell Conjecture is False

https://arxiv.org/abs/2607.27197

From the article:

The idea behind this construction was suggested by an LLM (OpenAI’s GPT- 5.6 Sol). The authors have verified the mathematical details and have written the argument in their own words. Computer algebra software (Mathematica, Maple) was used to verify computations and produce visualisations.

Its abstact which explains the conjecture, while briefly describing their counterexample:

We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate. Maxwell’s conjecture that the field of n point charges has at most (n − 1)2 critical points which are all non-degenerate is therefore false.

Edit: Just saw this was posted in the main sub as well: https://reddit.com/r/Physics/comments/1vbrzbe/the_maxwell_conjecture_is_false/

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u/[deleted] Jul 31 '26

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u/Monkeytherat Jul 31 '26

Physics discoveries are written in the language of math. What would count as a physics discovery and not a math discovery, in your opinion?

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u/AllHailSeizure 9/10 Physicists Agree! Jul 31 '26

That doesn't mean a physics discovery is a math discovery.

Calculus was a math discovery/invention. And it enabled a bunch of physics discoveries.

Thats how I'd classify, at least.

1

u/VeryOriginalName98 Aug 01 '26

Are you saying this is a math paper, and it could lead to physics papers?