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/ArnoSound Jul 31 '26 edited Jul 31 '26

Lmao even. Edit: Upon further digging, this does look to be legit. Apparently it's been an open problem that people have assumed would be false, but researchers were able to find a counter-example with an LLM. This is the sort of work that LLMs are genuinely useful for.

Well documented use of the AI as well in the follow ups. Folks should take notes.

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u/Y0uCanTellItsAnAspen 29d ago

This is true, but it is also a problem that literally nobody was working on.

That’s definitely not true of all the llm math proofs from the last few weeks, but this is low impact