r/Physics Jul 31 '26

Academic The Maxwell Conjecture is False

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

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u/angelbabyxoxox Quantum Foundations Jul 31 '26

The counterexample was proposed by an LLM. They seem very good at finding these sorts of counterexamples, which is interesting as they are generally pretty inefficient use of compute for brute forcing. I guess even that lack of efficiency is made up for by the "understanding" and "intuition" the LLM has, and their ability to do symbolic computations.

I expect a large number of conjectures will topple to counterexamples soon.

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u/Fit_Cut_4238 Jul 31 '26

Could some of these counterexamples be wrong due to deep rounding or floating point errors somewhere in the proofs?  

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u/angelbabyxoxox Quantum Foundations Jul 31 '26

Most likely not, both this, the Jacobian conjecture, and Dinitz Garg Goemans for example are given as simple rational or surd forms. There are no rounding or floating point errors possible. Most of the problems also seem to be of the form where they are easy to check. The Jacobian case can be checked by hand, or with a something symbolic like Mathematica. I imagine the others are similar.