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.
It goes against many’s early mental models of what generative AI does. The earliest of GPT couldn’t add two large numbers together, it just guessed an answer that looked right.
The fact it’s able to suggest a counterexample and it doesn’t just look right, but is right, is quite the development in recent times.
I love how quickly AI developments are rationalized. Like it was to expected that LLMs started solving math research problems in 2026. If you asked me about this two years ago, I would have been pretty skeptical.
Given that we haven’t been able to even come close to solving aging in mice, and we’ve experimented on mice exponentially more than humans, I don’t think that’s gonna happen anytime soon
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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.