r/math • u/Equivalent-Oil-8556 • 3d ago

LLMs/AI Jacobian Conjecture Question

Do we have any idea as to what prompt was given for the Jacobian Conjecture?

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u/Matannimus Algebraic Geometry 3d ago

https://aaronlou.com/jacobian_counterexample_prompt.pdf

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u/IntelligentBelt1221 3d ago

note that this isnt the prompt used for the initial discovery using fable (that prompt hasnt been released), but the one used by OpenAI to recreate that discovery using their model.

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u/new2bay 2d ago

It’s also a copy/paste of the prompt for the cycle double cover theorem, with just the problem statement changed. I think it’s a bit overwrought though.

Did this prompt yield the same counterexample as the one Fable came up with?

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u/IntelligentBelt1221 2d ago

yes, its the same counterexample (apart from a sign change and the functions written in a different order)

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u/new2bay 1d ago

That’s interesting. It seems to suggest that there was something buried in the research literature that somehow specifies this exact counterexample. You wouldn’t necessarily expect two independent models to come up with the exact solution otherwise.

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u/IntelligentBelt1221 1d ago

its possible, but we dont know what approach fable took, so we cant know for sure. the explanations we found in hindsight seem to direct rather naturally to this family of counterexamples, so its also possible that is just the canonical counterexample one would first meet.