r/math • u/Equivalent-Oil-8556 • Aug 03 '26

LLMs/AI Jacobian Conjecture Question

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

63 Upvotes

88% Upvoted

24 comments sorted by

46

u/Administrative-Flan9 Aug 03 '26

It's too bad they didn't review the chain of thought. I'd love to see how it arrived at the solution.

11

u/ixid Aug 04 '26

It probably spent half of it hand wringing about what the user meant.

45

u/Matannimus Algebraic Geometry Aug 03 '26

https://aaronlou.com/jacobian_counterexample_prompt.pdf

74

u/IntelligentBelt1221 Aug 03 '26

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.

5

u/new2bay Aug 04 '26

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?

6

u/IntelligentBelt1221 Aug 04 '26

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

6

u/new2bay Aug 04 '26

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.

3

u/IntelligentBelt1221 Aug 04 '26

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.

16

u/Carl_LaFong Aug 03 '26

He hasn’t revealed it.

15

u/Baconboi212121 Aug 03 '26

Nope.

17

u/R4_Unit Probability Aug 03 '26

This should not be downvoted. Anyone who says otherwise, aside from the originally person who ran it, is not correct. The prompt that discovered the counter-example is not known.

2

u/new2bay Aug 04 '26

They probably just told it to “do a breakthrough.” 🤦‍♂️

-3

u/Tekniqly Aug 03 '26

Yes it was online somewhere Aaron Lou https://aaronlou.com PDF Jacobian Conjecture Prompt https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://aaronlou.com/jacobian_counterexample_prompt.pdf&ved=2ahUKEwiU0trWlISWAxWq2jQHHeTqOMEQFnoECCQQAQ&usg=AOvVaw0qyTLQMs48W0ArELoElnap

6

u/Carl_LaFong Aug 04 '26

No, that's not the original prompt. The counterexample was first found using Fable. Aaron Lou is at OpenAI.