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Mathematicians grapple with a ‘very rapid and very unsettling change’ as AI cracks yet another century-old problem (fortune.com)
submitted 3 months ago by to c/ai_@lemmy.world
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[–] [S] 14 points 3 months ago (8 children)

I'd be interested in understanding how Claude "helped" here, though AFAIK there are no details. I suspect it's something like using the LLM to run some kind of optimised/filtered brute-force search and maybe getting a bit lucky, but maybe I'm way off base.

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  • [–] 10 points 3 months ago (1 child)

    Matt Parker (stand up maths on YouTube) has a video from the last solved problem about how they did it.

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  • [–] [S] 10 points 3 months ago* (last edited 3 months ago)

    This one? https://www.youtube.com/watch?v=ZJ8KThKAfbs

    Edit: Huh, interesting. So there's a few things going on:

    1. In some cases, LLMs have pulled together pre-existing knowledge that had not been connected before (sometimes across languages).
    2. Brute-forcing is sometimes part-of it (with searches informed by existing research)
    3. There are languages like LEAN that allow formal proofs to be written out and then tested logically. I guess this means that LLMs now have access to testing the logical validity of statements, which is helping to make a bunch of these most recent breakthroughs.

    That last one is particularly interesting, I think, because it expands LLM capability from being language-focused (with interfaces for agentic work) to something that can actually understand (in a way) the validity of logical statements. I think it doesn't get it to an understanding of truths in general, because logic is always built from axioms, and it can't know the validity of the axioms (except by assumption). If I'm understanding things correctly)

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  • [–] 7 points 3 months ago (1 child)

    I'm also way more interested in the details than the average news article on how AI can do maths now. Like how did they home in on this specific problem to solve? Destiny? Did they brute-force it and try 5000 other unsolved maths problems first? Was it AI assisted or does AI do this on its own? What's the prompt? How many tokens did it burn through? Has it been lucky by chance or would I be able to input the same thing and there's a 90% chance it'll solve it again?

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  • [–] 5 points 3 months ago (3 children)

    Wikipedia already has a full write up. It looks like Fable simply found an example of a function that had a constant Jacobian determinant (the determinant of the matrix of partial derivatives), but the function was not injective (3 different values of x, y, and z give the function the same value). Basically, the function is not "smooth", so it can't be inverted.

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  • [–] [S] 3 points 3 months ago (2 children)

    Thanks for adding that link. I had already read it before posting. Unfortunately it doesn't include any meaningful details of how that function was found (presumably because the anthropic guy didn't provide any yet).

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