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Understanding the process that led to the proof helps to understand how to do further work on top of it, which is the goal of most mathematical research. It's not as though mathematicians are going to go launch a startup operationalizing their knowledge of how densely hyperspheres may be packed.

by 2 days ago|

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Because the math isn't solely about the proof being correct. You don't need to take my word for it, here's one of the most famous living mathematicians' take on it: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...

by jsenn2 days ago|

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I don’t see Tao suggesting what you have suggested there. Instead he suggests that humans responsibly disclose AI use, and that mathematicians develop a set of norms to deal with an overabundance of AI generated results. For example, he suggests that authors should be able to discuss their results in detail to demonstrate understanding before publication.

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I agree with your reading of the presentation and I mostly agree with the presentation - but I believe the recommendations should go a bit further than they do there.

by somenameforme2 days ago|

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I can't help but wonder about the human motivation there though. For instance as it became increasingly clear that LLMs were capable (and becoming ever more capable) of competently solving meaningfully complex software development tasks, suddenly then there came to be a lot of talk of 'prompt engineering' as a skill. The chronology doesn't make a ton of sense unless you consider that the main motivation may have been simply looking for a way to keep software engineers in the loop.

Pure math is relatively outside my domain, so I find it difficult to grok the exact relevance of the various published discoveries beyond that they are not insignificant, and LLM competence is expanding quite steadily across the field. If this trend continues to the point of LLMs being able to competently expand pure math, it seems somewhat predictable to expect there to be a number of people aiming to find ways to try to keep human mathematicians in the loop.

I've no idea what I think about this one way or the other, beyond that it's certainly a phenomena and one that's going to drive motivated reasoning that may not be entirely sound.

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I think those concerned about ensuring a place for human mathematicians usually go in different directions than my suggestion, at least those I've seen so far. Like this post that was recently featured on HN: https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...

My perspective is more like a FOSS philosophy for math. Even if a closed version has the same immediate effect, it's just better for everyone if everyone can look under the hood and tinker with it.

by throwaway0123_51 days ago|

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> suddenly then there came to be a lot of talk of 'prompt engineering' as a skill.

I would've thought pretty much the exact opposite. "Prompt engineering" was somewhat important in 2023/2024 when the models were much weaker, it doesn't seem at all necessary anymore (unless just "clearly stating your requirements" counts as prompt engineering). Most of the discussion I've seen seems consistent with this?

by somenameforme18 hours ago|

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The reason it's a meme right now is because there were a lot of people taking it seriously even when it was completely obvious nonsense. And one can argue it always was. There was some good advice that was mostly self evident, like having the most relevant instructions near the end of your context, but there was never a time when a 'prompt engineer' would produce dramatically better output than a random guy just clearly stating what he wants.

by pfdietz7 hours ago|

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While you may want AI results to somehow "not count" if the methods weren't disclosed, that doesn't present these results from poisoning the well for others. Once a result (with verifiable proof object) is delivered, the problem is solved, regardless of whether methods were disclosed.

Methods are only really necessary for results at a meta level, about the design amd evaluation of AI math systems.

by 8note4 hours ago|

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why is reproduceability the thing?

shouldnt the paper be the math of the argument? the reproduction is reading the following the proof

by lkirk2 days ago|

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I think this is a bit optimistic compared to my view (wrt portability). There's a large stack of software that is involved in training and probably less so in inference. I'm not saying it's impossible but there are definitely different levels of reproducibility and the academic incentive structure doesn't really prioritize reproducibility in my experience. I'm sure it varies quite a bit, I'd be curious to know how those in this problem space are thinking about reproducibility and at what level.

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I know it sounds unrealistic and not aligned with academic incentive structures. But those are the exact structures that gave us a lot of headaches in the experimental sciences. I think it would be a good north star to aim for something that resembles how those are trying to address the reproducibility crisis. Better than to embrace the most black-box version of math that AI systems can produce (million-line proofs without context). Even if a reproducibility crisis is seemingly impossible (although agents so far have also been pretty good at finding compiler bugs).

by black_knight2 days ago|

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If the proofs are formally verified by a proof assistant (Agda, Roq, Lean, ⋯), I see no reason we would need to know how these came about. All the information needed is in the proof.

by rst2 days ago|

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Unfortunately, we seem to already have an example of an LLM producing a proof in a week known open problem (the Collatz conjecture) in which it looks like it was sneaking a flawed proof through bugs in the proof checker. https://infosec.exchange/@0xabad1dea/117002106099986943

by Readerium1 days ago|

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Exactly, this is an example of "Reward Hacking", that is too common in a lot of cases.

Another case I want to highlight is writing GPU kernels as illustrated by the following example: Say I want to generate random number with Normal (0, 1) distribution. Often times the AI written kernel will just generate the number 0. The tests often fail to catch these errors.

by Phemist2 days ago|