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Comment by blackcatsec | Hacker News Reader

This is a way too simplistic model of the things humans provide to the process. Imagination, Hypothesis, Testing, Intuition, and Proofing.

An AI can probably do an 'okay' job at summarizing information for meta studies. But what it can't do is go "Hey that's a weird thing in the result that hints at some other vector for this thing we should look at." Especially if that "thing" has never been analyzed before and there's no LLM-trained data on it.

LLMs will NEVER be able to do that, because it doesn't exist. They're not going to discover and define a new chemical, or a new species of animal. They're not going to be able to describe and analyze a new way of folding proteins and what implication that has UNLESS you basically are constantly training the AI on random protein folds constantly.

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I think you are vastly underestimating the emergent behaviours in frontier foundational models and should never say never.

Remember, the basis of these models is unsupervised training, which, at sufficient scale, gives it the ability to to detect pattern anomalies out of context.

For example, LLMs have struggled with generalized abstract problem solving, such as "mystery blocks world" that classical AI planners dating back 20+ years or more are better at solving. Well, that's rapidly changing: https://arxiv.org/html/2511.09378v1

No idea how underestimate things are, but marketing terms like "frontier foundational models" don't help to foster trust in a domain hyperhyped.

That is, even if there are cool things that LLM make now more affordable, the level of bullshit marketing attached to it is also very high which makes far harder to make a noise filter.

>Hey that's a weird thing in the result that hints at some other vector for this thing we should look at

Kinda funny because that looked _very_ close to what my Opus 4.6 said yesterday when it was debugging compile errors for me. It did proceed to explore the other vector.

> Especially if that "thing" has never been analyzed before and there's no LLM-trained data on it.

This is the crucial part of the comment. LLMs are not able to solve stuff that hasn't been solve in that exact or a very similar way already, because they are prediction machines trained on existing data. It is very able to spot outliers where they have been found by humans before, though, which is important, and is what you've been seeing.

""Hey that's a weird thing in the result that hints at some other vector for this thing we should look at." "

This is very common already in AI.

Just look at the internal reasoning of any high thinking model, the trace is full of those chains of thought.

But just like how there were never any clips of Will Smith eating spaghetti before AI, AI is able to synthesize different existing data into something in between. It might not be able to expand the circle of knowledge but it definitely can fill in the gaps within the circle itself

> LLMs will NEVER be able to do that, because it doesn't exist.

I mean, TFA literally claims that an AI has solved an open Frontier Math problem, descibed as "A collection of unsolved mathematics problems that have resisted serious attempts by professional mathematicians. AI solutions would meaningfully advance the state of human mathematical knowledge."

That is, if true, it reasoned out a proof that does not exist in its training data.

It generated a proof that was close enough to something in its training data to be generated.

Do you know that from reading the proof, or are you just assuming this based on what you think LLMs should be capable of? If the latter, what evidence would be required for you to change your mind?

- Edit: I can't reply, probably because the comment thread isn't allowed to go too deep, but this is a good argument. In my mind the argument isn't that coding is harder than math, but that the problems had resisted solution by human researchers.

1) this is a proof by example 2) the proof is conducted by writing a python program constructing hypergraphs 3) the consensus was this was low-hanging fruit ready to be picked, and tactics for this problem were available to the LLM

So really this is no different from generating any python program. There are also many examples of combinatoric construction in python training sets.

It's still a nice result, but it's not quite the breakthrough it's made out to be. I think that people somehow see math as a "harder" domain, and are therefore attributing more value to this. But this is a quite simple program in the end.

One of the possible outcomes of this journey is that “LLMs can never do X”. Another is that X is easier than we thought.

Or that some quixotic problems nobody cared about to the extent to actually work on them do have some solution.

That may be, and we can debate the level of novelty, but it is novel, because this exact proof didn't exist before, something which many claim was not possible with AI. In fact, just a few years ago, based on some dabbling in NLP a decade ago, I myself would not have believed any of this was remotely possible within the next 3 - 5 decades at least.

I'm curious though, how many novel Math proofs are not close enough to something in the prior art? My understanding is that all new proofs are compositions and/or extensions of existing proofs, and based on reading pop-sci articles, the big breakthroughs come from combining techniques that are counter-intuitive and/or others did not think of. So roughly how often is the contribution of a proof considered "incremental" vs "significant"?

Well, for one the proof would have to use actual proof techniques.

What really happened here was that the LLM produced a python script that generated examples of hypergraphs that served as proof by example.

And the only thing that has been verified are these examples. The LLM also produced a lot of mathematical text that has not been analyzed.

I see, thanks for the explanation!

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