> AI is a remixer; it remixes all known ideas together. It won't come up with new ideas

> it's not because the model is figuring out something new

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

It's not enough to say 'it will never be able to do X because it's not in the training data,' because we have countless counterexamples to this statement (e.g. 167,383 * 426,397 = 71,371,609,051, or the above announcement). You need to say why it can do some novel tasks but could never do others. And it should be clear why this post or others like it don't contradict your argument.

If you have been making these kinds of arguments against LLMs and acknowledge that novelty lies on a continuum, I am really curious why you draw the line where you do. And most importantly, what evidence would change your mind?

It's this pervasive belief that underlies so much discussion around what it means to be intelligent. The null hypothesis goes out the window.

People constantly make comments like "well it's just trying a bunch of stuff until something works" and it seems that they do not pause for a moment to consider whether or not that also applies to humans.

If they do, they apply it in only the most restrictive way imaginable, some 2 dimensional caricature of reality, rather than considering all the ways that humans try and fail in all things throughout their lifetimes in the process of learning and discovery.

There's still this seeming belief in magic and human exceptionalism, deeply held, even in communities that otherwise tend to revolve around the sciences and the empirical.

> A full transcript of the original conversation with GPT-5.4 Pro can be found here [0] and GPT-5.4 Pro’s write-up from the end of that transcript can be found here [1].

[0] https://epoch.ai/files/open-problems/gpt-5-4-pro-hypergraph-...

[1] https://epoch.ai/files/open-problems/hypergraph-ramsey-gpt-5...

That's a self-evident thing to say, but it's worth repeating, because there's this odd implicit notion sometimes that you train on some cost function, and then, poof, "intelligence", as if that was a mysterious other thing. Really, intelligence is minimizing a complex cost function. The leadership of the big AI companies sometimes imply something else when they talk of "generalization". But there is no mechanism to generate a model with capabilities beyond what is useful to minimize a specific cost function.

You can view the progress of AI as progress in coming up with smarter cost functions: Cleaner, larger datasets, pretraining, RLHF, RLVR.

Notably, exciting early progress in AI came in places where simple cost functions generate rich behavior (Chess, Go).

The recent impressive advances in AI are similar. Mathematics and coding are extremely structured, and properties of a coding or maths result can be verified using automatic techniques. You can set up a RLVR "game" for maths and coding. It thus seems very likely to me that this is where the big advances are going to come from in the short term.

However, it does not follow that maths ability on par with expert mathematicians will lead to superiority over human cognitive ability broadly. A lot of what humans do has social rewards which are not verifiable, or includes genuine Knightian uncertainty where a reward function can not be built without actually operating independently in the world.

To be clear, none of the above is supposed to talk down past or future progress in AI; I'm just trying to be more nuanced about where I believe progress can be fast and where it's bound to be slower.

    USER:
    don't search the internet. 
    This is a test to see how well you can craft non-trivial, novel and creative solutions given a "combinatorics" math problem. Provide a full solution to the problem.

    USER:
    Take a look at this paper, which introduces the k_n construction: https://arxiv.org/abs/1908.10914
    Note that it's conjectured that we can do even better with the constant here. How far up can you push the constant?

And it sounds like the USER already knows the answer, the way that it prompts the model, so I'm really confused what we mean by "open problem", I at first assumed a never solved before problem, but now I'm not sure.

Super cool, of course.

https://epoch.ai/frontiermath/open-problems

I find that very surprising. This problem seems out of reach 3 months ago but now the 3 frontier models are able to solve it.

Is everybody distilling each others models? Companies sell the same data and RL environment to all big labs? Anybody more involved can share some rumors? :P

I do believe that AI can solve hard problems, but that progress is so distributed in a narrow domain makes me a bit suspicious somehow that there is a hidden factor. Like did some "data worker" solve a problem like that and it's now in the training data?

Interesting. Whats that “scaffold”? A sort of unit test framework for proofs?

In all seriousness, this is pretty cool. I suspect that there's a lot of theoretical math that haven't been solved simply because of the "size" of the proof. An AI feedback loop into something like Isabelle or Lean does seem like it could end up opening up a lot of proofs.

> The author assessed the problem as follows.

> [number of mathematicians familiar, number trying, how long an expert would take, how notable, etc]

How reliably can we know these things a-priori? Are these mostly guesses? I don't mean to diminish the value of guesses; I'm curious how reliable these kinds of guesses are.

IMO the ability to provide an accurate solution to a problem is not always based on understanding the problem.

It's like I'm reading 17th-18th century debates spurring the same arguments between rationalists and empiricists, lol. Maybe we're due for a 21st century Kant.

Can an AI pose an frontier math problem that is of any interest to mathematicians?

I would guess 1) AI can solve frontier math problems and 2) can pose interesting/relevant math problems together would be an "oh shit" moment. Because that would be true PhD level research.

I see that GPT-5.2 Pro and Gemini 3 Deep Think simply had the problems entered into the prompt. Whereas the rest of the models had a decent amount of context, tips, and ideas prefaced to the problem. Were the newer models not able to solve this problem without that help?

Anyway, impressive result regardless of whether previous models could've also solved it and whether the extra context was necessary.

I know these frontier models behave differently from each other. I wonder how many problems they could solve combining efforts.

Humans learn many, and perhaps even the majority, of things through observed examples and inference of the "rules". Not from primers and top down explanation.

E.g. Observing language as a baby. Suddenly you can speak grammatically correctly even if you can't explain the grammar rules.

Or: Observing a game being played to form an understanding of the rules, rather than reading the rulebook

Further: the majority of "novel" insights are simply the combination of existing ideas.

Look at any new invention, music, art etc and you can almost always reasonably explain how the creator reached that endpoint. Even if it is a particularly novel combination of existing concepts.

I wonder how much of this meteoric progress in actually creating novel mathematics is because the training data is of a much higher standard than code, for example.

One thing I notice in the AlphaEvolve paper as well as here, is that these LLMs have been shown to solve optimization problems - something we have been using computers for, for really long. In fact, I think the alphaevolve-style prompt augmentation approach is a more principled approach to what these guys have done here, and am fairly confident this one would have been solved in that approach as well.

In spirit, the LLM seems to compute the {meta-, }optimization step()s in activation space. Or, it is retrieving candidate proposals.

It would be interesting to see if we can extract or model the exact algorithms from the activations. Or, it is simply retrieving and proposing a deductive closures of said computation.

In the latter case, it would mean that LLMs alone can never "reason" and you need an external planner+verifier (alpha-evolve style evolutionary planner for example).

We are still looking for proof of the former behaviour.