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PaperclipPerfector  7d ago (text post)   25105 thread views

Culture War Roundup for the week of April 13, 2026

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We formulated our understandings of the world and our interactions with it into techniques and theories, and when we build stuff we do so by employing those techniques and theories from a standpoint of engineering and design. LLMs are merely next word generators. They can recall many of the things in their databases and expurgate them to us, but their outputs aren't the products of strategically employed techniques and theories. This is inherently limiting for the complexity of the outputs they can give us.

I don't understand this claim. Who "we"? Most people learn almost everything they know about economically valuable complex domains from textbooks, manuals, teacher's answers and such second-hand information, and then polish it with on-site instructions and increasingly long-range, open-ended training. They don't build much in the way of their own "techniques and theories" and there's not a world of difference from what LLMs now do. Maybe you're overestimating how much they depend on pretraining at this point. Well, it's believed that >50% of compute in some of the last-generation models goes towards RL, not pretraining on human data.

And as I've said in the opening post: we have literally just seen an LLM employ a technique no human mathematician had thought of using in this specific context, to solve a problem that had remained unsolved since 1968 – over half a century! It wasn't some Riemann hypothesis tier challenge, but it wasn't exactly obscure either, smart professional mathematicians had been working on it for years before GPT 5.4 Pro came and did this. Moreover, GPT does this reliably. In the comments you can see Terence Tao, arguably the guy with the greatest knowledge of "techniques and theories" of math on the planet Earth, an expert of such level that he actively avoids getting roped into solving other people's frontier research level problems, seriously engage with GPT's work:

Thanks! So there does seem to be something special about the original von Mangoldt process - the associated invariant measure ν is extremely smooth (in the Archimedean sense), being asymptotic to 1/nlogn , while all the variants of this measure pick up arithmetic factors such as 1∏pvp(n)!

  • A little surprising to me that removing individual primes instead of prime powers makes it less likely to have prime multiplicity, but I'll chalk it up to one of the numerous probability paradoxes that arise when one tries to compare various weighted expectations. But these factors mean that one cannot immediately solve #1196 by using these processes instead of the von Mangoldt one, as the invariant measure is no longer asymptotic to 1/nlogn
  • So in some sense the AI was "lucky" in finding the one approach that actually worked; it would be interesting to publish the traces to see if there was a lot of brute force involved in trying nearby approaches which didn't quite work.

……

Arb Research has kindly shared with me ten separate runs of GPT 5.4 Pro on this problem #1196 (with a request not to use internet search). From a quick reading, it appears that 8 of them claimed successes, with the other 2 rating the claim as plausible. Interestingly, several of the successful runs actually obtained the sharper formula ∑n≤Aν(n)≤1 that was also derived here, with ν essentially the Mellin transform of 1/ζ(s)

  • Almost all of the runs latched on to the approach of constructing a random chain with a good hitting probability (many runs referred to this as the "Lubell method", after the Lubell of the LYM inequality).

Another notable fact is that none of the runs highlighted the von Mangoldt process that was a prominent feature of the original run (and none of them mention flow networks either). Runs 4 and 7 have an interesting alternate construction of the upward divisibility chain in terms of exponential clocks in the prime factorization indices that actually looks rather tractable to work with; I will need to study this construction further when I have more time.

Basically it seems that for this particular type of problem there are several natural ways to proceed that make the problem actually quite tractable; the literature had managed to focus on a somewhat suboptimal approach in which the opening move was to transfer the problem to a continuous setting, but the AI runs consistently stayed in the discrete world and managed to utilize various existing tools from discrete mathematics (mostly centering around methods relating to the LYM inequality) to reach a solution.

So I don't know. Where's this inherent limit on complexity that you're talking about? What in our culture is truly irreducibly complex, if not math that can surprise Terence Tao?

This is getting a bit comical, don't you think?

I must differ here as I do not see evidence (in domains I'm able to judge) of AI employing techniques and theory in its tasks. Ask it to mimic Stephen King and then compare the output to actual Stephen King. You'll understand what I mean.

I cannot speak to math here as I lack competency in that. But from what I hear from coders, its similar in that domain as well: AI can expurgate volumes of legible code, but it cannot utilize structure.

Humans have techniques and theories which inform their decisions high and low as they layer things together using judgement, intuition, etc., while AIs appear to generate text using probabilistic hacks. AI appears to be able to recreate low-complexity patterns from its dataset. I disagree that these processes are related except at a very basic level.

We have a good idea of how to train AI to solve mathematical problems, of virtually unbounded complexity. In the course of this, AI clearly learns "techniques" as shown here, if not "theories". I don't think King's prowess is theory-driven either, but in any case we don't have a good idea of how to train AI to be a good prose writer. We have some ideas, but are unlikely to act on them. There's not much money to be made in it, and plenty of highly motivated enmity – AI is already widely hated. and yes, autoregressive generation for the prompt "write like King" is not like King actually writing a novel. We have such tricks though.

My point is, it's not a general principle that AI will only rehash human techniques in some uninspired "probabilistic" way. If there is a hill to climb, such that "good" and "bad" outputs with regard to the problem statement can be distinguished, AI can bumble its way up the hill and also find new tricks. We've seen this before LLMs, with AlphaGo and move 37, we're starting to see it with LLMs.

while AIs appear to generate text using probabilistic hacks.

Human mind runs entirely on probabilistic mush. Neural networks were invented as approximation of our own approximate learning. But probabilistic decision processes can have clear enough decision boundaries that they become able to operate with "abstractions", "symbols" or "theories". They also remain able to fail. For example, you are failing to update on evidence, because you haven't been trained to take input like "Terry Tao is surprised" seriously and think it's infinitely less interesting than your preconceived notions, basically some dweeb noise. Unlike an LLM, you can update at lifetime, so maybe you'll reread the above post and see how it contradicts your position.

This is getting a bit comical, don't you think?

Seen on X:

"As the Earth is being disassembled:

"Guys, stop over-reacting! The concept of a Dyson Sphere was already in the training data!"

Heh. See, the AI making that Dyson Sphere doesn't have general intelligence, I bet it can't get the Wordle 6 days in a row like me.

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