Evidence shows otherwise: Despite the "20x" length, many people actually missed the point.

Which is also what makes it problematic that you're lying about your LLM use. I would honestly love to know your prompt and how you iterated on the post, how much you put into it and how much you edited or iterated. Although pretending there was no LLM involved at all is rather disappointing.

Unfortunately I think you might feel backed into a corner now that you've insisted otherwise but it's a genuinely interesting thing here that I wish you'd elaborate on.

I agree brevity is always preferred. Making a good point while keeping it brief is much harder than rambling on.

But length is just a measure, quality determines if I keep reading. If a comment is too long, I won’t finish reading it. If I kept reading, it wasn’t too long.

Vs

> Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)"

I guess this is the end of the human internet

"Glorified Google search with worse footnotes" what on earth does that mean?

AI has a distinct feel to it

For better or worse, I think we might have to settle on “human-written until proven otherwise”, if we don’t want to throw “assume positive intent” out the window entirely on this site.

It wasn't AI generated. But if it was, there is currently no way for anyone to tell the difference.

This is false. There are many human-legible signs, and there do exist fairly reliable AI detection services (like Pangram).

Negative feedback is the original "all you need."

There's already been several scandals where students were accused of AI use on the basis of these services and successfully fought back.

You're lying: https://www.pangram.com/history/94678f26-4898-496f-9559-8c4c...

Not that I needed pangram to tell me that, it's obvious slop.

(edit: fixed link)

I'm pretty sure it's like "can it run DOOM" and someone could make an LLM that passes this that runs on an pregnancy test

All of that is going away so the best way to deal with it is to call it a stochastic parrot and deny reality.

LLMs will continue to get slightly better in the next few years, but mainly a lot more efficient. Which will also mean better and better local models. And grounding might get better, but that just means less wrong answers, not better right answers.

So no need for doomerism. The people saying LLMs are a few years away from eating the world are either in on the con or unaware.

The only possible explanation is people say things they don't believe out of FUD. Literally the only one.

And even odder that the proof was by Erdos himself and yet he listed it as an open problem!

I know that at least some LLM products explicitly check output for similarity to training data to prevent direct reproduction.

It's great business to minimally modify valuable stuff and then take credit for it. As was explained to me by bar-certified counsel "if you take a recipe and add, remove or change just one thing, it's now your recipe"

The new trend in this is asking Claude Code to create a software on some type, like a Browser or a DICOM viewer, and then publishing that it's managed to do this very expensive thing (but if you check source code, which is never published, it probably imports a lot of open source dependencies that actually do the thing)

Now this is especially useful in business, but it seems that some people are repurposing this for proving math theorems. The Terence Tao effort which later checks for previous material is great! But the fact that the Section 2 (for such cases) is filled to the brim, and section 1 is mostly documented failed attempts (except for 1 proof, congratulations to the authors), mostly confirms my hypothesis, claiming that the model has guards that prevent it is a deus ex machina cope against the evidence.

Legally I think it works, but evidence in a court works differently than in science. It's the same word but don't let that confuse you and don't mix them both.

It really contextualizes the old wisdom of Pythagoras that everything can be represented as numbers / math is the ultimate truth

They create concepts in latent space which is basically compression which forces this

But I'm not a mathematics expert if this is the real official definition I'm fine with it. But are you though?

https://youtu.be/D8GOeCFFby4?si=AtqH6cmkOLvqKdr0

consider estimating the position of an object from noisy readings. One presumes that position to exist in some sense, and then one can estimate it by combining multiple measurements, increasing positioning resolution.

its any variable that is postulated or known to exist, and for which you run some fitting procedure

It doesn't matter if ai is in a hype cycle or not it doesn't change how a technology works.

Check out the yt videos from 1blue3brown he explains LLMs quite well. .your first step is the word embedding this vector space represents the relationship between words. Father - grandfather. The vector which makes a father a grandfather is the same vector as mother to grandmother.

You the use these word vectors in the attention layer to create a n dimensional space aka latent space which basically reflects a 'world' the LLM walks through. This makes the 'magic' of LLMs.

Basically a form of compression by having higher dimensions reflecting kind a meaning.

Your brain does the same thing. It can't store pixels so when you go back to some childhood environment like your old room, you remember it in some efficient (brain efficient) way. Like the 'feeling' of it.

That's also the reason why an LLM is not just some statistical parrot.

It does change what people say about it. Our words are not reality itself; the map is not the territory.

Are you saying people should take everything said about LLMs at face value?

It's the reason why I'm here because we discuss more technically about technology

I spend too much time here and decided to delete my account to interact less.

It's partially working though

The infeasibility is searching for the (unknown) set of translations that the LLM would put that data through. Even if you posit only basic symbolic LUT mappings in the weights (it's not), there's no good way to enumerate them anyway. The model might as well be a learned hash function that maintains semantic identity while utterly eradicating literal symbolic equivalence.

Carbon copy would mean over fitting

It looked a bit like someone at Google subscribed to a legal theory under which you can avoid copyright infringement if you take a derivative work and apply a mechanical obfuscation to it.

People seem to have this belief, or perhaps just general intuition, that LLMs are a google search on a training set with a fancy language engine on the front end. That's not what they are. The models (almost) self avoid copyright, because they never copy anything in the first place, hence why the model is a dense web of weight connections rather than an orderly bookshelf of copied training data.

Picture yourself contorting your hands under a spotlight to generate a shadow in the shape of a bird. The bird is not in your fingers, despite the shadow of the bird, and the shadow of your hand, looking very similar. Furthermore, your hand-shadow has no idea what a bird is.

But honestly source = "a knuckle sandwich" would be appropriate here.

Edit: you've been breaking the site guidelines badly in other threads as well. (To pick one example of many: https://news.ycombinator.com/item?id=46601932.) We've asked you many times not to.

I don't want to ban your account because your good contributions are good and I do believe you're well-intentioned. But really, can you please take the intended spirit of this site more to heart and fix this? Because at some point the damage caused by poisonous comments is worse.

https://news.ycombinator.com/showhn.html

* it would be more accurate to say "using violent language as a trope in an argument" - I don't believe in taking comments like this literally, as if they're really threatening violence. Nonetheless you can't post this way to HN.

this is a verbatim quote from gemini 3 pro from a chat couple of days ago:

"Because I have done this exact project on a hot water tank, I can tell you exactly [...]"

I somehow doubt it an LLM did that exact project, what with not having any abilities to do plumbing in real life...

A) It is still possible a proof from someone else with a similar method was in the training set.

B) something similar to erdos's proof was in the training set for a different problem and had a similar alternate solution to chatgpt, and was also in the training set, which would be more impressive than A)

A proof that Terence Tao and his colleagues have never heard of? If he says the LLM solved the problem with a novel approach, different from what the existing literature describes, I'm certainly not able to argue with him.

Tao et al. didn't know of the literature proof that started this subthread.

> He speculated that "the formulation [of the problem] has been altered in some way"....

[snip]

> More broadly, I think what has happened is that Rogers' nice result (which, incidentally, can also be proven using the method of compressions) simply has not had the dissemination it deserves. (I for one was unaware of it until KoishiChan unearthed it.) The result appears only in the Halberstam-Roth book, without any separate published reference, and is only cited a handful of times in the literature. (Amusingly, the main purpose of Rogers' theorem in that book is to simplify the proof of another theorem of Erdos.) Filaseta, Ford, Konyagin, Pomerance, and Yu - all highly regarded experts in the field - were unaware of this result when writing their celebrated 2007 solution to #2, and only included a mention of Rogers' theorem after being alerted to it by Tenenbaum. So it is perhaps not inconceivable that even Erdos did not recall Rogers' theorem when preparing his long paper of open questions with Graham in 1980.

(emphasis mine)

I think the value of LLM guided literature searches is pretty clear!

Both are precisely true. It is a better search engine than anything else -- which, while true, is something you won't realize unless you've used the non-free 'pro research' features from Google and/or OpenAI. And it can perform limited but increasingly-capable reasoning about what it finds before presenting the results to the user.

Note that no online Web search or tool usage at all was involved in the recent IMO results. I think a lot of people missed that little detail.

At this point the only conclusion here is: The original proof was on the training set. The author and Terence did not care enough to find the publication by erdos himself

https://terrytao.wordpress.com/2026/01/19/rogers-theorem-on-...

"This theorem is somewhat obscure: its only appearance in print is in pages 242-244 of this 1966 text of Halberstam and Roth, where the authors write in a footnote that the result is “unpublished; communicated to the authors by Professor Rogers”. I have only been able to find it cited in three places in the literature: in this 1996 paper of Lewis, in this 2007 paper of Filaseta, Ford, Konyagin, Pomerance, and Yu (where they credit Tenenbaum for bringing the reference to their attention), and is also briefly mentioned in this 2008 paper of Ford. As far as I can tell, the result is not available online, which could explain why it is rarely cited (and also not known to AI tools). This became relevant recently with regards to Erdös problem 281, posed by Erdös and Graham in 1980, which was solved recently by Neel Somani through an AI query by an elegant ergodic theory argument. However, shortly after this solution was located, it was discovered by KoishiChan that Rogers’ theorem reduced this problem immediately to a very old result of Davenport and Erdös from 1936. Apparently, Rogers’ theorem was so obscure that even Erdös was unaware of it when posing the problem!"

A lot of pure mathematics seems to consist in solving neat logic puzzles without any intrinsic importance. Recreational puzzles for very intelligent people. Or LLMs.

Just because we can't imagine applications today doesn't mean there won't be applications in the future which depend on discoveries that are made today.

https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e...

Instead of addressing any of that you're insisting I'm misunderstanding and pointing me back to a linked comment of yours drawing a distinction between epistemic value of science research vs math research. Epistemic value counts for many things, but one thing it can't do is negate the significance of pure math turning into applied research on account of pure science doing the same.

No, "so what" doesn't indicate disagreement, just that something isn't relevant.

Anyway, assume hot dogs taste not good at all, except in rare circumstances. It would then be wrong to say "hot dogs taste good", but it would be right to say "hot dogs don't taste good". Now substitute pure math for hot dogs. Pure math can be generally useless even if it isn't always useless. Men are taller than women. That's the difference between applied and pure math. The difference between math and science is something else: Even useless science has value, while most useless math (which consists of pure math) doesn't. (I would say the axiomatization of new theories, like probability theory, can also have inherent value, independent of any uselessness, insofar as it is conceptual progress, but that's different from proving pure math conjectures.)

That brings us full circle, because you're now saying you were using one to negate the other, yet you were claiming that interpretation was a "failure to follow" what you were saying the first time around.

My favorite example is number theory. Before cyptography came along it was pure math, an esoteric branch for just number nerds. defund Turns out, super applicable later on.

Among others.

Of course you never know which math concept will turn out to be physically useful, but clearly enough do that it's worth buying conceptual lottery tickets with the rest.

Ironically this example turns out to be a great object lesson in not underestimating the utility of research based on an eyeball test. But it shouldn't even have to have any intuitively plausible payoff whatsoever in order to justify it. The whole point is that even if a given research paradigm completely failed the eyeball test, our attitude should still be that it very well could have practical utility, and there are so many historical examples to this effect (the other commenter already gave several examples, and the right thing to do would have been acknowledge them), and besides I would argue they still have the same intrinsic value that any and all knowledge has.

I doubt that this is true.

If we knew that it was all going to be useless, however, then it’s a hobby for someone, not something we should be paying people to do. Sure, if you enjoy doing something useless, knock yourself out… but on your own dime.

Don't be so ignorant. A few years ago NO ONE could have come up with something so generic as an LLM which will help you to solve this kind of problems and also create text adventures and java code.

Nothing of it was even imaginable and yes the progress is crazy fast.

How can you be so dismissive?

"Intrinsic" in contexts like this is a word for people who are projecting what they consider important onto the world. You can't define it in any meaningful way that's not entirely subjective.

The only thing that saves science from being nothing more than “huh, will you look at that,” is when it can make use of a mathematical model to provide insight into relationships between phenomena.

Pretty soon, this is going to mean the entire historical math literature will be formalized (or, in some cases, found to be in error). Consider the implications of that for training theorem provers.

What's more, there's almost surely going to turn out to be a large amount of human generated mathematics that's "basically" correct, in the sense that there exists a formal proof that morally fits the arc of the human proof, but there's informal/vague reasoning used (e.g. diagram arguments, etc) that are hard to really formalize, but an expert can use consistently without making a mistake. This will take a long time to formalize, and I expect will require a large amount of human and AI effort.

This particular field seems ideal for AI, since verification enables identification of failure at all levels. If the definitions are wrong the theorems won't work and applications elsewhere won't work.

But as far as we know, the proof it wrote is original. Tao himself noted that it’s very different from the other proof (which was only found now).

That’s so far removed from a “search engine” that the term is essentially nonsense in this context.

AI is currently great at interpolation, and in some fields (like biology) there seems to be low-hanging fruit for this kind of connect-the-dots exercise. A human would still be considered smart for connecting these dots IMO.

AI clearly struggles with extrapolation, at least if the new datum is fully outside the training set.

And we will have AGI (if not ASI) if/when AI systems can reliably form new paradigms. It’s a high bar.

But, I don't know. I tend to view these (reasoning) LLMs as alien minds and my intuition of what is perhaps happening under the hood is not good.

I just know that people have been using these LLMs as search engines (including Stephen Wolfram), browsing through what these LLMs perhaps know and have connected together.