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Erdos 281 solved with ChatGPT 5.2 Pro

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Re: Erdos 281 solved with ChatGPT 5.2 Pro

#251

Post by Workaccount2 »

fweimer wrote: post #210
glemion43 wrote: post #156

Earlier quoted context omitted.

Do you have a source for this? Carbon copy would mean over fitting

I saw weird results with Gemini 2.5 Pro when I asked it to provide concrete source code examples matching certain criteria, and to quote the source code it found verbatim. It said it in its response quoted the sources verbatim, but that wasn't true at all—they had been rewritten, still in the style of the project it was quoting from, but otherwise quite different, and without a match in the Git history. It looked a b…

LLM's are not archives of information.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#252

Post by habinero »

CamperBob2 wrote: post #233
mmooss wrote: post #215

Earlier quoted context omitted.

> A proof that Terence Tao and his colleagues have never heard of? Tao et al. didn't know of the literature proof that started this subthread.

Right, but someone else did ("colleagues.")

No, they searched for it. There's a lot of math literature out there, not even an expert is going to know all of it.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#253

Post by glenstein »

cubefox wrote: post #244
glenstein wrote: post #222

Earlier quoted context omitted.

That's an odd choice, because prime numbers routinely show up in important applications in cryptography. To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography. And solving it would be valuable in its own right, a kind of mathematical equivalent to discovering a fundamental law in physics which permanently change…

> To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography. I doubt that this is true.

It already has! The progress that's been made thus far, involved the development of new ways to probabilistically estimate density of primes, which in turn have already been used in cryptography for secure key based on deeper understanding of how to quickly and efficiently find large prime numbers.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#254

Post by Workaccount2 »

energy123 wrote: post #113

A surprising % of these LLM proofs are coming from amateurs. One wonders if some professional mathematicians are instead choosing to publish LLM proofs without attribution for career purposes.

>One wonders if some professional mathematicians are instead choosing to publish LLM proofs without attribution for career purposes.

This will just become the norm as these models improve, if it isn't largely already the case.

It's like sports where everyone is trying to use steroids, because the only way to keep up is to use steroids. Except there aren't any AI-detectors and it's not breaking any rules (except perhaps some kind of self moral code) to use AI.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#255

Post by Workaccount2 »

kristopolous wrote: post #125
energy123 wrote: post #113

A surprising % of these LLM proofs are coming from amateurs. One wonders if some professional mathematicians are instead choosing to publish LLM proofs without attribution for career purposes.

It's probably from the perennial observation "This LLM is kinda dumb in the thing I'm an expert in"

Perennial doesn't make sense in the context of something that has been around for a few months. Observations from the spring 2025 crop of LLMs are already irrelevant.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#256

Post by lostmsu »

utopiah wrote: post #70
anonzzzies wrote: post #26

Earlier quoted context omitted.

HN will be the last place to admit it; people here seem to be holding out with the vague 'I tried it and it came up with crap'. While many of us are shipping software without touching (much) code anymore. I have written code for over 40 years and this is nothing like no-code or whatever 'replacing programmers' before, this is clearly different judging from the people who cannot code with a gun to their heads but stil…

Both can be correct : you might be making a lot of money using the latest tools while others who work on very different problems have tried the same tools and it's just not good enough for them. The ability to make money proves you found a good market, it doesn't prove that the new tools are useful to others.

No, the comment is about "will", not "is". Of course there's no definitive proof of what will happen. But the writing is on the wall and the letters are so large now, that denying AI would take over coding if not all intellectual endeavors resembles the movie "Don't look up".

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#257

Post by CamperBob2 »

habinero wrote: post #252
CamperBob2 wrote: post #233

Earlier quoted context omitted.

Right, but someone else did ("colleagues.")

No, they searched for it. There's a lot of math literature out there, not even an expert is going to know all of it.

Point being, it's not the same proof.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#258

Post by cwnyth »

cubefox wrote: post #243
glenstein wrote: post #237

Earlier quoted context omitted.

I think you lost track of what I was replying to. Thorrez noted that "There are many cases where pure mathematics became useful later." You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former which doesn't follow. The utility of pure math research isn't negated by noting there's also value…

"You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former" 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…

It really speaks to the weakness of your original claim that you're applying this level of sophistry to your backpedaling.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#259

Post by glemion43 »

mmooss wrote: post #218
glemion43 wrote: post #157

Earlier quoted context omitted.

They are not just statistical models They create concepts in latent space which is basically compression which forces this

What is "latent space"? I'm wary of metamagical descriptions of technology that's in a hype cycle.

I'm disappointed that you had to add the 'metamagical' to your question tbh

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#260

Post by glemion43 »

jrmg wrote: post #204
glemion43 wrote: post #157

Earlier quoted context omitted.

They are not just statistical models They create concepts in latent space which is basically compression which forces this

You’re describing a complex statistical model.

Debatable I would argue. It's definitely not 'just a statistical model's and I would argue that the compression into this space fixes potential issues differently than just statistics.

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

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