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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

#301

Post by int_19h »

comp_throw7 wrote: post #71
threethirtytwo wrote: post #64

Earlier quoted context omitted.

Your intuition on AI is out of date by about 6 months. Those telltale signs no longer exist. It wasn't AI generated. But if it was, there is currently no way for anyone to tell the difference.

> 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).

There are no reliable AI detection services. At best they can reliably detect output from popular chatbots running with their default prompts. Beyond that reliability deteriorates rapidly so they either err on the side of many false positives, or on the side of many false negatives.

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

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#303

Post by int_19h »

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.

It is also very much a moving target. A year ago I tried those tools and they were very meh at the kinds of stuff I do. Today, they are much better.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#304

Post by int_19h »

user3939382 wrote: post #286
danielbln wrote: post #171

Earlier quoted context omitted.

Real HN comment right here. "LLMs are a joke" - maybe don't drink the anti-hype kool aid, you'll blind yourself to the capability space that's out there, even if it's not AGI or whatever.

I’ll look past the disrespectful flippant insult on the hope that there’s a brain there too. They’re a probabalistic phonograph. They can sharpen the funnel for input but they can’t provide judgement on input or resolve ambiguities in your specifications. Teams of human requirements engineers cannot do it. LLMs are not magic. You’re essentially asking it; from my wardrobe pick an outfit for me and make sure it’s the…

Humans aren't magic either. LLMs don't need to be magic to be useful, or to replace humans for that matter.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#305

Post by anonzzzies »

fc417fc802 wrote: post #217
jerkstate wrote: post #187

Earlier quoted context omitted.

There's a big difference between "I tried it and it produced crap" and "it will replace developers entirely any day now" People who use this stuff everyday know that people who are still saying "I tried it and it produced crap" just don't know how to use it correctly. Those developers WILL get replaced - by ones who know how to use the tool.

> Those developers WILL get replaced - by ones who know how to use the tool. Now _that_ I would believe. But note how different "those who fail to adapt to this new tool will be replaced" is from "the vast majority will be replaced by this tool itself". If someone had said that six (give or take) months ago I would have dismissed it as hype. But there have been at least a few decently well documented AI assisted proj…

You probably mean antirez porting Flux to c. There were not too many shortcomings in his breakdown; his biggest one as I saw was that his knowledge and experience building large c programs really was a requirement. But given one of these experts, you don't see how that person and claude code just replaces a team. The less capable people on the team cannot do what he does so before they were just entering code and getting corrected in reviews or asking for help. Now the AI can do that, but on 10 projects in parallel. In a weekend you wont have time for that but not everything has to be done in a weekend.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#306

Post by antonvs »

cubefox wrote: post #297
antonvs wrote: post #249

Earlier quoted context omitted.

> "intrinsic importance" "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.

Mathematical theorems at least have objectively lower information content, because they merely rule out the impossible, while scientific knowledge also rules out the possible but non-actual.

You have it backwards. Mathematical theorems have objectively higher information content, because they rule out the impossible and model possibilities in all possible worlds that satisfy their preconditions. Scientific knowledge can never do more than inductive projections from observations in the single world we have physical access to.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#307

Post by davidhs »

p-e-w wrote: post #213
davidhs wrote: post #194

Earlier quoted context omitted.

It looks like these models work pretty well as natural language search engines and at connecting together dots of disparate things humans haven't done.

Every time this topic comes up people compare the LLM to a search engine of some kind. 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.

Maybe if Terence Tao had memorized the entire Internet (and pretty much all media), then maybe he would find bits and pieces of the problem remind him of certain known solutions and be able to connect the dots himself.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#308

Post by pfdietz »

nl wrote: post #41
xeeeeeeeeeeenu wrote: post #18

> no prior solutions found. This is no longer true, a prior solution has just been found[1], so the LLM proof has been moved to the Section 2 of Terence Tao's wiki[2]. [1] - https://www.erdosproblems.com/forum/thread/281#post-3325 [2] - https://github.com/teorth/erdosproblems/wiki/AI-contribution...

Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)" And even odder that the proof was by Erdos himself and yet he listed it as an open problem!

The theorem is implied by an older result of Erdos, but is not a result of Erdos. Apparently this is because the connection is something called "Roger's Theorem" that was quite obscure.

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!"

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#309

Post by user3939382 »

int_19h wrote: post #304
user3939382 wrote: post #286

Earlier quoted context omitted.

I’ll look past the disrespectful flippant insult on the hope that there’s a brain there too. They’re a probabalistic phonograph. They can sharpen the funnel for input but they can’t provide judgement on input or resolve ambiguities in your specifications. Teams of human requirements engineers cannot do it. LLMs are not magic. You’re essentially asking it; from my wardrobe pick an outfit for me and make sure it’s the…

Humans aren't magic either. LLMs don't need to be magic to be useful, or to replace humans for that matter.

Humans are magic from the LLMs perspective because the token window sizes they would need to approach human experiential disambiguation of requirements would be orders of magnitude larger. Useful in general or replace in general some human activities is a goal post shift that was never the discussion here.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#310

Post by glenstein »

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…

So when you said "so what, hamburgers (science) taste good (is useful)", you were implicitly making a point about how bad (mostly not useful) the hot dogs (math research) was? And that's the thing that supposedly wasn't being followed on the first pass?

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.

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