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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

#281

Post by nl »

mmooss wrote: post #269
CamperBob2 wrote: post #257

Earlier quoted context omitted.

Point being, it's not the same proof.

Your point seemed to be, if Tao et al. haven't heard of it then it must not exist. The now known literature proof contradicts that claim.

There's an update from Tao after emailing Tenenbaum (the paper author) about this:

> 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!

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#282

Post by pvab3 »

mmooss wrote: post #215
CamperBob2 wrote: post #208

Earlier quoted context omitted.

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

> 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.

there is an immense amount of stuff out there on ArXiv that no one has ever looked at

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#283

Post by layer8 »

jojobas wrote: post #180
cubefox wrote: post #117

Earlier quoted context omitted.

This illustrates how unimportant this problem is. A prior solution did exist, but apparently nobody knew because people didn't really care about it. If progress can be had by simply searching for old solutions in the literature, then that's good evidence the supposed progress is imaginary. And this is not the first time this has happened with an Erdős problem. A lot of pure mathematics seems to consist in solving nea…

It's hard to predict which maths result from 100 years ago surfaces in say quantum mechanics or cryptography.

The likelihood for that is vanishingly low, though, for any given math result.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#285

Post by [deleted] »

cma wrote: post #191
magneticnorth wrote: post #52

Earlier quoted context omitted.

I think that was Tao's point, that the new proof was not just read out of the training set.

I don't think it is dispositive, just that it likely didn't copy the proof we know was in the training set. 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)

[deleted]

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#286

Post by user3939382 »

danielbln wrote: post #171
user3939382 wrote: post #33

Earlier quoted context omitted.

They can only code to specification which is where even teams of humans get lost. Without much smarter architecture for AI (LLMs as is are a joke) that needle isn’t going to move.

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 one I would have picked.

If you’re dazzled into thinking LLMs can solve this you just don’t understand transformer architecture and you don’t understand requirements engineering.

You’ll know a proper AI engine when you see it and it doesn’t look like an LLM.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#287

Post by drob518 »

Ar-Curunir wrote: post #273
drob518 wrote: post #202

Earlier quoted context omitted.

I’m an engineer, not a mathematician, so I definitely appreciate applied math more than I do abstract math. That said, that’s my personal preference and one of the reasons that I became an engineer and not a mathematician. Working on nothing but theory would bore me to tears. But I appreciate that other people really love that and can approach pure math and see the beauty. And thank God that those people exist becaus…

Even if pure math is useless, that’s still okay. We do plenty of things that are useless. Not everything has to have a use.

I’m not sure I agree. Pure math is not useless because a lot of math is very useful. But we don’t know ahead of time what is going to be useless vs. useful. We need to do all of it and then sort it out later.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#288

Post by inimino »

glemion43 wrote: post #260
jrmg wrote: post #204

Earlier quoted context omitted.

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?

I am, and yes, that's what a statistical model is.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#289

Post by inimino »

magicalist wrote: post #61

Funny seeing silicon valley bros commenting "you're on fire!" to Neel when it appears he copied and pasted the problem verbatim into chatGPT and it did literally all the other work here https://chatgpt.com/share/696ac45b-70d8-8003-9ca4-320151e081...

Knowing which problem to copy and paste into the model is also a skill.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#290

Post by casey2 »

nl wrote: post #281
mmooss wrote: post #269

Earlier quoted context omitted.

Your point seemed to be, if Tao et al. haven't heard of it then it must not exist. The now known literature proof contradicts that claim.

There's an update from Tao after emailing Tenenbaum (the paper author) about this: > 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…

This whole thread is pretty funny. Either it can demo some pretty clever, but still limited, features resulting in math skills OR it's literally the best search engine ever invented. My guess is the former, it's pretty whatever at web search and I'd expect to see something similar to the easily retrievable, more visible proof method from Rogers' (as opposed to some alleged proof hidden in some dataset).
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