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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

#211

Post by cubefox »

TheOtherHobbes wrote: post #170
cubefox wrote: post #159

Earlier quoted context omitted.

No, I'm not confusing that. Read the linked comment if you're interested.

You are confusing that. The biggest advancements in science are the result of the application of leading-edge pure math concepts to physical problems. Netwonian physics, relativistic physics, quantum field theory, Boolean computing, Turing notions of devices for computability, elliptic-curve cryptography, and electromagnetic theory all derived from the practical application of what was originally abstract math play.…

There is a difference between inventing/axiomatizing new mathematical theories and proving conjectures. Take the Riemann hypothesis (the big daddy among the pure math conjectures), and assume we (or an LLM) prove it tomorrow. How high do you estimate the expected practical usefulness of that proof?

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#212

Post by glenstein »

cubefox wrote: post #196
Thorrez wrote: post #195

Earlier quoted context omitted.

There are many cases where pure mathematics became useful later. https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e...

So what? There are probably also many cases where seemingly useless science became useful later.

Exactly, you're almost getting it. Hence the value of "pure" research in both science and math.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#213

Post by p-e-w »

davidhs wrote: post #194
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...

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#214

Post by glenstein »

TheOtherHobbes wrote: post #170
cubefox wrote: post #159

Earlier quoted context omitted.

No, I'm not confusing that. Read the linked comment if you're interested.

You are confusing that. The biggest advancements in science are the result of the application of leading-edge pure math concepts to physical problems. Netwonian physics, relativistic physics, quantum field theory, Boolean computing, Turing notions of devices for computability, elliptic-curve cryptography, and electromagnetic theory all derived from the practical application of what was originally abstract math play.…

Just to throw in another one, string theory was practically nothing but a basic research/pure research program unearthing new mathematical objects which drove physics research and vice versa. And unfortunately for the haters, string theory has borne real fruit with holography, producing tools for important predictions in plasma physics and black hole physics among other things. I feel like culture hasn't caught up to the fact that holography is now the gold rush frontier that has everyone excited that it might be our next big conceptual revolution in physics.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#215

Post by mmooss »

CamperBob2 wrote: post #208
cma wrote: post #191

Earlier quoted context omitted.

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)

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#216

Post by cubefox »

glenstein wrote: post #212
cubefox wrote: post #196

Earlier quoted context omitted.

So what? There are probably also many cases where seemingly useless science became useful later.

Exactly, you're almost getting it. Hence the value of "pure" research in both science and math.

You are not yet getting it I'm afraid. The point of the linked post was that, even assuming an equal degree of expected uselessness, scientific explanations have intrinsic epistemic value, while proving pure math theorems hasn't.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#217

Post by fc417fc802 »

jerkstate wrote: post #187
fc417fc802 wrote: post #81

Earlier quoted context omitted.

I don't dispute that the situation is rapidly evolving. It is certainly possible that we could achieve AGI in the near future. It is also entirely possible that we might not. Claims such as that AGI is close or that we will soon be replacing developers entirely are pure hype. When someone says something to the effect of "LLMs are on the verge of replacing developers any day now" it is perfectly reasonable to respond…

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 projects done by veteran developers that have made the front page recently. Importantly they've shown clear and undeniable results as opposed to handwaving and empty aspirations. They've also been up front about the shortcomings of the new tool.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#218

Post by mmooss »

glemion43 wrote: post #157
ffsm8 wrote: post #139

Earlier quoted context omitted.

It's mind boggling if you think about the fact they're essential "just" statistical models It really contextualizes the old wisdom of Pythagoras that everything can be represented as numbers / math is the ultimate truth

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#219

Post by wasabi991011 »

nddkdkfk wrote: post #209
heliumtera wrote: post #201

Earlier quoted context omitted.

Don't feel bad for being out of the loop. The author and Tao did not care enough about erdos problem to realize the proof was published by erdos himself. So you never cared enough and neither did they. But they care about about screaming LLMs breakthrough on fediverse and twitter.

This Tao dude, does he get invited to a lot of AI conferences (accommodation included)?

He's the most prolific and famous modern mathematician. I'm pretty sure that even if he'd never touched AI, he would be invited to more conferences than he could ever attend.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#220

Post by guenthert »

mikaraento wrote: post #143
TZubiri wrote: post #118

Earlier quoted context omitted.

forgive the skepticism, but this translates directly to "we asked the model pretty please not to do it in the system prompt"

That might be somewhat ungenerous unless you have more detail to provide. I know that at least some LLM products explicitly check output for similarity to training data to prevent direct reproduction.

Should they though? If the answer to a question^Wprompt happens to be in the training set, wouldn't it be disingenuous to not provide that?
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