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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

#191

Post by cma »

magneticnorth wrote: post #52
TZubiri wrote: post #45

Earlier quoted context omitted.

Maybe it was in the training set.

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)

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#194

Post by davidhs »

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#195

Post by Thorrez »

cubefox wrote: post #188
jstanley wrote: post #146

Earlier quoted context omitted.

Applications for pure mathematics can't necessarily be known until the underlying mathematics is solved. 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.

Well, read the linked comment. The possible future applications of useless science can't be known either. I still argue that it has intrinsic value apart from that, unlike pure mathematics.

There are many cases where pure mathematics became useful later.

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

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#196

Post by cubefox »

Thorrez wrote: post #195
cubefox wrote: post #188

Earlier quoted context omitted.

Well, read the linked comment. The possible future applications of useless science can't be known either. I still argue that it has intrinsic value apart from that, unlike pure mathematics.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#197

Post by heliumtera »

>no prior solutions found.

They never brothered to check erdos solution already published 90 years ago. I am still confused about why erdos, who proposed the problem and the solution would consider this an unsolved problems, but this group of researchers would claim "ohh my god look at this breakthrough"

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#198

Post by GeoAtreides »

rzmmm wrote: post #102
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.

The model has multiple layers of mechanisms to prevent carbon copy output of the training data.

does it?

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...

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#199

Post by heliumtera »

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)

Does it matter if it copied or not? How the hell would one even define if it is a copy or original at this point?

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

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#200

Post by judahmeek »

becquerel wrote: post #128
dust42 wrote: post #126

Personally, I'd prefer if the AI models would start with a proof of their own statements. Time and again, SOTA frontier models told me: "Now you have 100% correct code ready for production in enterprise quality." Then I run it and it crashes. Or maybe the AI is just being tongue-in-cheek? Point in case: I just wanted to give z.ai a try and buy some credits. I used Firefox with uBlock and the payment didn't go through…

You get AIs to prove their code is correct in precisely the same ways you get humans to prove their code is correct. You make them demonstrate it through tests or evidence (screenshots, logs of successful runs).

Yes! Also, make sure to check those results yourself, dear reader, rather than ask the agent to summarize the results for you! ^^;
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