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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

#201

Post by heliumtera »

doctoboggan wrote: post #17

Can anyone give a little more color on the nature of Erdos problems? Are these problems that many mathematicians have spend years tackling with no result? Or do some of the problems evade scrutiny and go un-attempted for most of the time? EDIT: After reading a link someone else posted to Terrance Tao's wiki page, he has a paragraph that somewhat answers this question: > Erdős problems vary widely in difficulty (by se…

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#202

Post by drob518 »

cubefox wrote: post #144
MattGaiser wrote: post #131

Earlier quoted context omitted.

There is still enormous value in cleaning up the long tail of somewhat important stuff. One of the great benefits of Claude Code to me is that smaller issues no longer rot in backlogs, but can be at least attempted immediately.

The difference is that Claude Code actually solves practical problems, but pure (as opposed to applied ) mathematics doesn't. Moreover, a lot of pure mathematics seems to be not just useless, but also without intrinsic epistemic value, unlike science. See https://news.ycombinator.com/item?id=46510353

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 because they sometimes find amazing things that we engineers can use during the next turn of the technological crank. Instead of seeing pure math as useless, perhaps shift to seeing it as something wonderful for which we have not YET found a practical use.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#203

Post by retsibsi »

GeoAtreides wrote: post #198
rzmmm wrote: post #102

Earlier quoted context omitted.

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...

Isn't that easily explicable as hallucination, rather than regurgitation?

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#204

Post by jrmg »

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

You’re describing a complex statistical model.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#205

Post by pfdietz »

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.

They're finding them very effective at literature search, and at autoformalization of human-written proofs.

Pretty soon, this is going to mean the entire historical math literature will be formalized (or, in some cases, found to be in error). Consider the implications of that for training theorem provers.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#206

Post by CamperBob2 »

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).

If such a thing did exist, it would exist only until people started training models to hide from it.

Negative feedback is the original "all you need."

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#207

Post by falcor84 »

yosefk wrote: post #122
CGamesPlay wrote: post #75

Earlier quoted context omitted.

> I then gave both proofs to Opus and it confirmed their equivalence. You could have just rubber-stamped it yourself, for all the mathematical rigor it holds. The devil is in the details, and the smallest problem unravels the whole proof.

How dare you question the rigor of the venerable LLM peer review process! These are some of the most esteemed LLMs we are talking about here.

It's about formalization in Lean, not peer review

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#208

Post by CamperBob2 »

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)

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#209

Post by nddkdkfk »

heliumtera wrote: post #201
doctoboggan wrote: post #17

Can anyone give a little more color on the nature of Erdos problems? Are these problems that many mathematicians have spend years tackling with no result? Or do some of the problems evade scrutiny and go un-attempted for most of the time? EDIT: After reading a link someone else posted to Terrance Tao's wiki page, he has a paragraph that somewhat answers this question: > Erdős problems vary widely in difficulty (by se…

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)?

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#210

Post by fweimer »

glemion43 wrote: post #156
rzmmm wrote: post #102

Earlier quoted context omitted.

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

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 bit like someone at Google subscribed to a legal theory under which you can avoid copyright infringement if you take a derivative work and apply a mechanical obfuscation to it.

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