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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

#41

Post by nl »

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!

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#43

Post by fc417fc802 »

anonzzzies wrote: post #26
mikert89 wrote: post #7

I have 15 years of software engineering experience across some top companies. I truly believe that ai will far surpass human beings at coding, and more broadly logic work. We are very close

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…

> holding out with the vague 'I tried it and it came up with crap'

Isn't that a perfectly reasonable metric? The topic has been dominated by hype for at least the past 5 if not 10 years. So when you encounter the latest in a long line of "the future is here the sky is falling" claims, where every past claim to date has been wrong, it's natural to try for yourself, observe a poor result, and report back "nope, just more BS as usual".

If the hyped future does ever arrive then anyone trying for themselves will get a workable result. It will be trivially easy to demonstrate that naysayers are full of shit. That does not currently appear to be the case.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#44

Post by nurettin »

threethirtytwo wrote: post #37
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...

[flagged]

Why not plan for a future where a lot of non-trivial tasks are automated instead of living on the edge with all this anxiety?

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#45

Post by TZubiri »

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!

Maybe it was in the training set.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#46

Post by threethirtytwo »

dernett wrote: post #9

This is crazy. It's clear that these models don't have human intelligence, but it's undeniable at this point that they have _some_ form of intelligence.

I don't think they will ever have human intelligence. It will always be an alien intelligence.

But I think the trend line unmistakably points to a future where it can be MORE intelligent than a human in exactly the colloquial way we define "more intelligent"

The fact that one of the greatest mathematicians alive has a page and is seriously bench marking this shows how likely he believes this can happen.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#47

Post by johnfn »

threethirtytwo wrote: post #37
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...

[flagged]

I suspect this is AI generated, but it’s quite high quality, and doesn’t have any of the telltale signs that most AI generated content does. How did you generate this? It’s great.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#48

Post by nsoonhui »

sequin wrote: post #10

FWIW, I just gave Deepseek the same prompt and it solved it too (much faster than the 41m of ChatGPT). I then gave both proofs to Opus and it confirmed their equivalence. The answer is yes. Assume, for the sake of contradiction, that there exists an \(\epsilon > 0\) such that for every \(k\), there exists a choice of congruence classes \(a_1^{(k)}, \dots, a_k^{(k)}\) for which the set of integers not covered by the f…

I am not familiar with the field, but any chance that the deepseek is just memorizing the existing solution? Or different.

https://news.ycombinator.com/item?id=46664976

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#50

Post by magnio »

threethirtytwo wrote: post #37
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...

[flagged]

Pity that HN's ability to detect sarcasm is as robust as that of a sentiment analysis model using keyword-matching.
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