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Erdos 281 solved with ChatGPT 5.2 Pro
241–250 of 310 posts
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#242Has anyone confirmed the solution is not in the training data? Otherwise it is just a bit information retrieval LLM style. No intelligence necessary.
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Re: Erdos 281 solved with ChatGPT 5.2 Pro
#243Earlier quoted context omitted.
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.
I think you lost track of what I was replying to. Thorrez noted that "There are many cases where pure mathematics became useful later." You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former which doesn't follow. The utility of pure math research isn't negated by noting there's also value…
"You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former"
No, "so what" doesn't indicate disagreement, just that something isn't relevant.
Anyway, assume hot dogs taste not good at all, except in rare circumstances. It would then be wrong to say "hot dogs taste good", but it would be right to say "hot dogs don't taste good". Now substitute pure math for hot dogs. Pure math can be generally useless even if it isn't always useless. Men are taller than women. That's the difference between applied and pure math. The difference between math and science is something else: Even useless science has value, while most useless math (which consists of pure math) doesn't. (I would say the axiomatization of new theories, like probability theory, can also have inherent value, independent of any uselessness, insofar as it is conceptual progress, but that's different from proving pure math conjectures.)
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#244Earlier quoted context omitted.
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?
That's an odd choice, because prime numbers routinely show up in important applications in cryptography. To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography. And solving it would be valuable in its own right, a kind of mathematical equivalent to discovering a fundamental law in physics which permanently change…
> To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography.
I doubt that this is true.
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#245Earlier quoted context omitted.
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.
See this video
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#246A surprising % of these LLM proofs are coming from amateurs. One wonders if some professional mathematicians are instead choosing to publish LLM proofs without attribution for career purposes.
I think a more realistic answer is that professional mathematicians have tried to get LLMs to solve their problems and the LLMs have not been able to make any progress.
I think it's a bit early to tell whether GPT 5.2 has helped research mathematicians substantially given its recency. The models move so fast that even if all previous models were completely useless I wouldn't be sure this one would be. Let's wait a year and see? (it takes time to write papers)
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#247Earlier quoted context omitted.
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.
its a statistical term, a latent variable is one that is either known to exist, or believed to exist, and then estimated.
consider estimating the position of an object from noisy readings. One presumes that position to exist in some sense, and then one can estimate it by combining multiple measurements, increasing positioning resolution.
its any variable that is postulated or known to exist, and for which you run some fitting procedure
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#248> 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...
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…
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Re: Erdos 281 solved with ChatGPT 5.2 Pro
#249> 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...
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…
> "intrinsic importance"
"Intrinsic" in contexts like this is a word for people who are projecting what they consider important onto the world. You can't define it in any meaningful way that's not entirely subjective.
Re: Erdos 281 solved with ChatGPT 5.2 Pro
#250Earlier quoted context omitted.
I think a more realistic answer is that professional mathematicians have tried to get LLMs to solve their problems and the LLMs have not been able to make any progress.
I think it's a bit early to tell whether GPT 5.2 has helped research mathematicians substantially given its recency. The models move so fast that even if all previous models were completely useless I wouldn't be sure this one would be. Let's wait a year and see? (it takes time to write papers)
It's helped, but it's not correct that mathematicians are scoring major results by just feeding their problems to gpt 5.2 pro, so the OP claim that mathematicians are just playing off AI output as their own is silly. Here, im talking about serious mathematical work, not people posting (unattributed AI slop to the arXiv).
I assume OP was mostly joking, but we need to take care about letting AI companies hype up their impressive progress at the expense of mathematics. This needs to be discussed responsibly.