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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

#21

Post by jadenpeterson »

ekianjo wrote: post #19
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.

It's pattern matching. Which is actually what we measure in IQ tests, just saying.

There's some nuance. IQ tests measure pattern matching and, in an underlying way, other facets of intelligence - memory, for example. How well can an LLM 'remember' a thing? Sometimes Claude will perform compaction when its context window reaches 200k "tokens" then it seems a little colder to me, but maybe that's just my imagination. I'm kind of a "power user".

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#23

Post by amluto »

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 find it interesting that, as someone utterly unfamiliar with ergodic theory, Dini’s theorem, etc, I find Deepseek’s proof somewhat comprehensible, whereas I do not find GPT-5.2’s proof comprehensible at all. I suspect that I’d need to delve into the terminology in the GPT proof if I tried to verify Deepseek’s, so maybe GPT’s is being more straightforward about the underlying theory it relies on?

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#24

Post by rurban »

ekianjo wrote: post #19
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.

It's pattern matching. Which is actually what we measure in IQ tests, just saying.

I call it matching. Pattern matching had a different meaning.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#25

Post by marktl »

daxfohl wrote: post #14
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

They already do. What they suck at is common sense. Unfortunately good software requires both.

Or is it fortunate (for a short period at least).

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#26

Post by anonzzzies »

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 still are shipping apps: it does not really matter if anyone believes me or not. I am making more money than ever with fewer people than ever delivering more than ever.

We are very close.

(by the way; I like writing code and I still do for fun)

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#27

Post by brendyn »

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.

If LLMs weren't created by us but where something discovered in another species' behaviour it would be 100% labelled intelligence

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#28

Post by anonzzzies »

daxfohl wrote: post #14
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

They already do. What they suck at is common sense. Unfortunately good software requires both.

[flagged]

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#29

Post by keeda »

qudat wrote: post #11
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.

My take is that a huge part of human intelligence is pattern matching. We just didn’t understand how much multidimensional geometry influenced our matches

Yes, it could be that intelligence is essentially a sophisticated form of recursive, brute force pattern matching.

I'm beginning to think the Bitter Lesson applies to organic intelligence as well, because basic pattern matching can be implemented relatively simply using very basic mathematical operations like multiply and accumulate, and so it can scale with massive parallelization of relatively simple building blocks.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#30

Post by DrewADesign »

sdwr wrote: post #13
qudat wrote: post #11

Earlier quoted context omitted.

My take is that a huge part of human intelligence is pattern matching. We just didn’t understand how much multidimensional geometry influenced our matches

I don't think it's accurate to describe LLMs as pattern matching. Prediction is the mechanism they use to ingest and output information, and they end up with a (relatively) deep model of the world under the hood.

Which is even more true for humans.
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