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https://chatgpt.com/share/696ac45b-70d8-8003-9ca4-320151e081...
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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.
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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.
It wasn't AI generated. But if it was, there is currently no way for anyone to tell the difference.
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
I guess the first question I have is if these problems solved by LLMs are just low-hanging fruit that human researchers either didn't get around to or show much interest in - or if there's some actual beef here to the idea that LLMs can independently conduct original research and solve hard problems.
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It's bizarre. The same account was previously arguing in favor of emergent reasoning abilities in another thread ( https://news.ycombinator.com/item?id=46453084 ) -- I voted it up, in fact! Turing test failed, I guess. (edit: fixed link)
I thought the mockery and sarcasm in my piece was rather obvious.
I guess the first question I have is if these problems solved by LLMs are just low-hanging fruit that human researchers either didn't get around to or show much interest in - or if there's some actual beef here to the idea that LLMs can independently conduct original research and solve hard problems.
There is still value on letting these LLMs loose on the periphery and knocking out all the low hanging fruit humanity hasn’t had the time to get around to. Also, I don’t know this, but if it is a problem on Erdos I presume people have tried to solve it atleast a little bit before it makes it to the list.
I believe the ones that are NOT studied are precisely because they are seen as uninteresting. Even if they were to be solved in an interesting way, if nobody sees the proof because they are just too many and they are again not considered valuable then I don't see what is gained.
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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
Sure but if so wouldn't ChatGPT 5.2 Pro also "just memorizing the existing solution?"?
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…
The ability to make money proves you found a good market, it doesn't prove that the new tools are useful to others.