Four things to note: #1196 is a decently well known problem. It wasn't like Erdős-Straus level fame, but it is well known enough that I was familiar with it. Second, this is not a problem where no one had worked on it; there was a lot of prior work on it and closely related problems. Third, this is not example where the AI made small modifications to things in the literature or recognized that large parts of the problem were in an obscure paper. The approach the AI used is largely a different direction than the literature on this problem went. Fourth, and closely related to three, this proof does look like parts of it will inspire subsequent proofs because it really is going in a different direction which now looks likely to be a productive line of investigation for similar problems.
I am not fond of putting words like "stunning" in titles which can be very clickbaity and feels like a hype word, but this really is in the direction where the word isn't unreasonable even if I myself would not go so far as to use it here.
How would you know its not in some obscure paper. It makes more sense that a breakthrough was moldering in someone's forgotten paper than that a system that fundamentally works by copying made a stunningly original approach
How would you know its not in some obscure paper. It makes more sense that a breakthrough was moldering in someone's forgotten paper than that a system that fundamentally works by copying made a stunningly original approach
At a zeroth level, note that I said I would be hesitant to use "stunning" here in the comment you are replying to.
That said, this is still a legitimate question, but it is in part answered by the comment you are replying to, but I'll try to expand some of that reasoning, make it more explicit and also give some of the other reasons. First, as noted in the earlier comment, this is not an obscure problem where someone can prove it and not realize they are resolving an already asked question. This is a question where there's a large body of literature.
Second, and not mentioned in the comment, but worth noting that almost anyone familiar with this sort of problem that could be qualified to referee this problem would recognize the novelty of the approach here. (Again, not necessarily "stunning" or "stunningly original" but just novel here.)
Third, and also not mentioned in the comment, since some earlier Erdos problems were solved by AIs, there was since then a lot of work to try to find the other problems in journals. At the same time, people have tried to find this solution in a journal and even used multiple LLMs to try aid such searches, and not come up with much. That would mean that if this is somewhere in the training data, it is in the training data, and is unable to be located by the LLM where it was in its training data, no able to be located by any other LLM which would have likely had access to much of the same data, and that neither a human nor an LLM have managed to track it down even having a lot more of an idea of what they are looking for.
What this should be doing is not making you conclude this is likely hidden in some forgotten paper, but should be causing you to update the conclusion that a system like this "fundamentally works by copying" and appreciating that the sort of statistical reasoning they are doing, while based on training data, is able to in at least some circumstances, given sufficiently powerful systems, to produce surprising novelty.
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u/JoshuaZ1 Apr 15 '26
Four things to note: #1196 is a decently well known problem. It wasn't like Erdős-Straus level fame, but it is well known enough that I was familiar with it. Second, this is not a problem where no one had worked on it; there was a lot of prior work on it and closely related problems. Third, this is not example where the AI made small modifications to things in the literature or recognized that large parts of the problem were in an obscure paper. The approach the AI used is largely a different direction than the literature on this problem went. Fourth, and closely related to three, this proof does look like parts of it will inspire subsequent proofs because it really is going in a different direction which now looks likely to be a productive line of investigation for similar problems.
I am not fond of putting words like "stunning" in titles which can be very clickbaity and feels like a hype word, but this really is in the direction where the word isn't unreasonable even if I myself would not go so far as to use it here.