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Comment by ashleyn | Hacker News Reader

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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That's the first warning from the wiki : <<Erdős problems vary widely in difficulty (by several orders of magnitude), with a core of very interesting, but extremely difficult problems at one end of the spectrum, and a "long tail" of under-explored problems at the other, many of which are "low hanging fruit" that are very suitable for being attacked by current AI tools.>> https://github.com/teorth/erdosproblems/wiki/AI-contribution...

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.

Is there though? If they are "solved" (as in the tickbox mark them as such, through a validation process, e.g. another model confirming, formal proof passing, etc) but there is no human actually learning from them, what's the benefit? Completing a 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.

You don't see value in having a cheap way to detect when a problem is easy or hard? That would seem unimaginative.

Some problems are ‘uninteresting’ in that they show results that aren’t immediately seen as useful. However, solutions may end up having ‘interesting’ connections or ideas or mathematical tools that are used elsewhere.

More broadly, I think there’s a perspective that literally just building out thousands more true statements in Lean is going to keep cementing math’s broadening knowledge framework. This is not building a giant castle a-la Wiles, it’s laying bricks in the outhouse, but someday those bricks might be useful.

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