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Notes -
I have the same question as I did with the erdos problems.
As someone not well versed in math, I don't know how hard these problems are. Are they mundane research work, where most phd students in the field could solve the problems? Or are they difficult math questions where only the best minds can come up with the right insights to get the solution?
If it's mundane work that many math grad students could take care of, then I would be considerably less impressed with 5/10 problems solved than if it ws the latter.
I think the paper does a decent job explaining how hard these problems are, but there's admittedly not a clear 1-sentence description anywhere and it's written for a mathematician audience.
My summary is:
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Math professor Daniel Litt discusses the challenge here.
Summarizing, these are unpublished lemmas from math professor’s own work. Lemmas tend to be minor theorems or helper results used as little pieces to help prove larger more interesting ideas. So at least somewhat novel (supposedly), but not grand theorems or crucial results. Litt says that in his field, figuring out what lemmas to prove is the hard part, and then proving them is typically much easier. He said that overall proving results like these take up a relatively small fraction of his time, but a tool to automate their proofs would be very helpful.
As for the problems themselves, Litt said they vary greatly in difficulty. Two of them, including two of the 5-6 that Aletheia got right, apparently had nearly identical statements already proven in the literature. Another one had the proof sketched out in literature, but no model managed to fill in the details.
What most interests me is reliability. Litt writes that overall a lot of garbage was produced, and in a ‘real’ scenario where no one actually knows the answer that is a serious problem. Both Aletheia variants didn’t answer 4 of the questions, either because the model said “I don’t know how to solve it” or it hadn’t finished in the allotted time. I couldn’t find the breakdown from a quick skim, which is a shame - I would be very impressed if the model said it couldn’t solve it rather than giving a wrong proof. Still, it seems of the 12 solutions submitted by the two variants to 6 problems, 3 were considered substantially incorrect, for a ‘precision’ of 75% and a ‘recall’ of 45%, given the problems that it didn’t give an attempt for.
Overall, I would say this is better than I would have expected (not that I have any particular insight to the problems themselves), but still seems like it will pose an immense difficulty when these tools are applied to actual problems where the solution isn’t known ahead of time.
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