The Ledger
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Litt: AI mathematical results can only be properly evaluated in retrospect
“One thing I always say about a model result is, like, you cannot evaluate it except in retrospect, and like, this is also true of human mathematics. Like, sometimes a problem we thought was really important or would require really deep new ideas does not, and …”
Litt: AI harnesses designed to elicit proofs often decrease reliability
“When you make a harness whose goal is to elicit a proof, I think it often decreases reliability, because you're just trying to produce output.”
Litt: Open mathematical problems serve as benchmarks measuring lack of understanding
“At least for me the point of an open problem is it's, like, supposed to measure your failure to understand something. So it's kind of like a benchmark.”
Litt: Reinforcement learning struggles to reward intermediate mathematical theory building
“I think what is definitely true is that, like, the skill of, like, developing a theory or, like, building your understanding of some poorly understood object is, like, a fuzzier one. So it might be harder, you know I guess you can try, you can tell it, you kno…”
Litt: Human inability to brute-force calculations drives profound mathematical discoveries
“And in fact, I think it's, like, kind of, like, our inability to just grind is kind of important to our ability to make discoveries.”
Litt: Cheaper, lower-quality AI outputs risk displacing high-quality human work
“Like, you have a new technology that's doing something a little bit worse than was previously done, but much cheaper, and so you get a lot of, suddenly, a lot of, like, low-quality outputs that are displacing previous high-quality outputs.”
Litt: AI cannot produce long proofs due to limits in verifying correctness
“The reason they're not producing long, complicated proofs is that they cannot. Like the, just like the ability to check correctness is not yet there.”
Litt: Math education remains valuable for clear thinking despite advanced AI
“I think a lot of what we educate people for is, like, pretty robust changes in the nature of the world. Like I think the reason to learn math has always been, like, to think clearly and, like, better understand the world, and, like, presumably that's something…”