roystgnr
23hr ago
The intuitions required for formal proof verification are "it's worth rewriting this proof in another language that's an order of magnitude more verbose just so you can get a computer to tell you what you're sure you already know" and "the verifier doesn't have any soundness bugs that will invalidate any of its verifications" Historically the latter has sometimes been untrue and the former has usually been untrue. LLMs are fixing the first problem, which is exposing and leading to fixes for the second problem, but that's all a relatively new development. It's going to take a while to go back through all the mathematical literature and see how much of it might have problems due to predating the coming era of formal verification.
Consider the recent construction of a complex structure on the six-sphere. The simplest English explanation I've seen is under a thousand lines of (admittedly difficult!) writing and mathematical notation. The Lean formalization is a quarter-million lines of code. It's ... probably correct, people seem to think? But if it is correct, the construction would (reportedly; this is outside my field and way beyond me) contradict a 2020 paper (which itself was a correction to a 1998 paper), so we're almost certainly either producing new broken proofs or revealing old invalid proofs here.
I'm sorry to join the "reading QCs a month later" pile-on, but I have to ask: are you sure this is true?
I've always thought of it as a bit of genius for Rowling to make Hermione a side character. From a Watsonian perspective Hermione is halfway to being a Mary Sue, but that turns out to be fine, because she doesn't fit the most important part of the Doylist definition of a Mary Sue: she's not Our Main Character. We don't live in her head, we spend a bunch of time away from her, and we don't even meet her until several chapters into the first book, so we don't ever begin to relate to her as a Wish Fulfillment stand-in. She can face a threat capable of incapacitating her for half a book without readers missing the climax. She can be a Double Witch with extra-secret time-turner powers or be the focus of a love triangle with a celebrity athlete, without those things feeling like just a Twilight-style annoying paean to how great Our Protagonist is, because we see those things from the outside. She doesn't need to break characterization and seize the Idiot Ball to get into interesting conflicts, because we get emotionally invested enough into Harry that we don't get too annoyed when he's idiot enough for the both of them. (which he kind of has to be; since he fits a ton of other Mary Sue traits, he'd get pretty annoying too if he wasn't regularly failing and getting smacked around)
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