AI, novelty, and human blind spots

1:33:58some insight into how it got to this particular functional map, >> right? >> Right. and whether it used all of those all of that knowledge. Like that was my that was my suspicion when there was that one discovery that we talked about with the the gluon tree and like how there's like a seven gluon fineman diagram that it could calculate that's non zero and that's something that we have to worry about. I was like, okay, maybe there's some mathematics that's happening elsewhere that is like bleeding into this physics, right? It's however very rare to go up the chain of logical inquiry. >> And so, and to >> and that's why I'm like freaked out kind of. >> So, and this I think this is an important point because I wanted to lay that out there.

1:34:39>> Yeah. to this exact note which is like even if that's true what I just walked through >> what we're talking about with this solution to the Jacobian conjecture seems to be outside of that potentially outside of that sandbox. >> Yeah. Yeah. which seems it seems >> I don't know I don't know enough but see >> and I'd love to talk to Levant >> even the potential >> that it's not obviously what we just talked about which has been the case for other things where it's like oh this is they made the connection here and you can draw the through line >> even just the potential that that's true >> is um you know and people part of it's you know the leavant who discovered it is obviously one of the world's greatest mathematicians has been so for a long

1:35:20time >> but he's not >> oh he's not >> no >> I mean look no offense Leavant. >> Look, I I don't want that heat. I >> look Look, I love Professor Leavant. He's got a PhD from Princeton, so he's clearly like in the top 1% of mathematicians, I'd say, right? So on and so forth. But he he's a he's not like an active researcher, I would say. Right. Um and >> but he he knows clearly. I mean, he's he's a researcher and anthropic and he's very good at understanding how to use and leverage anthropic, right? And clearly he knows a lot about mathematics, right? But this isn't like someone like Peter Sarnac that's like a number theorist using this stuff, right? And that's what I really want to know what the what the um what the prompt was,

1:36:02>> which which almost makes it again even more. >> Yeah. >> Um >> like he's clearly gifted, but he's not at at that top level that's getting Fields medals. [sighs] >> Fascinating. I I just there's so many angles to this story that I think are you know again a lot of the CEOs and people around who are at the frontier of these systems who have unlimited compute with them by the way. Yeah. >> Which is part of part of the value ad there have been sort of >> the canary in the coal mine around that look they've been saying that this is where it's headed. >> This is >> and everyone's kind of been like yeah show me. >> Yeah. Well, yeah. And there's several examples. Right. Now, before we get into the other examples, one thing I wanted

1:36:43to talk about was like how humans have been approaching this problem, right? Right. Um, there's been this degree paradox where human researchers have spent decades brute forcing variables. Like we've been doing a lot of the brute forcing up to 16 variables, degree 100 plus. So for 2D for example, we've been focusing as humans a lot on the 2D case because we thought 2D would be where we could find with the least amount of computation some kind of um counter example, right? But it turns out there's there's proofs that show that the that the smallest 2D case would have to have a polomial of degree like a 100 like x to the 100 plus x to the 99 da da da da

1:37:26da right and so we've been focusing on this like highly complicated thing but here claude fable 5 proves that a low degree degree 7 it's just in a higher dimension >> dimension three >> right >> that counter example exists it's kind of like a human blind spot that We didn't really consider there's not a lot of papers about the Jacobian conjecture in degree 3. Sorry, in dimension three. >> Yes. Yeah. Which which goes back to then what is the source material for the inside >> and and historically there's there's kind of an irony. If you look at um Yeetang, he's a very famous number theorist. Um he's one of the first guys to bring down the prime gaps to

1:38:07something like I think it was like 79 million. prime gaps meaning you know the twin prime conjecture where like there's an infinite number of primes that are two apart three and five 11 and 13 101 103 so we still don't know if there's an infinite number of those but he's the first guy to bring down and he said there are an infinite number of primes that are like less than 70 million and everyone's like ah right but his story is insane because like during his PhD um at Purdue University he was under the advice of um Tuang Singh Mo and his work