OpenAI and the Erdős conjecture

1:40:01This is the proof for it. It has to do with like the it asks like the maximum number of pairs of points that can be exactly one unit apart >> in 2D. So like trivially you could imagine a grid of points, right? A grid of points. All of these points are one distance apart. And you would think that that's like the best way to pack all the points, right? Erdog showed that there's like an upper bound on how many points I can pack with this amount of distance. um and the open AI model disproved that bound and showed that there's a better bound. And then later on, mathematicians took that proof and made a short digested humanverified version of that

1:40:44counter example. Again, it's a counter example, but here the the authors are a who's who of mathematicians. We've got Timothy Gowowers from Trinity College at the University of Cambridge >> in the UK. Um he's a fields medalist. We've also got Jacob Zimmerman, which it's been leaked, is the Fields Medalist this year. If you go on Poly Market, it's all collapsed to 99% [laughter] for people. It's like, okay. So, somehow it got leaked and now no one's like betting anymore. Jacob Zimmerman, actually, I think he was my um my he was my TA in freshman year. >> Oh, we love that. >> Yeah, cuz he was a PhD student of Peter Sarn teaching. >> Come on the show. We'd love to talk to

1:41:24you about it. >> Yeah. Yeah. We'd love to talk to you about how you how you gave me a never mind. Let's not talk [laughter] about how you graded my midterm, but um you know, so this is a who's who and what they're doing is taking the work of Open AI >> and trying to make it human digestible. So is that what mathematicians are going to just end up doing? >> Right. Right. Right. Being translators of the machine genius. >> Yeah. And and funny thing about this, right? So um Open AI solved that Aeros conjecture. Um, Leavant, our hero from this story at Anthropic, he tweeted again in all lower caps. He's like, um, over the weekend I checked the obvious thing, which is whether Mythos is able to solve the Aeros unit distance

1:42:05problem. Um, aka Ardos problem. Um, the answer is yeah, [laughter] >> I love >> I think he's just trolling. It's just all all lowercase [laughter] >> gen Z capitalization. Then his colleague is like, you know, huge huge credit to the Open AI team and but he's like retweeting, but he they're are colleagues and he's like trying to make it a little bit more >> Yeah. Yeah. Good. [laughter] Corpo speaking. >> Yeah. Yeah. Yeah. But but the it's just so funny. I think the guy's just trolling. This is so there's so much here. Sorry. Continue though. >> Yeah. Um and the final thing I want to end with is this is clearly now becoming an existential crisis for mathematics,

1:42:47right? If AI is going to prove everything, what are pure mathematicians going to do? And it makes me kind of sad if I'm not going to lie. It makes me happy that we're we're seeing such obvious counter examples for things and like stuff that I can understand. And you know, who knows? We'll maybe find a proof for the reman zeta or maybe we'll find a counter example for the reman zeta hypothesis where um it's going to just come up with a a zero for the remon function that's like I don't know two billion on the 1/ half real line. Who knows, right? Probably not because every mathematician that I know says that the remon hypothesis is true. >> But who knows, right? At this point, it

1:43:28would be kind of cool to find it because that I could also check >> like not by hand maybe cuz I'd have to do it a bunch of times, but I could probably check on Wolf Ram, right? So,