Correction: the Riemann Hypothesis

1:02:08is. And that's the one and it was apparently terrible. So, we don't care about that. But we have one one correction from our previous episode which was on the Remon hypothesis. >> Yes. So, um the the previous episode, um a lot of you saw it and um most of it I'm very proud of. Um there's one segment where I think I could have done better. Um and it was when we were discussing some of Claude's results and um specifically this particular graphic came up. Um as background um Claude made some progress in a related problem to the Remon hypothesis where the remon hypothesis is where are the zeros of the

1:02:49remon zeta function um are they all on the critical line where the real part of the zeros is is 1/2. Now Claude showed that the previous bound of something like 44% had gone up to 67%. which means that 67% of all of the non-trivial zeros are on the on that line, right? And and I mistakenly said that if we get to 100% that's going to be the remon hypothesis. And it's because that graphic um showed 100% line over there and it said remon hypothesis and I just wasn't really thinking it's it's a lot richer than

1:03:30that because this is a statistical argument, right? Um, and you actually brought it up earlier when you said that, you know, um, with infinities, it's hard to talk about percentages. Like when we say that we when we say that 67% or let's say 2/3, let's say 2/3 of all zeros are on the critical line. Um, GH Hardy had already proved that there are an infinite number of zeros on the critical line. So what does it mean for the infinite number of zeros to only at least be 2/3? Well, what that means is two out of three in that infinite set are on the line. That's what that's what Claude is saying, right? There's an infinite set and just like how one out

1:04:10of two of the infinite set of natural numbers are even numbers, one can say or two out of three of all of the numbers are not multiples of three. That's another way of saying it. That's another way of saying like in the infinite set two out of three of all of the elements are going to be on that line, right? Um and then and then I mistakenly said that if we get to 100 that'll mean the remon hypothesis is true. That's not it's not the case, right? Because of infinities. >> So you could have for example an infinite number of zeros on the critical line and then a single zero somewhere else. >> That would still give you 100% on the critical line, but the remon hypothesis

1:04:51would still be false because not every zero is on the critical line. Statistically, we can reach a hundred and you still haven't proven the remon hypothesis. That's the point. >> And so, AI, you're still you're still not there. There's a song. If I find it, I'll play it in the next episode because now there's like counterculture rap music about like wanting data centers in your neighborhood. >> No way. >> But it's like they don't really want a data center in the neighborhood. >> But some people know what I'm talking about. It's like, I want a data center in my neighborhood. >> I need a data center in my neighborhood. I want a data center in my town. Please put a data center in my neighborhood. That way my rent might actually go down.

1:05:33>> I don't care if I lose my hearing with like like I don't care if my wife like you know and it's like obviously satire satire around it but um it's funny how culture and these issues related to AI are so intertwined. But we after quite a fun break again the best show in science. Not only do you get a deep dive, you get some background context on the latest happenings at the frontier. No other show provides you the best frontier breaking news science experience with a depth of understanding where you're going to walk away not only learning something, but understanding the context in which these discoveries

1:06:15were made. And so we're going to jump back now into our breakdown of quantum computing in our part one of our two-part deep dive. So we left off with