650 approaches and the E2 breakthrough

1:03:44>> Um out of 650 different mathematical approaches that were tested and discarded. There were two specific sub aents that were dubbed E2 and E2 pairs that discovered the path that breached this 41.6% barrier. And it's the story of these two sub aents that we're going to get into because remember Claude actually published its own version of what happened. So you get to see these sub agents like talking to the orchestrator and so on. And it actually also gives you the internal transcript of the E2 sub aent. >> So from that this is what I've gathered happened. It's kind of crazy. that you can peer into it, right? So here's the first thing. The first thing is the orchestrator. It tasks E2 with

1:04:27investigating something called the U pontrian pontrean index of the condition space. I don't know what that means, but the point is there's some kind of there's some kind of matrix. The matrix it thinks has negative igen values. Something like 33 to 153 negative IGEN values. And this whole thing is inspired by Bombiieri and his like speech his spiel about um one way to tackle the reman hypothesis using like algebraic techniques. Algebraic techniques are like you know linear algebra is part of the algebraic techniques. That's why we're getting into values and things like that. Okay. Turns out the prompt's suggestion of doing this was wrong.

1:05:09>> Mhm. >> Okay. So the E2 sub aent after 50 minutes of silent contemplation, it wrote a Python script to test what the orchestrator was telling it to do. And it turns out that there's like some warp sync operator like hyperbolic sign operator in there that's like causing some artifact of negative values. So it goes back to the orchestrator and it says, "Yo, actually what you're telling me to do doesn't make any sense." like um you know you're wrong effectively >> it does not compute >> it does not compute but I can pivot because I've realized something the exact same matrix structure could be used in reverse I'm

1:05:50going to pivot in something that it called a dual use of inertia so it has like inertia it's now pivoting to use whatever insight that it had gathered to prove its orchestrator wrong to now try a different approach right this is a sub aent >> right >> okay now this sub agent it it it doesn't just like fail the task and give up. It independently starts executing this pivot. Um and then it finds like that the total number of positive igen values of whatever matrix is bounded by some number. Um it starts to compute that is strictly from the prime numbers and then successfully it proves that you can get to 50%. On the zeros okay it goes back to the orchestrator >> on the non-trivial zeros. on the

1:06:31non-trivial zero. We're now all from 41 whatever 41% to now we're at 50%. >> There was this singular insight by making the pivot to this dual use of inertia that that now when it cuz one of the things that's great about math with these models is it's test it's immediately because they can execute you can test and it's like oh I got whatever one 4% 1%. >> Yeah. And so now it's at 50%. Right. Okay. It goes back to the orchestrator and the orchestrator expresses intense skepticism. [laughter] Right? Because all I don't think I mean I'm not I'm not trying to assign feelings to this thing, right? But if I if I were an orchestrator and one of my postocs or something came back like I got to 50. Yeah. My first

1:07:12>> my first inclination would be what did you do wrong? Right. Where's where's the mistake? No. No, you didn't. You're not that guy. Right. [laughter] >> Right.