00:23:32 · John Coogan
[00:23:32] S1: to know this. I'm not a... An advanced mathematician by any stretch of the imagination. Oh. Oh. Okay. Break it down for us. Get out the whiteboard. Explain the exponential time hypothesis. Explain the cocky conjecture. Everyone was asking. But, but people people were excited about this. There's a big long post from, Rashaab Karnawat, who says, many of you don't understand how serious this is. That's me. So let me break it down for you. In computer science, there's a famous kind of puzzle called 3SAT. You are given a long list of yes or no switches and a set of rules about how they must be arranged, and you have to find a combination that satisfies every rule. The obvious way to solve it is to try every combination, but each new switch doubles the number of possibilities. So a puzzle with a few 100 switches would take longer than the age of the universe to brute force, so it becomes exponentially complex. For decades, the smartest people in the field found clever tricks that made this a little faster, but every trick still hit the same wall. The time required kept exploding as the puzzle grew. For about about twenty five years ago, two computer scientists, Russell Impaghlazio and Ramamohan Mapatturi, working with Francis Zane, turned that wall into a formal idea. They proposed the exponential time hypothesis, which says this explosion is no longer a failure of human cleverness, but a law of nature, no algorithm, however brilliant, will ever solve three SAT without the time blowing up exponentially. Nobody could prove it, but almost everyone believed it, and it became one of the foundations of modern computer science. Researchers used it as a measuring stick. If you could show that solving some other problem quickly could... Would also crack three SAT quickly, you had shown that the problem was hopelessly hard too. Hundreds of papers across scheduling graphs, logic, and much more rest on this one assumption. Now an internal model at OpenAI claims to have broken it. It says it found an algorithm that solves these puzzles meaningfully faster than the hypothesis allows, and it has checked the proof in a computer verification system called Lean. And here's the remarkable part. The very people who propose the hypothesis, along with MIT's Ryan Williams, are now leading the public review of whether a machine has disproved their own idea.
00:25:50 · John Coogan
So what happens next? If the disproof holds, a large part of theoretical computer science has to be revisited. Every result that said, This problem cannot be solved faster, assuming ETH loses its foundation, and researchers will have to work out which of those walls were real and which were simply stopped looking which they stopped looking at. It does not mean everything becomes easy. The new algorithm is still slow in absolute terms, and this is not the famous P versus NP problem being solved, but it means our map of what's possible was wrong in a place where we were very confident about it and that AI redrew the line. If the disprove falls, the hypothesis survives and the field breathes out, but we still have watched an AI produce serious, checkable work on one of the deepest questions in the discipline closely enough that the founders of the idea had to take it seriously. Either way, something has shifted. So there... You you had a take on this of, like, okay. A lot of people are just like, okay. Cool. Math result. Right? But, like, what's the practical application? And there are some knock on effects that are interesting. Do you have anything to lay out there? Is the trend
00:27:00 · Jordi Hays, John Coogan
[00:27:00] S0: Yeah. My my continued take is that anytime you see a breakthrough like this that is, like, against a sort of an open problem that's just generally expanding humanity's knowledge, isn't exactly immediately commercial. Yep. You have to assume there's many other highly commercial discoveries happening Yep. In the background that people, both the labs and people individually, are not sharing broadly because they made a discovery and there's an opportunity to monetize it. Sure. And so I think that that is like... That any anytime there's like a big breakthrough, my head is just going to everything that's not being shared. Yeah. And that's what I'm actually like So stuff like Probably more. [00:27:41] S1: Advances in AI research, advances in bio that need to go through actual testing. [00:27:46] S0: Yeah, material science.
00:27:46 · Jordi Hays, John Coogan
[00:27:46] S0: Yeah, material science. [00:27:47] S1: Material science that might need to be patented at the very least. Advances in cybersecurity that need to be rolled out incrementally and can't just be sort of thrown over the fence. A lot of these math results, it's totally fine to just get them out into the math community, have everyone engage with them immediately, but every other industry is sort of more unique. We were talking to Doug O'Loughlin about what's the next leg up, white collar work, this type of stuff, obviously, like, the the coding agent boom has, like, fully arrived. But what's what's next? And I was wondering, like, how close do you think the models are to being able to, like, answer that Tyler Cowen Dorcache debate about, like, when will you walk into Walmart and see just, a fully AI run business? And then would that live within the... Like, it could live within the labs. Like, you could have a a big lab, say, like, go and build a business, and it could just do that. And it could do the market analysis, and then it could, like, create a new product and model it in CAD and send it to a factory and send it to a distribution center and pitch it to Walmart and get it on the shelves and, like, make the money and and run that flywheel. Like, it could do that. And if you added up a bunch of those, you might have something economically interesting. [00:29:05] S0: Yeah. I don't think CPG would be there first. [00:29:08] S1: Yeah. Yeah. Maybe maybe Doricas is is correct in the sense that it's just like not the best Yeah.
00:29:08 · John Coogan, Jordi Hays, Tyler
[00:29:08] S1: Yeah. Yeah. Maybe maybe Doricas is is correct in the sense that it's just like not the best Yeah. [00:29:15] S0: Use of product. Can... I mean, in that in that exact context, it would be interesting to think about a retailer running an AI that looks at all the store wide data Yeah. And figures Yeah. Out white space with basics. White figures space and then and then autonomously introduces products. [00:29:31] S1: Yeah. [00:29:32] S0: But but again, it's like how much is that... How relevant is that when Amazon and every retailer has sort of always done this naturally? Can you speed it up faster? Yep. Can you... Can it be more niche? Like, who knows? [00:29:44] S1: And you have, like, you know, effectively But [00:29:47] S0: the thing the thing always, like, [00:29:48] S1: with People are people are jumping on those opportunities and using the tokens for that, like, independently. They're they're mathematicians are not like, yeah, let me go risk 10,000,000 to, like, buy a bunch of compute to, like [00:29:59] S4: Yeah. [00:29:59] S1: Churn on this question. So... [00:30:02] S0: But, yeah, this reminds me of, the the vanity metric of, the the one person, $1,000,000,000 company. Right? Like, it's possible that will happen in some shape or form. It's possible it's already happened. But if you have a billion dollar opportunity, do you care more about like magical fake internet points of being like, I'm the one person, $1,000,000,000 company or do you just wanna win? [00:30:23] S1: Yep.
00:30:23 · John Coogan, Jordi Hays, Rahul Sengottuvelu, S6
[00:30:23] S1: Yep. [00:30:24] S0: So most people are just gonna be like, yeah, well, we can bring this person on and they would be helpful with this or that, and we're more likely to win, so let's do that. Yeah. And I think the same thing with like the the fully AI run company where [00:30:37] S1: It's arbitrary. [00:30:38] S0: There's, like, a strong incentive if something is starting to work to, like, add more human capitals Yeah. To the [00:30:44] S1: All all sorts of people. [00:30:44] S0: But, again, that's from where we're sitting at today. [00:30:49] S1: Mhmm. [00:30:49] S0: And there's a possibility that you get such a increase in capabilities that adding humans actually does just slow it down and and derail the potential of of a certain project. [00:31:02] S1: That's true. Well, let me tell you about public.com. Invest across all asset classes, automate anything with AI agents, run training strategies, risk management, money movements, and monitor markets with AI agents for investing on public. You wanna pull up this GPT video? Yeah. [00:31:19] S0: Let's pull it up. [00:31:20] S1: He's really [00:31:21] S0: A little palate. [00:31:22] S1: Getting in stride. There is a new level to the content. [00:31:25] S5: I'm excited for this bright AI future. Let's keep these fun AI vibes going. [00:31:30] S6: Absolutely. We are full on embracing these unstoppable AI vibes knowing that this bright AI future is just getting brighter, and we'll keep soaring forward with full AI moment.