OpenAI just broke physics...

Video authored by the channel shown, not by IANIA; all rights belong to the creator. Transcript and summary generated automatically; the original-language content is preserved.

Original language: English

Original video: OpenAI just broke physics… · Channel: Wes Roth · 32:49 · Watch on YouTube

Topics: AI agents, Cybersecurity and software security, Health and science

Summary

The video discusses OpenAI’s reported AI-generated mathematical and physics results, focusing on a claimed disproof of the Exponential Time Hypothesis (ETH) and its connection to the P versus NP question. It explains why computational complexity matters for cryptography and optimization, while emphasizing that the ETH result does not prove P = NP or establish immediate practical applications. The host also covers other reported results, including work related to Yang–Mills theory and quantum field theory, and considers how these findings might affect science and technology. The overall message is that the results could challenge assumptions about computational limits, but their significance still requires scrutiny and further research.

Key points

OpenAI reported AI-generated results in mathematics, physics, and computer science, including a result that the video describes as disproving ETH.
ETH is presented as the belief that certain computational problems require exponentially increasing work as their size grows.
The video explains P versus NP using problems that are difficult to solve but easy to check, such as Sudoku or scheduling.
The host stresses that disproving ETH does not establish that P = NP.
If P = NP were true and practically usable, it could threaten much of the cryptography used on the internet while making many optimization tasks easier.
Even if shortcuts exist, they might only help at problem sizes too large to be useful in practice.
OpenAI’s work was described as being shepherded by researchers, including people associated with the development of ETH.
The video also discusses reported AI work on Yang–Mills theory, quantum field theory, and mathematical conjectures.
The host presents the results as potentially important but says their practical implications remain uncertain.

Chapters

Start	Chapter	Summary
00:00	OpenAI’s reported breakthroughs and the ETH claim	The host introduces OpenAI’s reported scientific results and explains why the claim about ETH has drawn particular attention.
04:12	Millennium Prize problems and recent AI results	The video places the reported work alongside famous unsolved problems and mentions a Yang–Mills result described as a byproduct.
06:17	Explaining P versus NP	Combination locks, scheduling, and Sudoku are used to explain exponential search, efficient checking, and the basic P versus NP question.
12:32	What ETH says and why it matters	The host describes ETH as a widely used assumption about exponential computational difficulty and discusses how OpenAI presented its work.
14:06	Researchers, credit, and reactions to AI mathematics	The video discusses the human researchers shepherding the work and reactions to AI entering mathematical research.
17:13	The claimed shortcut and its possible meaning	The host explains the reported sub-exponential approach with a metaphor of finding tunnels through a mountain, while cautioning that its applications are unclear.
21:53	Hypothetical consequences if P equaled NP	The video considers possible effects on cryptography, optimization, science, and the economy, while noting that a theoretical shortcut may not be practical.
27:34	Arguments for efficient computation and further results	The host cites a computer scientist’s earlier argument about unexpected algorithms, then turns to OpenAI’s reported physics and mathematics results.
29:40	Quantum field theory and concluding uncertainties	The video describes a reported rigorous existence proof related to quantum field theory and concludes that the implications of the ETH result remain uncertain.

Quotes

This ETH was this sort of limit, this computational wall that we thought was there. — 00:31

But what if P equals NP? What if every solution that’s easy to check, what if that means that there’s some shortcut to solving it? — 10:29

But, we know that we don’t have to climb all the way to the peak and all the way back down. — 21:23

Well, that wall, that’s an illusion. — 32:18

Concepts and entities

Exponential Time Hypothesis (ETH), P versus NP, OpenAI, Scott Aaronson, Greg Brockman, Russell Impagliazzo, Ramamohanarao Paturi, Ryan Williams, Yang-Mills theory, quantum chromodynamics, Standard Model, Anthropic

Full transcript (original language)

00:00 Opening I just randomly publishes a blog post with bombshell breakthroughs. These are distinct, world-altering scientific breakthroughs in math, physics, and computer science generated entirely by AI models. Now, if you’ve been following along, if you’ve heard kind of the chatter surrounding this release, you know that one of these is not like the others. And that thing is the fact that this Opening I model proved that the exponential time

00:31 hypothesis, or ETH, well, that is false. This ETH was this sort of limit, this computational wall that we thought was there. It was just a law of physics, kind of like the idea that you can’t travel faster than light. And one day AI comes out and says, “No, you silly, silly monkeys. Of course you can travel much faster than light.” This is kind of like that. But here’s the thing, why are people freaking out? Well, as Opening I says here, this problem this exponential time hypothesis, ETH. It’s funny cuz ETH

01:03 is now trending, but we’re not talking about Ethereum, all right? This is This is going to get confusing. But this ETH sort of problem, it’s a problem deeply related to the P versus NP problem. Now, P versus NP, what does that mean? I’ll try to explain exactly what it is in a second, but here’s kind of the basic overview. Basically, most people believe that in this universe, P does not equal NP. A lot of technology and society and civilization we kind of lean on this

01:35 really, really hard. If P does not equal NP, we’re fine and we can kind of just keep on a trucking. If, however, P equals NP, well, then we have kind of discovered a certain cheat code to this universe. Now, most of society collapses, but also we kind of get this pretty awesome new thing that’s a cheat code to the universe. Now, let’s not get too ahead of ourselves. Here’s Greg Brockman, the president of OpenAI. He’s quick to reassure everybody that P still

02:05 probably doesn’t equal NP. So, we’re still in the everything is cool universe. Probably. But, here’s the thing. There’s also very smart people that believe that P equals NP. This is Scott Aaronson. We’ve been bringing him up a lot recently, haven’t we? But, I just have to bring it up here because about 18 hours ago this podcast was released. In the first few seconds of the intro, he’s saying, “When I talk to my friends in physics, it seems like AI that it still hasn’t come for them, but

02:36 a lot of them are watching it nervously.” So, you get what happened here, right? So, this was a few hours before OpenAI released all of this. You can just imagine Emmett sitting somewhere at OpenAI and going, “Oh, he said that, did he? Okay, unleash with the physics.” But, that brings us to this question of what is P versus NP. But, you know who did a lot of work in this field? It’s Scott Aaronson. This is literally a paper that he wrote. He’s saying, “In 1955, John Nash sent a remarkable letter to the National Security Agency, the NSA.” John Nash,

03:09 Russell Crowe, Beautiful Mind, you know what I’m talking about. So, we have Nash, we have the NSA, the P versus NP question, a question that reaches inward to ask about the mathematical reasoning itself, and also outward to everything from philosophy to natural science to practical computation. So, Scott Aaronson saying, “Just start with the obvious. Essentially, all cryptography that we use currently on the internet, for example, sending credit card numbers, would be broken if P equals NP.” So, that’s kind of what I was talking about earlier. We lean really

03:41 hard on this idea that those two things don’t equal that P does not equal NP. And if it does, well, number one, you know, a lot of the internet is gone, a lot of the privacy is just broken. By the way, there’s a a bit of a asterisk next to that. We’ll get back to that in a second. He also mentions a letter from Kurt Gödel to John von Neumann where they’re saying if this was the case, this would have the consequences of the greatest magnitude. So, you get what this is saying. Some of the greatest, brightest minds were really, really,

04:12 really concerned with this particular question. In fact, it’s one of the seven millennium prize problems. So, this first one was solved in the 2002-2003 by a human and the prize declined. Maybe Stokes was of course the big OpenAI thing and the whole drama that unfolded what less than 30 days ago, but it does seem like the AI one-shotted this one. Then we have the P versus NP, so still unsolved. We have the Riemann

04:42 hypothesis, although as we’ve covered before, AI had a lot of breakthroughs that were kind of relevant, close to it. They were kind of like supporting little pieces that AI has solved. Then we have this Yang-Mills existence, which Google says it’s unsolved, but if you scroll it down through this OpenAI blog post, well, as it was working on a different problem, kind of a as a side quest of sorts, if you will. As OpenAI says here, as a subproblem, this work also includes

05:13 a proof of the existence of pure Yang-Mills theory, which is part of the quantum Yang-Mills theory Clay Mathematics Millennium Prize Problem. So, it did create a proof for that theory, you know, kind of as a byproduct. It was like, “I’m I’m kind of in the area. Might as well just knock this one out.” Now, that’s not the full Millennium Prize. It doesn’t qualify for that and we’ll talk about that later because OpenAI is doing something very interesting with this. You see how those problems, they were around for like almost 30 years, not too much human progress, and then these models start

05:45 coming out and they’re just knocking them down. So, here’s the one solved problems. Here are the unsolved ones. Maybe Stokes they put under active problems as in the OpenAI’s proof, it’s undergoing peer review, etc. And as for these unsolved problems, AI you could say it kind of has them surrounded. So, it’s kind of solving a lot of things in the vicinity and it’s slowly sort of approaching it. And all of this in the last 90 days, I believe. So, this these new models, this level of abilities very

06:17 new. It’s very recent. All right, P versus NP. Let’s break it down. What is this magical equation that gives us magical superpowers but also destroys a society? So, imagine you have like a combination lock, right? And if you have the right combination of numbers in there, it opens. So, let’s say you have one dial on there with 10 different numbers, right? So, 0 to 9, let’s say, right? Let’s say this number is 9. Now, at most it’s going to take you 10 tries to crack the combination. You start at 0, 1 2 3 4 5 6 7 8 9. One of those

06:50 numbers it goes click and it opens. But, if you have two, well, the number of attempts you would have to make is 100. So, with two combinations, it’s 100. So, with two dials, 100 tries. Add a third dial and it’s a thousand. If you add it 10 of those dials, the number of combinations is 10 billion. So, in the beginning it’ll take you under a minute. With a few more, it’ll take you over an hour. And if you keep going, it’ll take longer than you’re going to be alive. So, that’s part one to understand is this sort of exponential growth. And

07:20 this works for passwords for example, right? The longer the password, the more characters it has. If you just add one more character, it keeps increasing exponentially. All right, so that’s point number one. Most of us know that. We kind of at this point intuitively kind of understand this. We just need to understand one other point. The second point is that there are certain types of puzzles, let’s say, or math problems that are difficult to solve and they have that kind of kind of exponential growth of difficulty, but once you solve them, the answer is very easy to check. So, imagine if you’re trying to assign

07:52 shifts to workers, right? So, you have to make sure that somebody’s there at any given point in time. Also, some people just can’t work together cuz they hate each other. And then some people have certain days off. This person requested half a week off, etc. So, somebody gives you a proposed schedule, you can check to see if it works or doesn’t very, very easily. But, coming up with one from scratch that works and satisfies all those constraints is much more difficult. The little Sudoku puzzles are kind of similar cuz what you’re supposed to have is all the numbers 1 through 9 across every column

08:24 and row and also each little these this 3 by 3 square. So, I can quickly verify that this is correct. But, for me to actually solve it might take a lot longer. So, the P versus NP problem, so the P is polynomial time. This just means the more work you have to do when more work is added, it grows in a manageable way. Like if somebody dumps a bucket of dirty laundry in front of you, it may take you 10 minutes to sort it. If they dump like a five buckets, it might take you, you know, not to five times longer, it might take even longer

08:55 cuz you have more stuff to sort of sort, but it’s still manageable. That time grows in a manageable way. It doesn’t grow in exponential way, right? Where if one bucket takes you 10 minutes, but 10 buckets takes you, you know, billions of years, it doesn’t grow like that. It doesn’t grow exponentially. So, that’s the the exponential growth, right? So, this is where just stuff explodes. I’m just going to write boom, you get it, right? It’s too much. And then next there’s NP, so non-polynomial. So, this is that idea of a fast check, right? So, if I hand you a solution to a Sudoku

09:25 puzzle, you can quickly check if it’s correct. So, a lot of our cybersecurity, how we transfer credit cards, and a lot of other stuff, they’re kind of based on the bottom two things here. I hope it’s obvious I’m really simplifying stuff here so that everyone can understand kind of all the concept without understanding all of the math that goes into it. The point is if somebody’s trying to brute force a password or some lock or whatever, we want them doing this exponential work. So increase our password by one character and now that

09:56 person instead of having to spend a thousand years trying to guess it, now they have to spend, you know, 10,000 years trying to guess it. So that kind of exponential work is what keeps the attackers at bay. And we also want the solution to be NP, meaning we can quickly check the answer because otherwise there kind of not be a point. That’s what makes this lock usable, right? So we put the key inside and we’re able to quickly check is this the right key and then the door opens, right? The password opens where we’re trying to get into. So exponentially increasing work keeps the bad guys out and the fast ability to check the NP,

10:29 that allows us to get in if we have the right key. And all the P problems, the ones that are fast to solve, they’re kind of underneath this umbrella of NP that are fast to check because if you can quickly solve them, that means you can quickly check them. But what if P equals NP? What if every solution that’s easy to check, what if that means that there’s some shortcut to solving it? If it’s easy to check, it’s also easy to solve.

10:59 So if you’ve noticed we’ve brought up some extremely intelligent people in this discussion, mathematicians, physicists. The case could be made, I think, that von Neumann was the smartest human to ever live. He once gave a lecture about how a self-copying machine, like how it would work. So he described a machine with all the parts, but it also had this tape that had the instructions for how to create that machine and they would make a copy of the tape and then he they would kind of build that machine and give it the instructions, the copy of the

11:30 instructions of how to make that machine. And that sounds more or less exactly like DNA and how humans and most other animals, everything else kind of recreates itself. But here’s the thing, that lecture happened years before DNA was discovered. But the point is that a lot of extremely intelligent people they kind of look at this and something about this kind of just kept itching at their brain. They were saying, “We need to figure this out, either disprove it or or prove it because this is a very important thing to make sure we know.”

12:00 So the thing that kind of kept itching at their brain, they were thinking to themselves, they were wondering, “What if this is the same as this in disguise? What if the ability to quickly check, what if that had some fundamental application to quickly solve those exponentially growing problems?” But 50-plus years and all of the brilliant people that were trying to either find that this is a true by finding example or finding some way to disprove this, well, they weren’t able to find anything that would lean this one way or another.

12:32 So over time people were kind of like, “Well, it’s probably not true.” Okay, so what is this ETH, exponential time hypothesis? It’s very similar to what we were talking about, only here we’re looking at a massive checklist of variables. For example, like if A is true, then B has to be false and therefore C has to be true. So imagine we have like a 10,000 checklist of these items, we hand it to a system and it has to find some combination that is, you know, true across the board. And of course, we believed this to be

13:03 exponentially hard, right? So as you add more and more variables, eventually even a supercomputer, it would take it more time than the universe will be around for to solve it. And that exponential wall is the ETH. And for 30 years, this was thought of to be just a fundamental law of computing. So you can see how it’s really kind of tangled with that P versus NP problem. And this ETH has been widely believed to be true and has been used in hundreds of papers to derive additional computational hardness

13:34 results across many fields like graph theory, computational biology, databases, computational geometry, and more. So, there are tons of scientific papers that are based on this. They’re saying, “I believe this is true.” And you know, they they reference ETH as why they think this is true. So, it’s like a piece of land and you build a tons of buildings on that land. And then somebody comes along and is like, “Oh, that land just doesn’t exist. It’s just going to fall through.” Like we built a lot of stuff on top of this belief. By the way, how OpenAI is approaching

14:06 releasing this work is very different from how they used to, just because of the massive backlash that that has received. I do want to touch on that in just a second cuz that’s a whole other fascinating thing. But, in a nutshell, OpenAI will not take any credit for these discoveries. And they’re getting researchers in the field to shepherd these discoveries. So, that means that those humans, those experts, those researchers, they will get the credit for this work. In this case, so this work is a shepherded by Russell Impagliazzo, Ramamohanarao Paturi, and

14:39 Ryan Williams. Why is that important? Well, so so get this. So, Impagliazzo and Paturi, well, they discovered, made, created, they are the people behind ETH. So, they created this theory, they developed a lot of work on top of this theory, then 30 years later OpenAI releases a model that goes, “Well, this is just wrong, but you can be my shepherds and sort of lead me into the world and get credit for that work.” Now, there’s a very interesting

15:10 discussion that’s forming kind of around this idea of AI releasing various math proofs, physics, etc. And there’s some of mathematicians that are having a real hard time with it. And a lot of their their posts are kind of strange to read because for example math isn’t some sort of a massive religion and mathematicians aren’t priests. They can’t decide who is and isn’t allowed to do math or or how it’s allowed to be done. And again huge respect to Scott Aaronson here who as

15:40 you can see like AI is intruding very very much on his field. Apparently his 9-year-old son is taunting his wife who is the complexity theorist Dana Moshkovitz saying hey mommy I heard you got cut. I heard that a robot solved the math problem you worked on your whole career. Oof. So if anybody has the right to be upset I think it’s him. But as he says here we are not the arbiters of who gets to work on our problems. These little coalitions of the mathematicians that pop up and they’re like gatekeeping

16:11 like you’re allowed inside our club and you’re not and they’re like no AI allowed. I’m sure there were scribes back in the olden days who you know tried to resist the the emergence of the printing press. You know, good luck but I don’t think it’s going to work out. But huge props to these people who again created something a theory but now that potentially AI created something new some new data comes in they look at it with a clear mind with no bias and they see if it’s true or not and if it’s true then they change their viewpoint based

16:42 on this new data. Right? That’s what scientists do. Right? That’s what adults do. I went on a tangent and I forgot what I was talking about. I apologize. The point being is that this Eath theory was saying that the complexity grows exponentially. So as you added more and more of these little lock dials that you had to guess to figure out which number it is it would exponentially increase how long it would take you to brute force that approach. And that Eath theory was basically saying that in order to figure out what the answer is you were saying that the amount of work would grow exponentially. But this AI

17:13 from OpenAI and by the way Anthropic has it seems like something very very similar. So, it’s almost like they they they both have found these solutions at roughly the same time. Very curious as to why that keeps happening, cuz this might be, you know, the the second time at least something like this has happened. But, the AI finds a sub-exponential way of solving this. So, either saying you have to blindly spin all those little things until you stumble upon a solution, the AI says, “No, no. You got to listen to the tumblers inside and they’ll kind of guide your way.” In

17:44 other words, there’s a some underlying possibility for some logical formula that can eliminate a massive, massive amount of answers. So, it’s almost like they’re saying, “Okay, so if the first number is nine, then the third number, well, it can’t be a four or five or whatever.” And that instantly skips massive amounts of combinations without ever having to test them. All right, so how to kind of get your head around this? What does this actually mean? Here’s how I’m thinking about it and what we can expect as the actual

18:17 practical things that will come out of this. So, like imagine there’s point A and a point B, and they’re, you know, a short distance apart. But, in order to get from point A to point B, you have to climb this Mount Everest, right? This massive sort of mountain. You have to go all the way up and all the way down, takes tons of time. And if you want to move a greater distance than the mountain is even bigger. And this is that P does not equal NP, right? So, that means you got to do the whole work. You got to do everything and there’s no shortcuts. You got to climb all the way

18:48 to the top of a Mount Everest and climb all the way down to get to where you’re going. And this is what we’ve understood the world to be. This is the reality that I think people think that we’re living in. I’m not saying anything to the contrary. I’m just explaining this is how I think the scientific community, most of them, this is what they believe to be true. To go that distance, you you to uh the mountain, no shortcut. But, some people are like, “What if there’s like this tunnel that just goes directly from point A to point B? Then we don’t

19:19 have to climb the entire mountain, we can just take the shortest route from point A to point B.” And that is the P equals NP, right? So, those things are the same, they’re equal. So, all of the problems that are easy to check also have a {quote} {unquote} easy solution. And again, easy means not exponential. Okay, so this this tunnel, that’s of course like we we don’t know if it exists or not. We we just know this path up and down Everest. All right, so what is this ETH and the fact that it was disapproved? Kind of like, what does

19:50 that mean? And by the way, if you’re an expert, if you’re a math whiz, if you really get this stuff, please comment down below if you disagree with kind of my perspective. I don’t have a background in this. It’s like 3:00 a.m. right now, so I could be just completely off of my What’s the expression? Off of the Off of I I don’t remember. I’m just It’s 3:00 a.m. I’m off of my Is it gourd? Gourd? I don’t remember. I know there’s an expression. Let’s continue. In this mountain example where P equals NP is the tunnel, and you know, the the climbing up and down, that’s P does not

20:21 equal NP. What is this new discovery? The best way I I I think to describe it is we did some like scan of this mountain and we’re like, “You know what? There are obviously some tunnels that are in the mountain.” Right? We’ve proved there exist tunnels. Tunnels that the human beings, the smartest human beings alive in the last 50 years, how many years? We were not able to figure it out. We thought you had to climb all the way to the top and all the way to the bottom. And some very smart people thought, “Maybe there’s a tunnel,” but

20:51 we couldn’t find. Now, here AI says, “You know what? I found a tunnel.” The reason that people are a little taken aback by this is not necessarily that this is an amazing tunnel. As OpenAI states here, to the fact that we disproved it, we proved that it was not true, It reopens questions about how much faster these tasks could become. But, finding such algorithms, turning theoretical advances into actual practical uses, well, that’s going to be significant further research. That’s why I’m using kind of this sort of tunnel analogy, right? So, we know there are

21:23 tunnels. Is it this P equals NP tunnel mean Does it Does it say that this is might be available? This might exist? Or are we after a lot of research we’ll find that maybe it like shaved just a little bit off the top? Like we don’t know. We have no idea. I don’t think this gives us any insight right now into that. But, we know that we don’t have to climb all the way to the peak and all the way back down. That there exists some shortcuts. By the way, OpenAI did release the paper with the lean proof

21:53 and kind of like the natural language explanation of it. Here it is, you know, it’s so obvious now that you look at it. But, what happens if, you know, P equals NP? And again, I’m not saying that. I’m not implying that. This doesn’t prove it. As Greg Brockman here says, P still probably doesn’t equal NP. So, understand, I’m just a sort of a theoretically speaking. I’m not saying this is the case. But, let’s imagine what if we find out that yes, there is

22:23 some shortcut for solving these very, very complex problems and puzzles, whatever you want to call them. What happens? Well, first and foremost, like we mentioned, so cryptography is cooked. Websites, banking, you know, cryptocurrency, obviously, a lot of this stuff would I don’t know if how well it could survive. As Scott Aaronson says here, you know, essentially all cryptography that we currently use on the internet, right? All of that would be broken. There are some exceptions and other methods, but they have huge pain

22:55 points. So, that’s the bad stuff and all the bad stuff that goes along with it. I mean, that seems like it could be a huge deal, obviously, for the world as we know it. Maybe not the end of the world, but, you know, it would be rough. You’d probably have to shut down the internet. I’d still be here talking to the camera, but I I would just be talking to myself. But, it would also kind of be sort of a cheat code to the universe. A lot of the optimization problems would become dramatically easier. Scheduling, logistics, chip design, chip layout,

23:26 supply chain optimizations, like a lot of the optimizations would just become very, very easy. So, some simple script could find the optimal points for a lot of this this stuff that we’re slowly trying to uncover right now. Protein modeling, drug design. I mean, there would be massive, massive applications. There would be an explosion in math and science. Everything would accelerate. AI progress could potentially speed up dramatically. This, by the way, might have been something that Rune from OpenAI was hinting at a few weeks ago.

23:57 Kind of saying that it’s not that big of a leap to think that some of these foundational improvements in our understanding of physics and math and the computer science, that it would be kind of a tailwind for, you know, developing AI. Of course, this would also impact the economy quite a bit cuz a lot of the economy and companies, they do rely on certain advantages from being able to do computations fast. That’s true for hardware design, a lot of the financial sectors. That edge could be erased if there were these shortcuts to

24:28 optimization. Now, by the way, just because we figured out that P equals NP, doesn’t automatically mean this gets sort of triggered. Right? So, you can imagine like if from point A to point B, it’s Mount Everest, then from point B to point C, it’s an exponentially higher mountain. Right? So, you can imagine that let’s say here is Mount Everest. Right? So, this is already a massive, massive hill to climb. And then, you know, it gets further and further, and it’s like you’re climbing to the moon and back, you’re climbing to the sun and back, whatever, just exponentially sort

24:59 of increases. We may very well find those sort of easier solutions, but they only are easier, more efficient at sort of massive numbers. So, in our lock example, this might take me a few seconds, a few minutes, an hour plus. So, if it’s sort of low enough, right, I can do it myself, and then it exponentially increases. What if we find some shortcut, some solution, but it only saves you time if the amount of time it takes to do the normal way is greater than, let’s say, like 1,000

25:29 years. So, this P = NP might technically be true, but those hard problems only become easy at really just absurd sort of amounts. So, you could, for example, have a number where just the amount of like matter in the entire universe it won’t be enough to build a computer able to to calculate that high. So, there might be this shortcut, this cheat code that we find, but no one inside of this universe could ever use it. It would kind of be like having a cheat code, but

26:02 the cheat code takes so long to type in that you could never possibly type it in time. If that was the case, that would be extremely suspicious, because nature doesn’t usually work that way. Most of these constants and algorithms, they’re they come from kind of obvious sources. Some random and massive number wouldn’t look like a natural formation, so to speak. It would feel like a deliberately placed barrier, like one of those invisible walls in video games. As this person, Alex Ellis, is saying, if that

26:32 happened, the only reasonable conclusion is that we are in a simulation, and these constants were chosen to be inaccessible to denizens of the simulation, and personified in this case by us. Maybe a simulation is capping the speed of light. Maybe it’s lazy development practices. You can always hear that development meeting, right? They’re like, “How do we make sure all those critters don’t get everywhere?” They’re like, “Oh, we’ll just put them on on a little sphere, so it’s round, so they can’t go anywhere.” All right, but what if they like fly off of it? It’s like, just put a speed limit on on how

27:03 fast they can go. All right, but how do we make sure they don’t like speed run on the tech tree and just discover everything? Oh, for that, well, you see this P equals NP constant? Just hit nine a whole bunch of times and then just hit enter. You’re done. And you know there’s a chance that that is exactly how it happened. Like really, would you be shocked? And if that’s how it happened, they certainly will be constrained a little bit. But if you want to hear an opposing take, this is Emmanuel Viola, Harvard PhD in computer science, post-doc at Princeton, at Columbia, full

27:34 professor at Northeastern, co-authored research with Timothy Gowers, who is a Fields medalist, and he has a superpower that is rarely seen in in people that caliber. Look at this headline. You can understand what it’s saying. It says, “I believe P equals NP.” I’ll link this post down below. It’s an interesting read. And it was written in 2018. So, that was before most of us have heard about large language models. Whatever large language models existed then probably just have spit out

28:05 gibberish. The Transformers paper, I think, came out 2017. So, this is a shortly after that. And basically what he’s saying is that very often, very smart people, they declare something to be impossible. And then usually almost right after that, somebody finds a clever algorithm to do just that. In the 1950s, Kolmogorov said, “You can’t do something. It’s impossible.” He started doing a seminar about it, and within 1 week of the start of the seminar, one of the students will discovered the algorithm that proved him wrong. Kolmogorov became agitated and

28:36 terminated his seminar. Strassen wanted to prove that the current way they had to do matrix multiplication was optimal and proved exactly the opposite. He found a better approach. So, we often have these uh surprise breakthroughs that come out of nowhere when we were sure it’s impossible, something comes out and we’re like, “Nope, I guess it is possible and there’s room for improvement.” And on the flip side, kind of the lower bound, the things where you prove that it can’t get better than some level, they almost never happen. And the ones that do, they kind of use very boring techniques that are unsurprising.

29:08 And are of course, you know, even though this was written many, many years ago, the events of, you know, today, this week, make him seem like he saw the future a little bit. Like this fits with his theory. So, he’s saying we’ve grossly underestimated the reach of efficient computation. Meaning there’s usually a cheap, fast, quick algorithm that does something that seems overwhelming. Right? We think there’s a Mount Everest to climb, but there’s a tunnel that just shoots us there. He’s saying that’s keeps happening over and over again. The other breakthrough that

29:40 OpenAI has talked about was this existence of quantum chromodynamics and completion of the standard model. That’s the one that solved part of the Millennium Prize. So, it doesn’t get the Millennium Prize, but a portion of it, it it had a proof for the existence of that thing, which is half of it, you could say. And the standard model is kind of what us humans came up with. It’s sort of our rule book for the universe, right? So, if if the universe is a game board, this is kind of like we wrote the rule book. Like as we observed

30:11 it, this is what we think the rules are. So, you take these little particles and we accelerate them, we crash them together in this giant particle collider in Switzerland, and those actual physical results of the experiment, they match what we wrote in a little in a little rule book. So, hooray. But scientists, mathematicians, physicists couldn’t fully sort of work out how everything worked rigorously to prove that it was correct, especially kind of the edge cases. Like there wasn’t a sound, rigorous, fully comprehensive mathematical proof of everything. And

30:44 so, OpenAI model produced this result that is a mathematically rigorous existence proof of something something something. I’m not going to pretend that I understand this, but as OpenAI is saying here, this result marks the beginning of a transition in which quantum field theory, the most important framework in modern theoretical physics, becomes a mathematically rigorous field. So, if I’m understanding correctly, we humans, we got pretty far on our own efforts. We wrote this rule book of how things work, and it matched the actual

31:16 reality. So, when we tested these collisions of particles, like those seemed to reflect what we thought they would be. But our understanding, our math, there were still a lot of gaps in there. This model comes in and just fills in all those gaps. Again, this is as best as I understand it. They also released some work in the local smoothing and Kakeya conjecture. Again, taking some understanding that we’ve had and then the fully kind of a writing everything out across all dimensions and providing like a rigorous math around it. Again, don’t fully know what it is,

31:46 but it kind of seems like a big deal. The thing that I got stuck on was this, the exponential time hypothesis, ETH, and how it relates to the P equals NP problem. Because a lot of the other stuff that we talked about in math and the the results from today, they’re exciting, they’re earth-shattering. This is kind of in a league of its own because it’s kind of saying, “Hey, you know that limit that you thought existed, that wall that you could never get through, the thing that you thought would slow down or limit how far you could get? Well, that wall, that’s an

32:18 illusion.” Again, potentially, maybe. Cuz we might find that the wall is still there, it’s just a foot sort of a further than we thought it was. We still don’t know what the practical applications are. But if someone who is studying in this stuff has this intuition that we are nowhere near are of the edges of discovering these efficient computation algorithms as as he says. And he was saying that almost a decade ago before AI and large language models. So, definitely feels like something to keep an eye on. But, let me

32:49 know what you think. Put it in the comments down below. If you made this far, thank you so much for watching. My name is Wes Roth. I will see you in the next one.