**OpenAI just broke physics... — Transcript & Summary | SozAI**
Source: https://sozai.app/transcript/openai-physics-breakthrough-claim/

Wes Roth explains OpenAI's claimed AI-generated math breakthroughs, including a disproof of the exponential time hypothesis, and what P vs NP means for cryptography and science.

## Key Takeaways

- OpenAI claims AI disproved the exponential time hypothesis, a major result in computational complexity.
- P vs NP remains unsolved, and most experts believe P does not equal NP.
- If P equaled NP, widespread cryptography would be compromised, but science and computation would be transformed.
- AI systems appear to be making rapid progress on long-standing open math problems.

## What the video covers

- OpenAI published a blog post claiming AI-generated breakthroughs in math, physics, and computer science, most notably a proof that the exponential time hypothesis (ETH) is false.
- ETH is closely related to the P vs NP problem, which asks whether problems whose solutions are easy to verify are also easy to solve.
- Most researchers believe P does not equal NP; if it did, much of internet cryptography would be broken.
- Scott Aaronson's work and a podcast comment about physicists nervously watching AI progress are discussed as context.
- OpenAI reportedly also produced a byproduct proof for pure Yang-Mills theory, one of the Millennium Prize Problems, though not the full prize problem.
- The video notes AI has been making progress on several Millennium Prize Problems, including Navier-Stokes, in recent months.
- The combination lock analogy illustrates exponential growth in brute-force search versus easy verification.
- Emanuel Viola is cited as offering a skeptical perspective on the claims.
- The host speculates on consequences if shortcuts for hard problems exist, such as accelerated math, science, and AI progress.
- The host encourages expert viewers to comment and correct his understanding.

## Chapters

1. 00:00 OpenAI's Claimed AI Breakthroughs
2. 01:28 Exponential Time Hypothesis and P vs NP Basics
3. 04:00 Scott Aaronson and the Stakes of P vs NP
4. 07:10 Millennium Prize Problems and AI Progress
5. 13:00 Combination Lock Analogy and Exponential Growth
6. 18:00 Skeptical Perspectives and Implications
7. 23:00 Closing Remarks

Answers

## Questions about this video

What is the exponential time hypothesis according to the video?

The exponential time hypothesis is described as a computational wall researchers believed existed, closely related to P vs NP. The video says OpenAI's model claims to have proven it false.

Why would P equaling NP matter?

The video explains that if P equaled NP, much of internet cryptography, such as protecting credit card transmissions, would be broken. It would also give a powerful shortcut for solving hard problems.

Did OpenAI solve a Millennium Prize Problem?

Not the full prize problem. The video says OpenAI produced a proof for pure Yang-Mills theory as a byproduct, which is part of the Yang-Mills Millennium problem but does not qualify for the full prize.

## Full Transcript — Download SRT & Markdown

00:00

Speaker A

OpenAI just randomly publishes a blog post with bombshell breakthroughs.

00:20

Speaker A

These are distinct, world-altering scientific breakthroughs in math, physics, and computer science, generated entirely by AI models.

00:36

Speaker A

Now, if you've been following along, if you've heard the chatter surrounding this release, you know that one of these is not like the others.

00:42

Speaker A

And that thing is the fact that this OpenAI model proved that the exponential time hypothesis, or ETH, is false.

00:56

Speaker A

ETH was this sort of limit, a computational wall that we thought was there.

01:11

Speaker A

It was just a law of physics, kind of like the idea that you can't travel faster than light.

01:28

Speaker A

And one day AI comes out and says, "No, you silly, silly monkeys, of course you can travel much faster than light."

01:47

Speaker A

This is kind of like that.

02:00

Speaker A

But here's the thing: why are people freaking out?

02:21

Speaker A

Well, as OpenAI says here, this problem, the exponential time hypothesis, ETH, is funny because ETH is now trending, but we're not talking about Ethereum, right?

02:33

Speaker A

This is going to get confusing, but this ETH sort of problem is deeply related to the P versus NP problem.

02:47

Speaker A

Now, P versus NP, what does that mean?

03:01

Speaker A

I'll try to explain exactly what it is in a second, but here's the basic overview.

03:17

Speaker A

Most people believe that in this universe, P does not equal NP.

03:32

Speaker A

A lot of technology and society and civilization lean on this really, really hard.

03:47

Speaker A

If P does not equal NP, we're fine and we can keep on trucking.

03:58

Speaker A

If, however, P equals NP, then we have discovered a certain cheat code to this universe.

04:11

Speaker A

Now, most of society collapses, but we also get this pretty awesome new thing: a cheat code to the universe.

04:29

Speaker A

Now, let's not get too far ahead of ourselves.

04:45

Speaker A

Here's Greg Brockman, the president of OpenAI.

04:59

Speaker A

He's quick to reassure everybody that P still probably doesn't equal NP.

05:12

Speaker A

So we're still in the "everything is cool" universe, probably.

05:26

Speaker A

But here's the thing: there are also very smart people who believe that P equals NP.

05:37

Speaker A

This is Scott Aaronson, and we've been bringing him up a lot recently, haven't we?

05:53

Speaker A

I have to bring him up here because about 18 hours ago, this podcast was released.

06:07

Speaker A

In the first few seconds of the intro, he says, "When I talk to my friends in physics, it seems like AI hasn't come for them yet, but a lot of them are watching it nervously."

06:23

Speaker A

So you get what happened here, right?

06:38

Speaker A

This was a few hours before OpenAI released all of this.

06:43

Speaker A

You can just imagine Sam Altman sitting somewhere at OpenAI going, "Oh, he said that. Did he, okay, unleash the physics?"

06:55

Speaker A

But that brings us to the question of what P versus NP is.

07:09

Speaker A

You know who did a lot of work in this field?

07:19

Speaker A

It's Scott Aaronson.

07:31

Speaker A

This is literally a paper that he wrote.

07:43

Speaker A

He's saying, "In 1955, John Nash sent a remarkable letter to the National Security Agency, the NSA."

07:55

Speaker A

John Nash, Russell Crowe, A Beautiful Mind, you know what I'm talking about.

08:00

Speaker A

So we have Nash, we have the NSA, and 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.

08:11

Speaker A

Scott Aaronson says, to start with the obvious, essentially all cryptography that we currently use on the internet, for example, sending credit card numbers, would be broken if P equals NP.

08:23

Speaker A

So that's what I was talking about earlier.

08:37

Speaker A

We lean really hard on the idea that those two things don't equal each other, that P does not equal NP, and if it does, well, number one, a lot of the internet is gone and a lot of the privacy is just broken.

08:48

Speaker A

By the way, there's an asterisk next to that, and we'll get back to it in a second.

08:59

Speaker A

He also mentions a letter from Kurt Gödel to John von Neumann, where they say that if this was the case, it would have consequences of the greatest magnitude.

09:11

Speaker A

So you get what this is saying: some of the greatest, brightest minds were really, really concerned with this particular question.

09:16

Speaker A

In fact, it's one of the seven Millennium Prize Problems.

09:29

Speaker A

The first one was solved in 2002 or 2003 by a human, and the prize was declined.

09:43

Speaker A

Navier-Stokes was, of course, the big OpenAI thing, the whole drama that unfolded less than 30 days ago, but it does seem like the AI one-shotted this one.

09:54

Speaker A

Then we have P versus NP, still unsolved.

10:05

Speaker A

We have the Riemann hypothesis, although as we've covered before, AI has had a lot of breakthroughs that were relevant and close to it.

10:18

Speaker A

They were supporting little pieces that AI has solved.

10:30

Speaker A

And then we have Yang-Mills existence, which Google says is unsolved.

10:41

Speaker A

But if you scroll down through this OpenAI blog post, as I was working on a different problem, kind of as a side quest of sorts, as OpenAI says here, as a subproblem, this work also includes a proof of the existence of pure Yang-Mills theory, which is part of the quantum Yang-Mills theory, Clay Mathematics Institute Millennium Prize problem.

10:59

Speaker A

So it did create a proof for that theory as a byproduct.

11:16

Speaker A

It was like, I'm kind of in the area, I might as well knock this one out.

11:27

Speaker A

Now, that's not the full Millennium Prize, and it doesn't qualify for that.

11:42

Speaker A

We'll talk about that later, because OpenAI is doing something very interesting with this.

11:54

Speaker A

You see how those problems were around for almost 30 years, not much human progress, and then these models start coming out and they're just knocking them down.

12:06

Speaker A

So here are the solved problems, and here are the unsolved ones.

12:23

Speaker A

Navier-Stokes they put under active problems, as in OpenAI has a proof, it's undergoing peer review, and so on.

12:36

Speaker A

As for these unsolved problems, AI, you could say, has them surrounded.

12:50

Speaker A

It's solving a lot of things in the vicinity and slowly approaching them, all in the last 90 days, I believe.

13:01

Speaker A

So this level of ability is very new and very recent.

13:13

Speaker A

All right, P versus NP, let's break it down.

13:28

Speaker A

What is this magical equation that gives us magical superpowers but also destroys society?

13:43

Speaker A

Imagine you have a combination lock, right?

13:54

Speaker A

If you have the right combination of numbers, it opens.

14:07

Speaker A

Let's say you have one dial with 10 different numbers, 0 to 9.

14:19

Speaker A

Let's say the correct number is nine.

14:36

Speaker A

Most likely it's going to take you 10 tries to crack the combination.

14:56

Speaker A

You start at 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and one of those numbers goes click and it opens.

15:08

Speaker A

But if you have two dials, the number of attempts you would have to make is 100.

15:24

Speaker A

So with two dials, 100 tries.

15:40

Speaker A

Add a third dial and it's a thousand.

15:54

Speaker A

If you add 10 of those dials, the number of combinations is 10 billion.

16:06

Speaker A

So in the beginning, it will take you under a minute.

16:19

Speaker A

With a few more dials, it'll take you over an hour.

16:32

Speaker A

And if you keep going, it'll take longer than you're going to be alive.

16:43

Speaker A

So part one to understand is this exponential growth, and it works for passwords, for example.

16:57

Speaker A

The longer the password and the more characters it has, the more the difficulty increases exponentially if you add just one more character.

17:05

Speaker A

All right, that's point number one.

17:17

Speaker A

Most of us intuitively understand this at this point.

17:30

Speaker A

We just need to understand one other point.

17:43

Speaker A

The second point is that there are certain types of puzzles, or math problems, that are difficult to solve and have that exponential growth of difficulty, but once you have a solution, the answer is very easy to check.

17:59

Speaker A

So imagine you're trying to assign shifts to workers.

18:12

Speaker A

You have to make sure somebody's there at any given point in time.

18:25

Speaker A

Also, some people just can't work together because they hate each other.

18:34

Speaker A

And then some people have certain days off.

18:46

Speaker A

This person requested half a week off, and so on.

18:58

Speaker A

So somebody gives you a proposed schedule, and you can check to see whether it works or doesn't very, very easily.

19:10

Speaker A

But coming up with one

19:22

Speaker A

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 quoteunquote easy solution. And again, easy means not

19:39

Speaker A

exponential. Okay. So this 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

19:48

Speaker A

that it was disapproved kind of like what does that mean? And by the way, if you're an expert, if you're a math wiz, if you really get this stuff, please comment down below if you disagree with kind of my perspective. I don't have a

19:59

Speaker 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

20:12

Speaker A

remember. I know there's expression. Let's continue. In this mountain example where P= MP is the tunnel and you know the the climbing up and down. That's P does not equal NP. What is this new discovery? The best way I I I think to

20:26

Speaker A

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 that there exist tunnels, tunnels that the human beings, the smartest

20:40

Speaker A

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

20:50

Speaker A

people thought maybe there's a tunnel, but we couldn't find it. 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

21:03

Speaker A

states here. So the fact that we disproved it we proved that it was not true. It reopens questions about how much faster these tasks could become.

21:11

Speaker A

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 tunnels. Is it this P equals NP tunnel?

21:27

Speaker A

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 shaves just a little bit off the top like we don't know. We have

21:37

Speaker A

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.

21:47

Speaker A

That there exists some shortcuts. By the way, OpenI did release the paper with the lean proof 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

22:03

Speaker A

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.

22:16

Speaker A

So understand, I'm just sort of theoretically speaking. I'm not saying this is the case but let's imagine what if we find out that yes there is some shortcut for solving these very very complex problems and puzzles whatever you want to call them what happens well

22:31

Speaker A

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 how well it could survive as Scottson says here you know essentially all cryptography that we currently use on

22:48

Speaker A

the internet, right? All of that would be broken. There are some exceptions and other methods, but they have huge pain 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

23:01

Speaker A

deal, obviously, for the world as we know it. Maybe not the end of the world, but, you know, it would be rough. It would probably have to shut down the internet. I'd still be here talking to the camera, but I I would just be

23:13

Speaker A

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, supply chain optimizations, like a lot of the

23:29

Speaker A

optimizations would just become very very easy. So some simple script would find the optimal points for a lot of this the stuff that we're slowly trying to uncover right now. protein modeling, drug design. I mean, there would be

23:43

Speaker A

massive, massive applications. There would be an explosion in math, science, everything would accelerate. AI progress could potentially speed up dramatically.

23:53

Speaker A

This, by the way, might have been something that run from OpenAI was hinting at a few weeks ago, kind of saying that it's not that big of a leap to think that some of these foundational improvements in our understanding of

24:04

Speaker A

physics and math and computer science that it would be kind of a a tailwind for, you know, developing AI. Of course, this would also impact the economy quite a bit because a lot of the economy and companies, they do rely on certain

24:17

Speaker A

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 optimization. Now, by the way, just because we figure out that P equals NP

24:34

Speaker A

doesn't automatically mean that 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

24:46

Speaker A

imagine that let's say here is Mount Everest, right? So this is already a a massive a 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

24:57

Speaker A

back whatever it just exponentially sort of increases. We may very well find those sort of easier solutions, but they only are easier and more efficient at sort of massive numbers. So in our lock example, this might take me a few

25:12

Speaker A

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

25:27

Speaker A

takes to do the normal way is greater than, let's say, like a thousand years.

25:30

Speaker A

So this P equals 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

25:46

Speaker A

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 this universe could ever use it. It would kind of be like having a cheat code but

26:02

Speaker A

the cheat code takes so long to type in that you could never possibly type it in in time. If that was the case, that would be extremely suspicious because nature doesn't usually work that way.

26:15

Speaker A

Most of these constants and algorithms there, they come from kind of obvious sources. Some random massive number wouldn't look like a a natural formation, so to speak. It would feel like a deliberately placed barrier, like one of those invisible walls in video

26:29

Speaker A

games. As this person Alex Ellis is saying, if that happened, the only reasonable conclusion is that we are in a simulation and these constants were chosen to be inaccessible to Dennis of the simulation and personified in this case by us. Maybe it's similar to just

26:45

Speaker A

capping the speed of light. It's lazy development practices. You can always hear that development meeting, right?

26:51

Speaker A

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

27:01

Speaker A

like just put a speed limit on on how fast they can go. All right, but how do we make sure they don't like speedrun the tech tree and just discover everything? Oh, for that? Well, you see this P= MP constant and just hit nine a

27:14

Speaker A

whole bunch of times and 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, certainly will be constrained a little

27:26

Speaker A

bit. But if you want to hear an opposing take, this is Emanuel Viola, Harvard, PhD in computer science, postoc at Princeton at Colombia, full professor at Northeastern, co-authored research with Timothy Gowowers, who is a fields medalist, and he has a superpower that

27:43

Speaker A

is rarely seen in in people of 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

27:59

Speaker A

was before most of us have heard about large language models. Whatever large language models existed then probably just spit out gibberish. The transformers paper I think came out 2017. So this is shortly after that. And basically what he's saying is that very

28:12

Speaker A

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, Kaggorov said, "You can't do something. It's impossible." He started doing a seminar about it, and

28:28

Speaker A

within one week of the start of the seminar, one of his students discovered the algorithm that proved them wrong.

28:35

Speaker A

Komaov became agitated and terminated his seminar. Straan 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 surprise breakthroughs that come out of

28:50

Speaker A

nowhere when we're sure it's impossible. Something comes out 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

29:02

Speaker A

level, they almost never happen. And the ones that do, they kind of use very boring techniques that are unsurprising.

29:09

Speaker A

And 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

29:23

Speaker A

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. And he's saying that

29:37

Speaker A

keeps happening over and over again. The other breakthrough that opening eye has talked about was this existence of quantum chromodnamics 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

29:53

Speaker A

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 uh our rule

30:05

Speaker A

book for the universe, right? So if the universe is a game board, this is kind of like we wrote the rule book like as we observed it, this is what we think the rules are. So we take these little

30:15

Speaker A

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,

30:29

Speaker A

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 so opening a model produced this result

30:47

Speaker A

that is a mathematically rigorous existence proof of something something. I'm not going to pretend that I understand this, but as opening eye is saying here, this result marks the beginning of a transition in which quantum field theory, the most important

31:02

Speaker A

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 rulebook of how things work and it matched the actual reality. So when we tested these

31:18

Speaker A

collisions of particles like those seem to reflect what we thought they would be but our understanding our math there was still a lot of gaps in there. This model comes in and just fills in all those gaps. Again this is as best I understand

31:31

Speaker A

it. They also released some work in the local smoothing and CA conjecture again taking some understanding that we've had and and fully kind of writing everything out across all dimensions and providing like rigorous math around it. Again, don't fully know what it is, but it kind

31:48

Speaker A

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= NP problem because a lot of the other stuff that we talked about in

32:00

Speaker A

math and the results from today, they're exciting. They're earthshattering. 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

32:12

Speaker A

get through, the thing that you thought would slow down or limit how far you could get? Well, that wall, that's an illusion. Again, potentially, maybe, cuz we might find that the wall is still there. It's just a foot sort of further

32:25

Speaker A

than we thought it was. We still don't know what the practical applications are. But if someone who is studying this stuff has this intuition that we are nowhere near kind of the edges of discovering these efficient computation algorithms as as he says and he was

32:41

Speaker A

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 know what you think. Put it in the comments down below. If you made it this far, thank

32:54

Speaker A

you so much for watching. My name is Wes Roth. will see you in the next

Topics: OpenAI P vs NP exponential time hypothesis Millennium Prize Problems Scott Aaronson computational complexity AI mathematics Yang-Mills cryptography Wes Roth

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