OpenAI's secret model just BROKE math...

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’s secret model just BROKE math… · Channel: Wes Roth · 21:16 · Watch on YouTube

Topics: AI evaluation and benchmarks, AI models, Health and science

Summary

The video discusses OpenAI’s release of 722 Lean-verified mathematical manuscripts, describing a rapid increase in AI-generated mathematical results while emphasizing that the claims still need review by mathematicians. The examples include partial progress on problems related to the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, and the Goldfeld conjecture; none of the Millennium Prize problems is said to have been solved. The host frames mathematics as a test case for how other fields may handle AI-generated discoveries, raising questions about verification, human understanding, and whether mathematics will remain a human-led pursuit. The video closes by arguing that the significance of the release depends heavily on how many results withstand verification, followed by a joke about a mathematician working as a plumber.

Key points

OpenAI released 722 mathematical manuscripts with Lean verification, alongside proofs, conjectures, and reasoning traces.
The host describes a sharp rise in output: around 10 results in August, more than 100 in September, and 722 manuscripts by October 6.
The manuscripts cover 17 subject areas, and the host stresses that the results have not yet been fully verified by mathematicians.
The reported results include a fixed 0.875 boundary related to the Riemann hypothesis, but do not settle the hypothesis or earn its prize.
Other examples discussed include a formula for a broad class of Birch and Swinnerton-Dyer problems and results related to the predicted 50/50 split in the Goldfeld conjecture.
The host presents mathematics as relatively checkable and therefore a useful early test of how AI discoveries might affect other fields.
A central challenge is shifting from producing proofs to verifying and understanding them, especially if AI output grows faster than expert capacity.
The video raises concerns that industrialized mathematics could reduce incentives for people to become mathematicians, while also noting potential benefits for research and technology.
The host says the impact of the release depends on how many manuscripts prove correct, and suggests that a high verification rate would make it a historic moment for mathematics.

Chapters

Start	Chapter	Summary
00:00	OpenAI’s release of 722 mathematical manuscripts	The host introduces OpenAI’s large collection of AI-produced mathematical work and describes its rapid growth over recent months.
04:08	Examples of mathematical progress	The video explains, in broad terms, partial results involving the Riemann hypothesis, Birch and Swinnerton-Dyer, and Goldfeld.
07:12	Verification and the consequences of AI discoveries	The host considers how mathematicians can review the papers and what a flood of AI-generated results could mean for other fields.
10:20	How mathematical results might improve AI	The video argues that mathematical breakthroughs could feed into machine learning and discusses whether humans will be able to understand the resulting work.
13:58	The future role of human mathematicians	The host raises questions about preserving a human mathematical community and contrasts possible risks with benefits to human well-being.
16:34	AI in other fields and concerns about releasing results	The discussion extends to biology and medicine, considers alignment and verification, and mentions mathematicians’ objections to the release.
18:09	Potential benefits and the need to verify	The host reflects on possible health benefits of future AI discoveries and emphasizes that the accuracy of the manuscripts remains crucial.
20:14	The plumber joke	The video ends with a story about a mathematics professor who becomes a plumber and is helped by fellow plumbers in math class.

Quotes

Math just became an industrial process. — 01:34

math is moving from can we prove it to can we check it? — 07:12

That would really be I think the best case outcome. — 13:28

So, definitely keep an eye on this. — 19:42

Switch the limits of the integral. — 21:16

Concepts and entities

OpenAI, Lean, Riemann hypothesis, Birch and Swinnerton-Dyer conjecture, Goldfeld conjecture, Navier–Stokes equations, Scott Aaronson, AlphaEvolve, Sakana AI

Full transcript (original language)

00:00 Well, it looks like the rumors were true. OpenAI just published 722 mathematical manuscripts, all of them produced by this unreleased insider internal model. Did it solve the Riemann hypothesis? Did it prove that P equals NP? Did it solve all math forever? Well, not quite. But, what it released is absolutely insane. Some people refer to it as the quasi Riemann hypothesis. To the people that have no idea what any of that stuff is, basically there’s a set

00:31 of math problems that are incredibly complicated. And also, if we make some progress on them or solve them, they will really, we hope, unlock a lot of new understanding in math, fundamental understanding. Some of these problems, if solved, carry millions of dollars in prizes. OpenAI already published Navier-Stokes, which sounds like it would qualify for that prize. Now, OpenAI is not claiming it because it was solved by an AI model. But, forget the individual problems for a second and just zoom out a little bit. In August of this year, about two months ago, OpenAI

01:03 published something like 10 results on 10 problems. In the next month, September, right? That’s when they published Navier-Stokes plus 100 plus other math problems. And today, we’re six days into the month and they published 722 manuscripts with Lean verification. And this is the important part to understand. Whatever you might think about any of those individual papers or individual problems, pay attention to the curve. It’s the same thing I’ve been

01:34 saying about how well AI is going to code. Back in the days when people say, “Oh, it’s so stupid. It can’t do this.” I’m like, “Yeah, but it’s getting a lot better very, very fast.” And think about where we are today. So, from August when we published 10 papers to September when we published 100 plus to October 6th, six days into the month, 722 manuscripts, that’s roughly 10x every month. It’s a 10x increase every single month. Math just became an industrial

02:05 process. Take a look at this. As OpenAI says here on this blog post, by the way, they’ve released all of these proofs and conjectures and reasoning traces and lean verification, whatever you want, it’s on github.com/openai/math. Each one of these results used the equivalent compute of roughly 3 hours of ChatGPT Pro thinking. So, I I hope that makes sense, right? We as humans, we’ve dedicated decades the humanity as a whole trying to move some of these fields, some of these problems forward. A genius mathematician might devote

02:37 decades of their lives trying to make some progress, or this internal model, you know, thinks for 3 hours and moves the whole field forward. As you’ll see, we’ll go through some of these. They did move the field forward way more than we have, the humanity as a whole. They moved it forward more than all of us have. Last month, when OpenAI released a Navier-Stokes solution that that the AI model found, a lot of news publications tried to twist it as in they stole it. Like, there was this mathematician who

03:07 did all the work, and OpenAI they they stole it from him. Well, that, of course, was not true, but it will be interesting to see how they spin this one, cuz there’s a 722 papers here. Now, they haven’t been verified by mathematicians yet, but once it’s official, once it’s verified, I think it’ll be pretty hard to argue against the fact that we’re at a point in history where these AI models are now better at math than humans. So, these 722 problems, they span 17 different

03:38 subject areas, from prime numbers to plasma physics to quantum circuits. So, no human has ever been at the frontier of these problems, no more than maybe two or three of these areas. A mathematician might spend decades learning and working just to have sort of the chance that you can qualification to maybe approach one of these. That’s a very, very, very important point because the models don’t need to specialize. This isn’t even like a math model. This is a large language model. It can write

04:08 a rough draft of your email, write you a poem, and do some little coding, and also progress humanities understanding of mathematics on seven different frontiers at the same time, one model. General model. All right, so let’s kind of look at some of these and really fast because it’s important. I’m not pretending to understand any of this. When this came out, I tried to kind of do a little deep dive understand some of these problems and the mathematical principles. And after doing some reading, I feel like I understand less.

04:39 But, we have what people have called the quasi Riemann hypothesis. So, the Riemann hypothesis is basically looking at how prime numbers behave. The zeta function contains information about where prime numbers occur. We we think we believe that there might be some pattern to how these prime numbers occur. Better understanding about how math works fundamentally just gives us, you know, I guess I would say fundamentally a better understanding of math, if that makes sense. So, how big of an impact would this have on real-world technologies and situations?

05:09 I’m not quite sure. Some of the stuff is used for cryptography, cybersecurity, etc. But, apparently Riemann’s target was the 0.5 line. That was sort of like the goal to get to. By the way, for a lot of this math stuff, this is kind of how I think about it. Like, imagine there’s this mountain, but up here there’s a lot of fog or clouds, so we have no idea what’s up here. So, for a lot of these proofs, it’s sort of like us slowly climbing up the mountain. If we’re able to climb up here, then we know this mountain is at least this tall. Does that make sense, right? So,

05:40 if you get to this point, you can say the mountain is at least this tall, but it might be much taller. We might be near the peak or nowhere near the peak. And so, humans, we got here, right? And Riemann, I guess the target was somewhere up here. What AI was able to do is get us here, let’s say. So, it got a lot higher than humans were able to. So, it got this high in the mountain, say, “Okay, this this mountain is at least this tall.” So, AI established a fixed 0.875 boundary. Riemann’s target is 0.5, and

06:10 humans, we got to the 1.0 line. And of course, the million-dollar prize is for the full Riemann hypothesis, so this partial result does not settle it, but it gets us a lot closer than we ourselves could could ever get. Then we have the Birch Swinnerton-Dyer, and I don’t even know where to begin with this one. But the point is AI established the complete formula for some broad class of these problems. And again, we have a $1 million prize for the full set of these problems. So, these cases don’t settle

06:41 the entire problem. But again, it seems like it’s a big step forward. It looks like we had some big breakthroughs in the 1980s, and this seems like it’s next big breakthrough that happened with this internal OpenAI model. Then we have the Goldfeld conjecture. So, in this sort of a family of equations, half of them should have a finite amount of solutions and half an infinite. AI supplied many more to kind of complete the bridge to the predicted 50/50 split. So, the big question now is the verification. So,

07:12 722 papers were just dropped on on the world in one day. How many people in the world are capable of reviewing, let’s say, just like one of these? Maybe there’s a few hundred people, maybe a thousand, you know, for each one it would take a week or weeks to review this math. A lot of this already has machine-readable proofs in the Lean language, so there’s some sort of that makes it a little bit easier. But notice, math is moving from can we prove it to can we check it? Can we understand

07:43 it? But I think the bigger kind of wave is coming after this in in biology, physics, economics, etc. The reason being is that math is checkable. We can check it. If the AI model spits out some crazy theorem, we can have a human being go through it and say this is true or this is false. So, math is almost like a testing grounds of what happens when these frontier AI models or when these AI models reach the frontier of any given, let’s call it, industry or field

08:14 of study. What happens when these AI models start spitting out a flood of discoveries in any given field? We’re seeing it happen live to mathematics. And step one is going to be this scramble to figure out how do we verify these results? Because what if, let’s say, 10% of it is wrong? What does that mean? What if half of it is wrong? Or what if none of it is wrong? Or maybe there’s a few errors here and there, but it’s it’s mostly right. Those are very different stories. A lot of the stuff here really writes textbooks, right? It completely changes how we explain math in colleges and universities. So, if

08:46 this is mostly correct, this is probably the biggest shift in mathematics that we’ve ever had. Now, if a lot of it is wrong, well, then we can kind of maybe still good for machine learning cuz we can figure out, okay, where do these AI models where does their reasoning break down? By the way, the reason why OpenAI is doing this is because they’re kind of running out of benchmarks. So, instead of trying to come up with some crazy new benchmark, they just pointed at math at these unsolved issues, unsolved problems. But a lot of this kind of begs the question, okay, but how much of this is sort of actionable? Is this just like

09:18 cool breakthroughs that will have no impact on the real world? Is it just a new benchmark for AI models? And some people won’t be able to, you know, win the Millennium Prize and collect a million dollars because the AI got there first. By the way, as far as the Millennium Prizes go, so doesn’t seem like any of them were reached or solved with with what was it produced here, but they’re definitely being surrounded, right? All this stuff is kind of putting them in a chokehold, so to speak, because all of the little problems surrounding those big problems, they’re getting solved. Like it’s just getting

09:48 closer and closer and closer. So, the pattern here is kind of like encirclement, like right right. So, we’re solving every little problem around it and we’re encroaching closer and closer to the big problem. So, it does feel like soon that will be solved as well. But, the big question is like what actionable things will flow out of this? Will this affect the world in some observable way that we can see and see soon? I can’t find the post by Brune, who is an OpenAI researcher, from last couple days. I’ve covered it on a previous video. I just can’t find it right now, where he was kind of hinting

10:20 at all of this stuff being released. And his point, if I understand it correctly, but the point is some of these breakthroughs in math, they will affect machine learning. They will affect how we create and and train and understand these AI models. Some of them might even affect how we build the hardware, the GPUs, and the various AI chips, et cetera. AI is, as they say at the end of the day, is a matrix multiplication. And these mathematical breakthroughs, they’re certainly to sort of beget other mathematical breakthroughs. So,

10:51 definitely where this is very likely to have an impact is inside of these AI labs themselves. Right? Because in our little mountain example, where it’s tall and it’s in the in the clouds and it’s in the fog, so we don’t know how tall it is, right? Humans over decades and decades, we slowly got our understanding to be up here. So, that’s in some cases 100-plus years, in other cases decades. Then these new models come out, cuz keep in mind, this is like the last, what, two, three months, right? Again, so August, 10 problems, September, 100

11:22 problems, and now it’s October 6th and it’s 722 problems, right? So, so this is kind of the curve as we see it now, 10x-ing every single month. And then not only is that the curve like the the volume of things being produced, but but also understand that it’s it’s starting kind of where we got to over decades and century plus, right? And it it pushes that understanding forward. And I use the term understanding here very loosely because I I don’t know if we understand it, but the point is it pushes that

11:53 frontier up very much past where we as humans can get to. And at this increasingly faster and faster rate. And if those breakthroughs in math can be applied to various machine learning approaches and techniques, which seems obvious that they would be. I mean, I can’t imagine how that’s not going to happen. I’d be pretty shocked. In fact, if you looked at Google’s Alpha Evolve and a lot of the work by Sakana AI that we’ve covered in this channel, like I think that’s proof enough that of course

12:23 all these breakthroughs will be applied to making better and better models. If you sort of think about the progress of like human technologies and how well could, let’s say, monkeys, chimps, how well they could understand it, you know, when we were using like a stick or some animal bone as a weapon, the chimps they would look at it like, I get I get that little off technology. I understand it. I I grok it. And then later there was a point at which it’s like the fire and a wheel, building shelter, clothing, and etc. etc. etc. That’s where the monkeys’

12:56 understanding of the technology kind of rapidly fell off. Right? I’ll see a helicopter and I’ll say it’s like, I I I don’t know what that is. One huge huge question for me for a lot of stuff is, will it improve our understanding or will be completely lost just like the monkeys? So, right now for a lot of the stuff there’s not that many people in the world that truly understand it. But at least we can kind of say as a humanity as a whole that some of us get it. So, humanity gets it. And for me, I can use, for example, ChatGPT to hopefully have it explain to me some of

13:28 these things. And uh certainly I I’m hopeless at understanding these things, but hopefully there’s other people out there that are mathematicians that are pursuing this kind of track, this learning, for whom maybe this will be helpful, and maybe AI will also be able to kind of help our understanding just as it’s doing more and more discovery. That would really be I think the best case outcome. Because the other road is where it goes off and it just discovers more and more stuff, and it kind of goes over certain horizon and we can’t follow. We can’t follow what it’s doing.

13:58 So it continues expanding and learning and doing more and more and more, but it’s already many many sort of uh miles beyond anything that we can possibly comprehend. Recently we read a blog post by Scott Aaronson, who’s apparently now teaching a new course at UT Austin AI Alignment Theory, and 3 weeks or so ago he made a post basically, you know, saying that yeah, these rumors are true. OpenAI is sitting some on some pretty big mathematical breakthroughs. We’ve covered this in a previous video. If you’re not subscribed to this channel, you’re you’re just out of the loop, so subscribe. But the point is he asked

14:31 this question. As far as mathematicians go, do we is it our goal to maintain this human community across generations of people that are capable of understanding the sort of frontier math, right? Because right now we have this 4,000 year-old history of some small percentage of of the human population being mathematicians and learning and studying and proving new things and asking you questions, right? But that group of people they sort of understood the latest math available. They worked on it and they they pushed the field

15:01 forward. Moving forward, is that a goal? Is that Do we want to keep those people around? Do we want to have future generations have their own group of mathematicians who understand the latest math? Because right now if the entire math industry gets sort of industrialized, and the only thing that we need out of humans is just uh verifiers who sit there and just check its work, and eventually maybe not even that, then certainly no one will be sort of incentivized to go out there and to do math, to do this hard work. And of course, that’s kind of a scary to think about that that might go away as a

15:32 human-operated field. And on the flip side of the coin, what if this sort of industrialization of math, what if it leads to breakthroughs that improve, let’s say, human lifespan or our understanding of how our brains work, how our biology works? One of the best sci-fi books that I think really kind of like envisions what that looks like in the far, far future is the Culture series by Iain M. Banks, where superintelligent machines basically run the universe and the various humans, I mean, they have a great time. They’re taken care of, they have great health,

16:03 all the resources, they don’t have to work. They’re just kind of just having a good old time, and they don’t really have to worry about anything. They’re like really well taken care of house cats. Whatever the case is, watch this field and what’s happening here very closely because I think it’s going to kind of show us the future. Kind of a foreshadowing of things to come, if you will, when AI models reach the frontier of a certain industry. It’s happening here in mathematics first because it’s verifiable, among other things. But the point is, what will start unfolding here now is probably a sign of things to come

16:34 in other fields like biology. Next year, when some AI model spits out 722 medicines that fix all the ailments that any human being has ever had, we’re going to be asking a lot of the same questions. Number one, how do we verify it? How do we make sure that what it’s saying is true and it’s not just hallucinating hallucinating these medicines and interventions. Number two, do we put the foot on the gas and just let it kind of like carry that scientific discovery forward and just do more and more and more even though our understanding is is falling behind? Do we let it go at kind of a slower pace so

17:06 that our understanding can keep up so we’re kind of that speed control, cruise control, if you will, like our ability to understand the stuff that it’s coming up with. That’s the limit, that’s the speed limit at which it can go. Or, and this is another sort of side of it, a lot of people think that there’s no way to have these models be aligned. So, everything needs to either pause or or stop or or really slow down until we figure out how to make it aligned or if, you know, if we ever do figure out how to make it aligned. A lot of mathematicians are not very happy with OpenAI right now. 25 Field Medalists

17:38 have signed a letter. They’ve asked OpenAI, amongst other things, well, basically they said don’t do this what OpenAI just did. They said, “Do not do that. We take basically 722 mathematical breakthroughs and you just dump it on the internet, right? Like, here y’all go.” So, as you can see, there’s a lot of kind of tension here. There’s a lot of things at the intersection of AI and math, and it’s much bigger than as big as it seems. It’s even bigger than that because I do think it’s kind of like a bellwether, I think is the expression, for what’s what’s to come next. How we

18:09 deal with math is probably how we’re going to be dealing with physics and biology and everything everything everything. The thing that’s most interesting to me is medicine. That’s kind of under the umbrella of biology because I think AI does carry a promise to improve our lives, our health in a lot of interesting ways. In my experience talking to a lot of other people, some people are very worried about giving humans any sort of superhuman characteristics, like designing humans to be their best or whatever. Some people are worried about that. Some people are okay with that. Let me know, by the way, where you fall

18:40 on that line. But, here’s what I’ve found just talking to people. Everyone pretty much everyone is okay with the following. If you imagine a day where you were at your best, you felt good, you felt kind of happy, you felt energetic, it was just overall good day. It was one of your better days. Like, it was in the top 1% of your days in terms of how you felt, how happy you were, how focused you were. You got the right amount of sleep, the right amount of calories the the previous day. You just felt good. The question is, would you take a pill or do some treatment where you would just have a lot more of those

19:12 days. So, you weren’t superhuman, you weren’t more than what you could have been. You were within your sort of potential, just skewed towards kind of the best of those days. Right? So, you wouldn’t have days where you’re just kind of dragging, days where your brain just refuses to function, where you just want to lay on the couch all day, where you’re just not feeling good, you’re feeling a little bit depressed or sad or whatever. Like, you’d have a lot less of those days and a lot more of the good, energetic, positive days. What I found is most people would say yes to that. I found a very few people that are like, “No, keep the horrible days. I want

19:42 those as well. That’s part of the the human experience.” But, the the point here is that how we’re going to approach dealing with this, you know, AI factory producing a math. This will lay some of the groundwork, I think, for when the other industries, when the AI will reach the very frontier of those industries. So, definitely keep an eye on this. So, the very next step is verification. How much of this is correct? Right? Is it 100% correct? Is it 90% correct? Where we fall kind of on that line will make a big difference either way. This is a kind of a historic occasion. But, I mean, if this is like 90-plus percent

20:14 correct, this is the biggest thing in the history of math, I think, ever. So, yeah, definitely wild times ahead. A long-time family friend of mine that I knew had an issue and had to have a plumbing company come out to fix his sink or whatever. When the plumber handed him the bill after an hour or so of work, my friend was stunned. He was a mathematics professor. Years of schooling, years of hard work. He was shocked to realize that the plumber made far, far more than he did. The plumber did suggest that the professor might

20:45 join of the plumbing company, but tells him to be careful and hide the amount of education that he received. Tell them that you only finished seventh grade. And that’s exactly what the professor did. He got the job, he started making a lot more money, he started really enjoying life. Until one day, the company required everyone who worked there to join classes to finish eighth grade. One day in math class, the teacher calls on him to come to the whiteboard and calculate the area of the circle. Now, it’s been a while since he went to eighth grade, so he forgets the standard formula. So, he starts trying

21:16 to derive it from scratch. Pretty soon, he has the entire board covered in calculus. Eventually, he gets to negative pi r squared. He’s confused. That can’t be right. He’s trying to find the solution. He’s kind of panicked. So, he kind of glances back at the class, and all the plumbers in the class are whispering. They’re going, “Switch the limits of the integral.” So, on that note, I think I’ll leave it here. If you made it this far, thank you so much for watching. My name is Wes Roth. I will see you in the next one.