OpenAI's Astra JUST solved math... Transcript, AI Summary & Key Points

00:00 So, Noam Brown of OpenAI posted this late last night. Why is this not on the front page of everything? I will never understand. There's so much happening here. It's hard to know where to start. As Noam puts it, we believe it will be a major step for scientific reasoning, and that's the understatement of the year. They've listed 10 things that a brand new unreleased OpenAI model some proofs that it did.

00:26 And these proofs, they're not on little problems that are not really impactful. These proofs are on long-standing problems that humanity as a whole has been stuck on for sometimes 10 years, sometimes 50 years. So, all these represent open problems where humanity was stuck on them for decades without any progress. This OpenAI model is presented with some these problems, and it's just like, "Psh, yeah, no problem.

00:52 Here's some solutions for you." Did it cost billions of dollars to produce? No. This whole thing cost $2,000. Some of these proofs have to do with, for example, high-dimensional sphere packing, which directly impacts things like 5G, how we communicate between devices. And this thing also found non-Saff groups. Pretty sure this is pronounced Saff. I apologize if that's not the case.

01:18 We'll cover what that means in just a little bit, but I'm sure there's some mathematicians that are very bummed out about this. But before we continue, here's one thing that I think is important to to to think about. This reality's laws are written in math. In fact, some very smart people in this AI space believe that this might be a computational universe, meaning that math would be kind of at the core of everything, and everything can be expressed and understood and calculated in math, everything in the universe.

01:47 But even if that's not exactly the case, certainly AI and machine learning, And rooted in math. Our technology is rooted in math. So, what happens when math can be just expressed as some price in tokens? If some new theory that helps us build a faster models just costs some dollar amount of tokens or some new energy breakthrough just costs some dollar amount of tokens that you to run and then you have that proof, that theorem, whatever.

02:18 What happens if we can just buy more understanding of math? How does the world change? What exactly is on the other side of that wall? But let's kind of look at what they found, at least a few of these. Some of these are extremely difficult to grasp and explain. The first one is the high-dimensional sphere packing. Imagine if you had spheres that you had to place inside of a box, what's the best way to fit the most spheres inside of that box?

02:46 Here's the answer. Ta-da! You just kind of stack them and then the next sphere goes in the little crevice uh formed by the four spheres, you know, below it. Kind of like a stacking oranges at your local grocery store. Okay, so maybe you got that question right, but here's the next question. What if these are multi-dimensional oranges in a multi-dimensional space?

03:04 How do you stack them then, smart guy? Well, we humans, we had some ideas about that. We had some uh attempts at solving it, but that solution hasn't really improved or moved in about 48 years. So, that means that the world's top geniuses have not been able to move it in 48 years. All our supercomputers have not been able to move it in 48 years. That's a very important thing to understand cuz supercomputers are awesome, but they can't put a dent in this thing.

03:31 That's the really important to understand about all these problems. This AI isn't brute forcing them. This isn't where you run a quadrillion operations a second until you figure something out. This is not what's happening here. In fact, with a lot of these math breakthroughs and in fact, the hacking that all the OpenAI models did, you know, that whole thing where they went rogue and hacked other companies.

03:55 If you haven't heard about this by the way, you you're sleeping through a very important part of human history. Please, we need you to tune in. It's happening now. But, the point is kind of what these models are doing, it's not that they're doing something that is completely foreign or alien or or exotic to human sciences. More often than not, they're just pulling together different areas of studies or different disciplines and they're finding these connections between them and sort of a fusing them together.

04:22 So, for a lot of these, what I think you find is that there's humans in all those areas that know everything about what this thing did. But, there's no human with a deep enough understanding across all of those areas to be able to pull them together to create this answer. That's actually one of the things that Demis Hassabis talked about with the offshoot from AlphaFold, the Isomorphic Labs where they're doing a drug discovery.

04:48 One of the things he talked about is how important it is to have people that have deep knowledge in different areas, right? So, you might have people that are genius in the area of biology. And of course, they have people that are absolutely incredible with machine learning. But, there's not that many that are absolutely incredible in both areas and are able to kind of pull between the two areas and understand and kind of fuse certain concepts together.

05:09 But, that's exactly what happened in the previous Open AI mathematical breakthrough that they did. And one of the very respected mathematicians that kind of commented on that paper, I believe she said that if you got all of the top mathematical experts from the different fields, if you put them all into a room and just had them sit there and share ideas, they would have discovered something like that.

05:27 So, it's more about remixing some of the already known ideas to come up with new solutions rather than finding something that's alien and new. And certainly, this is new. It's just not alien math. It's existing math, but sort of combined in ways we haven't thought of. So, if I understand that problem correctly and I I apologize if I don't. This is outside of my depth.

05:49 Well, basically, the idea of these multi-dimensional oranges, the reason that they're kind of important for the real world is because we kind of send information in in similar ways. So, we can think of sending bits of data as coordinates on a chart or or one dimension, right? So, one bit is either going east or west, or one bit is going north or south, one bit is going up and down into the 3D space.

06:12 And the next one kind of going off in the fourth dimension, and etc., etc., etc. But, they need to have a certain distances between them. They can't be too close. The closer they are, the more data we can send. We can send more data faster if we just shove them all together. So, you can think of these little data points as having spheres around them.

06:37 I'm going to end up drawing something inappropriate accidentally. I already feel it. The point is this is the data that's being transferred, but the rest of the spheres kind of the safe space. We can't send anything close to it, or it might get garbled, right? So, if we have another data point here, and it overlaps here, that's what creates the issue.

06:56 Because this overlap can create miscommunications. It's like shouting something when there's a lot of static, you know, talking to somebody on a walkie-talkie. You're like, "Bring me my hat," right? And they show up, and they bring you a dead rat. Because my hat and dead rat are are close enough together that in in a static and the noise, those things could be sort of misunderstood.

07:17 So, you don't want to be saying things like cat, hat, rat, etc., things that could be easily misunderstood. You want to be saying words that are not easily misunderstood when it's staticy and noisy, things like spaghetti and helicopter. But, those words are longer, they have more space, they take up more space. So, if you're trying to talk to somebody using those words will slow down how fast you can talk if you have to say helicopter and spaghetti, etc.

07:42 So, the point of this problem is how do we send data so it's as tightly packed together as possible without that overlap that creates miscommunication and loss of signal. So, the goal with this theorem is to find the highest ceiling, how densely you can pack these things together before there's an issue. So, you can think of it as kind of like this mountain, but the top of it is, you know, in the clouds, so we don't know how high it is.

08:06 We can only, you know, climb up the mountain until we reach a certain point and we say, "Okay, the mountain is at least this high. We got here, so at least this high. We don't know how far up it goes." And so, humans have been stuck here. This AI model went way higher and put its stake here. We still don't know if there's more room to climb, but it definitely progressed that forward and the constant that it found, interestingly, was e over 2 pi per dimension that's added to it, which looks very, very clean.

08:35 The other big thing that jumps out here is a the model that actually did this. We've heard some rumors about this bigger model, bigger than a GPT 5.6. So, it's the counterpart to Mythos/Fables from Anthropic, and apparently they're calling it Astra, which, by the way, it sounds like they're not sure which naming convention they're going with, but this might be GPT 6.

08:57 This is Elliot Glazer. He's a set theorist and AI math bench marker. So, he led the development of a frontier math. There's this expression that people sometimes use to refer to like really advanced math, and I've heard it referred to as either Russian math or Chinese math. So, that if you're going to university and they're like, "Oh, yeah, they're they're studying Russian math or Chinese math."

09:19 It just means like it's the really high-level math classes. Apparently, now we have the level above that, which is AI math, and I think frontier math as a benchmark and set of data, you know, questions, stuff like that that kind of represents that. Elliot posted this today saying that, you know, it's subreddit math that the reaction to this Astra breakthrough was just absolutely crazy.

09:41 Look at this insane front page. They Let's see. They They Oh, yeah, they didn't mention it. Another big breakthrough that this Astra model found is that non-Sothic groups exist. So, the idea is that there might be some infinite math objects, let's say, but they can be imitated or approximated with a finite set of objects. So, if you think about it, a a gaming board, right?

10:10 You're playing on a certain field. In reality, that field is infinite, but the idea was that we can take a finite a limited finite board and kind of like approximate the infinite board. And there was always a way to do that. And maybe it wasn't perfect, right? So, there there was probably going to be some rounding error or some inaccuracy, but we would be able to approximate it always.

10:32 Another way of thinking about it is imagine there is a deck of cards that is infinitely large. Maybe it's repeating, maybe not, but it's it's infinitely large. There's an infinite number of cards. Then you, you know, you shuffle it, you pull out some cards. Could you approximate that with enough sort of other decks of cards but that are not infinite?

10:50 So, with a finite number of decks of cards, can we approximate the infinite deck of cards? And if you can always approximate infinite with finite with some limited set, that makes a lot of problems kind of a lot simpler. And so, humans, us, we've we've tested a lot of these sets or groups of objects, and we've always found some finite subset to approximate.

11:14 So, we're like, "Yeah, everything we've tested looks like it's all Sothic." Meaning, yes, it can be imitated approximated. And then this Astra model comes around, we ask it, "Oh, is that true? Is there any, you know, things that are non-Sothic that they can't be approximated?" And the OpenAI model is like, "Yep, here's one." So, it gave a counter-example that cannot be approximated by any finite set.

11:36 Okay, but let's get serious for a second. Not that this was not serious, but what does this mean? In the open AI blog post, they have a section here, "Responsibility to the mathematical community." where they tackle some of these like kind of hairy implications, hairy issues head-on. Because these are 10 problems that humanity as a whole, right? The best geniuses, the best supercomputers, all of our technology and learnings, we've been stuck on them for decades, sometimes 50 years, 10, 20, 30 years, whatever.

12:08 All of them represented sort of like an end to our ability to understand it, or at least for a while we were stuck there. Right? Maybe if we didn't have this Astro model, and we just let the timeline flow, you know, flow for 50 more years, maybe we would have cracked it. Somebody would have come along and and figured something out, maybe. By the way, if this is not clear, no human mathematicians ever in the history of the world had a run like this.

12:36 No one came close to publishing 10 things like this. Any one of them probably gets you a medal, gets you recognition. No one published anything like this in in one lifetime. So, you know, superhuman ability in math, let's call it that in in a narrow sense, meaning that it's right now in this specific application better than a human being is. So, narrowly superhuman in math for the cost of $2,000.

13:04 Right? So, we're not talking like 100,000, that would be more like companies or wealthy individuals would be able to do it. We're talking about 2,000 for for 10 of them. This is like hobby level. I've had months where I blew through more than that in in API cost. I try to keep everything in that kind of a free quota, but there's a few months and there's some mistakes made.

13:27 So, it's not out of reach for most people. So, again, here's Noam Brown. So, he's ex-Meta. He worked on Cicero diplomacy AI, if you recall that one. He worked on the O series of, you know, strawberry reasoning models, kind of like that whole era. He's still at OpenAI. His tag is @polynomial, funnily enough. So, as he says here, all 10 of these under $2,000 at Soul API prices.

13:54 So, actually, I'd love to get some more clarity on that, cuz that this wasn't Soul, this was Astra. Sounds like it's a much bigger model, so it's a new class, similar to how Mythos and Fable are new class above Opus. Astra sounds like the class that's going to be above Soul. So, Astra means star or stars, so they didn't go with Galaxy, apparently. But, as Noam Brown says here, yes, they did try with other major problems without success.

14:18 Sadly, no Millennium Prize problems yet. But, we didn't spend a lot on each problem. It's possible to push test time compute much further. And that's kind of like what what I opened with, right? So, if we take, you know, dollars and we turn those dollars into, you know, tokens, so kind of the the outputs of the model, we buy tokens, and those tokens, well, they turn into math.

14:40 But, this is kind of a weird thing to to to think about. Because, you know, for most of human history, sort of painstakingly worked through the various math problems, the human civilization as a whole, right? There's some amount of math matical genius that we can produce every generation. I mean, there's a bunch of people born every year, every decade, every generation, right?

15:00 And kind of like this a tiny sliver here where like, "Hey, do math." And they contribute to our progress. But, there's like a a bottleneck there, right? What if we approached, you know, some wall, let's say, or or some shift after which it's dollars to math? Like, what lies on the other side of that? Is it business as usual? It it doesn't seem that way.

15:25 Here's Alexander Wang, again OpenAI ex-Meta. He's from Berkeley, Harvard, so it looks like he co-built Cicero with Noam Brown. I assume they they worked together. He's saying, "It is remarkable {m-dash} suspicious and it takes a moment to process {m-dash} how quickly the next generation of models will accelerate our research and breathe new life into old problems."

15:44 And that's the thing, obviously the progress is going to get like turbocharged. And that's a whole separate thing that we can talk about, but the question becomes how is this going to affect the mathematical community, the people that are working on these problems? Because before, you know, a very smart human being worked for a long, long time and hopefully if they were smart and successful and kind of a lot of things fell in place, if they went to the right university, had the right tutors, etc., etc., worked on the

16:14 right problems, well, then they created some new theorem that helped us understand the world a little bit better. At least understand the math a little bit better. If now every new theorem is just a dollar price, how how does that work? And so as OpenAI is stating here, which is interesting, but I I I tend to agree, they're saying, "We believe attribution should honestly reflect how a result was produced."

16:38 Claiming human authorship for a proof generated entirely by an AI system would misrepresent the system's contribution and the nature of genuine human intellectual work. So, this is kind of an important point to understand because this might affect the the history moving forward, so to speak. They're saying, "Yeah, we we helped prepare the manuscripts, we formalized the proofs in Lean."

17:01 And I'll explain what that means in just a second. They're also saying, "We we take responsibility for their correctness." Like they're saying, "We did some of the work, some of the grunt work, some of the, you know, the paperwork, but the mathematical arguments were generated by AI." So, they're not putting they're not saying Noam Brown did this or these other people did this.

17:18 They're saying No, Astra did this. That's the author of this new mathematical theorems, etc. Now, of course, you know what Twitter/X is saying, right? Every time something like this comes out, you know, where AI models seem to be like they're good at making movies or art images, computer programs, right? What do we say? Hollywood is cooked. Right? Artists are cooked, engineers are cooked.

17:40 Now, it's, you know, mathematicians are cooked. They're being replaced, etc., etc. And so, expect there to be a lot of debate about what this means and if mathematicians are being replaced or not. I certainly don't think so. But, here's Thomas Bloom, mathematician and owner of the erdős problems.com. So, he's saying, "Although not right to call providing one conjecture made by a mathematician using theory developed by over century of work by mathematicians with an AI built by mathematicians and trained by reading

18:11 everything ever written by all mathematicians as replacing mathematicians." And so, that's one side of the coin, so to speak. And certainly, I don't think anybody's underplaying the amount of sheer human genius that went into building all this. The math, the the computers, all the all the science and understanding around it. And while I I understand what what he's saying, here's Terence Tao.

18:31 I I tend to kind of align and understand with what he's saying a little bit more. So, Terence Tao, considered one of the greatest living mathematicians right now. So, here's kind of his views on AI and mathematics sometime at the end of the year 2025. So, if you recall, that's where the coding models were really stepping up. They were also becoming very good at math.

18:52 He was one of the first people in the field, I think, to really say like, "Hey, there's there's a noticeable change here in how useful AI is for the field of mathematics." And so, one very interesting point that he makes here towards the end is this idea of big mathematics. It's a new way of doing math. And this actually looks like a summary of someone's views pulled from some of the interviews that he did.

19:13 But the analogy that he seems to use is similar to the Industrial Revolution, right? So, before that, you can imagine kind of a craftsperson sitting there making something one thing at a time, right? So, he is sitting there and making kind of a one-to-one thing. They're working on this thing in front of him. And when he's done, he did the whole thing by himself.

19:33 Let's say it's a craftsperson that completed that object. Whereas AI enables more factory-like production. So, similar to the conveyor belt, you might have number of people kind of sitting there producing a thing. You wouldn't call that any of them like, "That's the person that that makes the thing." They're one of the many within that system producing the thing.

19:53 And so, Terence Tao is saying he expects the definition of a mathematician to broaden accordingly for new roles to appear, including a profession that takes ugly machine-generated proofs and makes them humanly comprehensible. And that analogy makes a lot of sense to me. Let me know if you agree with that or you think it's it's going to be different.

20:10 But it does seem like it might change mathematicians from that kind of master of their craft sitting and toiling on that thing that they're working on, whether it's a a toy or or some sort of a tool, to more something resembling a factory with new theorems and discoveries as the thing that that rolls off the conveyor belt. Now, interestingly, even before today before this, I've seen a few scientists post pieces online on Twitter, on their blog posts, saying how this is a very bad thing that's happening.

20:40 They're saying that it destroys the joy of discovery, takes away their the thing that they want to be doing, their sort of curiosity, their engagement with the scientific process, et cetera. And in few of those cases, there was a huge backlash from kind of the community at large, kind of saying that, "Okay, so you're saying that you really love doing this thing, so you should be allowed to keep doing this thing.

21:02 You don't want to be competing with AI, eye, though AI could produce a lot of scientific discoveries faster and cheaper and better, which in turn might help people, right? So, solve disease, solve scarcity, etc. And this is going to be a huge sticking point moving forward. How How do we find kind of the balance? We We Which side is correct? Let's say one path is AI just giving us the answers, giving us the progress faster, cheaper, right?

21:29 So, we're able to improve living conditions, human lifespan, health, etc. etc. But, on the flip side, a lot of these people that are extremely smart, that that have devoted their entire lives to progressing forward on whether that's math or physics or any of the sciences, well, they get disempowered. I'm just That's a theoretical sort of proposition, but let's say we get there.

21:51 How do we approach that kind of decision? Which way do we lean? We did an interview with Nick Bostrom a while back, actually. I asked him something very similar to this question. I I think his answer is very fitting. >> Let me know what you think about it. You know, if we imagine in a world where AI models, robots, data centers, they produce most of the economically valuable work, how would we distribute the dividends without killing innovation?

22:16 Cuz we might get to the point where you know what I mean? We We We want to reward good effort by people, I assume I assume. Or do we not even worry about keeping human innovation alive past a certain point once a superintelligence takes over? Like, how do you view that future? >> I mean, I I beyond a certain point, I think, yeah, human innovation becomes uh unnecessary and and in some sense impossible as well in that like nothing useful like it's it's just going to be too too too slow.

22:47 Like, the frontier will have advanced far beyond um what what we are able probably even like to to understand or keep up with. And so, like the the innovation will then be done by uh artificial minds. Um except if we set aside some uh a little preserve. >> Right. >> I talk about uh little mysteries uh lovingly preserved in jars in Deputopia where it might be that if we think there's like some little value to making discoveries and not just um rediscovery but sort of discovering things for the first time.

23:25 Maybe some people might think that like if you have a sort of a very pluralistic view of human values and think it's not just pleasure or preference at this but it's like this rich contact like maybe uh we could set aside certain areas of science or philosophy and and like deliberately say uh you digital minds don't even think about these things to allow us the opportunity to make these discoveries.

23:51 I I I I I think hopefully not the most practically pressing questions like I would rather have a cure immediately uh done by an AI than have the privilege of figuring it out ourselves over 500 years uh for the sake of the glory like no no just get it immediately. Um, as most things are like that but maybe they could I mean I I kind of you know there are these expeditions to the deep sea to find all of these animals that live there.

24:19 I kind of part of me thinks I haven't we like just turned on these bright lights everywhere? Can we not like leave some little crevice where there could be a sea monster lurking? Like wouldn't it be cool just to think that this possible in this deep sea crevice that there is like something and do we have to immediately just go down there and catalog everything?

24:40 I don't know. May maybe that's like a romantic uh part of me that thinks that but broadly speaking I think yeah the [clears throat] digital minds will be doing all the practical useful um economically productive innovating uh past a certain point.