AI Progress Explained: From Math Olympiads to Navier-Stokes

And AI was perfectly good at these already, end of 2024, beginning of 2025. So we really saw this transition happening over time, to be clear. But this is certainly the year where AI capabilities are impacting work activities that humans were engaged in anyway for their own purposes. And so as these... capabilities grow, it's just important for us to keep tabs on them. They grow very rapidly in some qualitative sense. We see no measurement we have shows any slowdown in how AI is getting better and better at any tasks that we're able to measure. And so we think that just understanding the impact AI will have on the world, it's important to know what it can do, what it can't and keep tabs on how that trajectory is going.

I want to push back on one thing you said in terms of we're not seeing any slowdowns that can be looked at broadly, like in terms of maybe the number of, you know, benchmark data points that we're looking at, you know, certainly we're seeing this broad performance. But is it also true that like on a particular, I feel like on a particular benchmark, we're getting like the, you know, for expected reasons, when we went from, you know, GPT-2 to GPT-3, like we're taking these huge steps up these benchmarks. And now like there's just a lot less room left and we're making more incremental progress. Do you see that as a slowdown in AI performance or would you characterize it differently? I would say, well, I'd say there's two issues here. One is on the benchmarks we have, what does performance look like? Two is, are there things our benchmarks don't measure that maybe there has been less or could even be negative improvement on? And is there some reason why it's the things that are hard to measure where there's been the least progress?

But on the first point, because this is a very, this is a much more cut and dried statistical point, we absolutely see continued progress on benchmarks, like a benchmark that was challenging for GPT-3, you know, many years, whatever, six years ago, is now completely, you know, solved, aced by GPT-4, benchmarks challenging for GPT-4, same for GPT-5, now we've got GPT-6. So we do some statistical work to try to aggregate benchmarks over time, because the benchmarks that people used to track progress years ago, now every AI model off the shelf that you've heard of that you might use is too good at them.

So people make new benchmarks. And then you have to sort of do this like stitching of like, okay, well, a model that was pretty darn good at this benchmark was not so good at this next one. And you can use like, you can stitch those together and get this sort of composite score. We have a methodology for doing this. We call it Epoch Capabilities Index. And that's a unified way of tracking benchmarks over time. And we really do see this thing continuing to go up, you know, pretty smoothly, linearly. And that march of progress is steady. That's an important point. That's truly, if we've made more benchmarks and AI systems that are harder, that models start off at zero, and then within a year or two years, they're at 100%, and we have to make a new benchmark to keep up.

And that's really been the story of the last, certainly the last three years, I'll say with confidence there. It seems like that, like normalizing across different benchmarks to produce a result that is coherent, that sounds like a very challenging problem. like you describe the result as like, you know, kind of continued linear improvement. And I imagine if that's like a constraint, you can kind of map backwards to, you know, to factors that will show you that continuous linear. But, you know, starting from, you know, a set of disparate benchmarks that have their own kind of, you know, ranges and challenges and, you know, where AI sits in them and kind of mapping this across different generations of AI and coming up with, you know, something that makes sense, you know, objectively at the end and then having that thing show continued linear progress.

That sounds like, um, you know, almost like too good to be true and like suspicious that it is true. I, I, I, yeah, I, I agree.

You know, certainly Navier Stokes has been in the news quite a bit recently. Prior to that, There were some ERDOS results and others. Like, how do you think about the role that those math challenges play in this broader view of trying to understand AI's trajectory? Yeah, very good question.

gap so far. Like you might hear the phrase jagged frontier where the AI capabilities are jagged in the sense that There'll be superhuman on some axis and some, you know, not superhuman, still inferior in capability to human on some other axis. And that remains the case so far in math. In particular, there's a couple things.

In hindsight, the analysis by mathematicians of the solutions AI has found to these like big, important, previously unsolved math problems has, it's always, in first place, it's been nothing too super duper surprising. Maybe there was like a direction that humans had overlooked or could have invested more in and AI sort of had the persistence, maybe this is a good word, or the bravery or the temerity to like wade into these very in-depth, intricate computations and calculations and sure enough came out the other side with a solution. And humans look back and are like, ah, that's not a crazy direction to try at all.

And maybe if we'd gone in that direction, we would have come up with this. This isn't something that would be surprising. What I'm curious about is, are we seeing the AI systems come up with a solution to the problem or an algorithm to create the solution to the problem? And I think I'm trying to, like, ask a lot of different things here. You know, one is, like, creativity. One is maybe levels of abstraction or the way it's, like, you know, thinking, abstracting, you know, around these problems. Yeah, I'll kind of pause and let you react to that. Yeah, let me throw out a couple things there. Let me know if you want me to expand on any of them.

when humans solve these math problems, they write up the solutions in papers, proofs that this is true or this is not true. And those proofs are not usually, not exactly algorithms. They're written in natural language. They leave the reader to fill in some of the gaps. And AI systems are coming up with just the same kind of thing. It's the same products. There's a lot of complaints about their writing style but like the arguments the substance of the arguments really are the thing we expect to see from humans such that if a human came up with this and yeah maybe cleaned it up a little i don't know uh like would be lauded for having like made a very insightful connection between two different areas or having gotten a an intricate um argument just right and balanced different considerations to make everything come together to to land the proof a hundred percent like this is not a this is something we're past the point where we can say well ai systems are sort of like not really doing something that humans would you know be impressed by on human terms no ai systems are doing doing things and is there a way to categorize or qualitatively are we finding that and i think you spoke to this a little bit like our

you know is there a qualitative difference between you know the best human approach and the ai approach and a sense of like you know the ai brute forced it you kind of spoke to this versus like pulled in things from some other domain and like created some elegant solution

the things are always a little more qualitative than you know that you know than they are uh or continuous than discrete uh but you know so anyway this is this is where we are now which is kind of wild in its own right earlier when we were talking about frontier math you kind of characterize it as you know, one to four, I think, and then advanced, and we never circled back to your more recent work? Yeah, we've got a couple, two new sets of frontier math problems. We ditched the tier

Yeah, maybe what I was thinking was, you know, once you're in the regime of very challenging unsolved problems. Is it possible that AI systems are doing, you know, surprising or novel or creative things, but still not quite getting them to the full, you know, the full solution? And do we care about that? Do we want to track that? And is that part of the way you've constructed the benchmark? It's a great question. It's not central to how we construct the benchmark. It's probably like, it's certainly worth tracking. The problem is it's just labor intensive.

Like you could have AI review the AI. We do this occasionally. Say like, which problems did it make partial progress on? What if we let it think for longer on those problems? And nothing yet. Like it doesn't seem good at understanding how close it is to a solution.

real board game that that people play the real board game it's called uh or the first one we did this with we'll do this with more uh is called earthborn rangers It's fairly obscure. If you go to like boardgamegeek.com, it's like 500th most popular or something. So it's not like up there. It's a small devoted community to it. And AI systems don't seem to know that much about it. Like they've heard of it. They can give you some facts about it. But it doesn't seem like something they've been trained on specifically. It's impossible for us to tell this with high certainty, with high confidence, but that's sort of why we chose it.

it's just hard to make these things from scratch and know whether they're hard or whether they're broken. You know, so that's why we, but the risk which you might have in mind is what if AI systems like, you know, just know about it from their training data. It's a risk on our mind. It's just a risk. One thing we will do in the future is we're moving on to video games. Incidentally, it's another area where AI is like very much not like human reaction time and visual and spatial reasoning. Again, coming along fast, but not really there yet. um that so video games you can always test on a new game like a game that just came out uh not in the training data probably um or at least you know not as robustly in the training data uh and so we'll be testing can ai systems do well on those do they do better on like you know the older version of a video game than like you know grand theft auto 4 verse 5 or whatever uh like when gta 6 whatever it is comes out like i don't think we'll be doing this one but but uh you know are they worse at that it's interesting when you when you bring up video games it immediately calls to mind kind of the classical reinforcement learning approaches which is kind of learning on the fly

but kind of different yeah we call the second sometimes in context learning where the only like lever the ai system really has is managing its context and like look when we give it the strategy guides and they do much better clearly this is a powerful lever but it's not as powerful as updating the weights and like so yeah i i mean like what's the big picture here it's it's if you have this fast loop of in context on the fly learning uh then ai capabilities might sort of improve much more rapidly than the slower loop of uh collecting more training data doing more reinforcement learning uh which which is done on language models as well these days um and then deploying a new model now ai might automate that whole loop but it'll still be slower than if it can just you know work out its uh its own context on the fly yeah yeah it's interesting when you zoom out on some of the the questions that you focus on and we haven't talked explicitly about it but you have a blog post where you kind of uh write out these nine big hairy questions that you're tracking they kind of group into like how do i assess where ai is now that's like can it do my job like how is it you know competitively uh and you know where's the puck going like can it

learn on the fly you know can it do research can it come up with new ideas these are all it is kind of where it is now but also like what what you know is it positioned to like dramatically um you know self-improve or like you know what's the trajectory that's exact that's exactly right Right. The I mean, I think for for people thinking more broadly about what they need to know about AI, this is the second topic is, you know, just as important as the first. But it's really, you know, even if you take some of the recent incidents, like the hugging face incident, like there's sort of think of two axes.

alignment of is the ai doing what i want it to do holistically obviously hacking into some other companies computers is not well aligned and then capabilities just like what can it get done can it hack into you know reasonably well secured other companies uh computers um what that incident was was like an early example very like i think pretty robust example of well we don't have the alignment thing solved and capable and capabilities are getting so big so strong that this is becoming a problem and so paying attention to capabilities like what we should expect is becoming more important sort of day-to-day and we're just trying to produce benchmarks that both say where are we now exactly like you said like what can it do now uh this is maybe relevant for more you know mundane economic utility or whatever as well as uh you know do we see the the dynamics of the system changing in a way that might be alarming basically kind of also thinking about it as like first and second derivative of capability yeah i think that's right uh some of these things make it uh the slope goes you know much uh you know faster uh hyperbolic growth or whatever in some of these cases versus merely just like yep it's uh it's growing and it continues to grow both are

important i i mean i think we've seen the disruption we've seen to date has come from these kind of unpredictable thresholds like when you know gpt2 gpt3 suddenly you had the chat gpt moment and you're like oh this thing i want to talk to this thing i might use this thing instead of a search engine this thing is useful to me for finding information and then suddenly and then like a you know a little while years later whatever two years later you had the it's getting better slowly and steadily at helping me with coding or with like using my computer but suddenly and thinking models with the thinking models and you had the clawed code moment where it was like oh suddenly this thing can actually do software projects for me even if i'm not a very not an engineer myself uh and it's like hard to predict when these thresholds will be crossed so it's useful to still track but like the it's useful to track the mundane capabilities today and say look you know cyber is maybe the latest example where it's like look we see their ability in controlled settings to do hacking going up smoothly.

And at some point, it's going to cross some threshold where, oh, shoot, it can hack hugging face or whatever. Hard to predict where those thresholds are, but still very useful to track those capabilities. So even the first derivative, as you said, version of this, we find very useful. We've got a fun benchmark we hope to release. Maybe by the time this is published, we'll have it out on a furniture assembly where we build some Ikea furniture, make some mistakes and see if the AI system can like just give in photos, like say, oh, like, wait, you made a mistake and step back in step four, like stop, go back.

And they've, you know, we see the same smooth capabilities like Astra, GPT-6 Astra, pretty good at this actually. And, you know, but it wasn't out of nowhere. It was like from a smooth, and this is, you know, important because we haven't seen AI have much of an impact in physical industry yet. Like it's been mostly digital. And even before robotics hits the scene, we might expect that, you know, Claude in your glasses or something is saying like, hey, you know, I'm going to guide you through repairing your car or whatever. I'm going to help you fix this machine in the factory that broke. So, you know, we want to track those capabilities too, just for the mundane impact. Anyway, impact all over the place coming. Benchmarks, help us say so.

Awesome. Awesome. Well, Greg, thanks so much for jumping on and sharing a bit about what you're working on. It's super interesting stuff and a very thought provoking way of, of thinking about, you know, AI and where it is, where it's going. Thanks, Sam. Really appreciate it. Awesome. Thank you. We'll be right back.