# AI math progress depends on asking better questions

Markdown copy of https://realalpha.app/s/ai-math-progress-depends-on-asking-better-questions/ on Real Alpha, the best minutes from long interviews with the people building AI. Cite and link the page, not this copy.

- Speaker: [Jack Rae](https://realalpha.app/builders/jack-rae/) · Research Director, DeepMind · Led Gemini Thinking, co-led Gemini pre-training, and contributed to Gopher and Chinchilla language-model scaling research.
- Host: [Jacob Effron](https://realalpha.app/people/jacob-effron/) · Partner, Redpoint · Growth investor in Abridge, Ramp and Physical Intelligence; ex-Flatiron Health.
- Show: Unsupervised Learning
- Episode: [Noam Shazeer and Jack Rae: Scaling Test-time Compute, Reactions to Ilya & AGI](https://realalpha.app/v/atMRWzgHEGg/), Mar 17, 2025
- Moment: 25:29 to 31:55 of the episode (6 min), playing on https://realalpha.app/s/ai-math-progress-depends-on-asking-better-questions/; the episode from there: https://realalpha.app/v/atMRWzgHEGg/?t=1529

## Quote

> “Whether it's possible, I'm not sure, but I would agree maybe the key crux is can I **ask actually novel questions**?”
> — [Jack Rae](https://realalpha.app/builders/jack-rae/) at [31:30](https://realalpha.app/v/atMRWzgHEGg/?t=1890) · Unsupervised Learning

## Takeaways

1. Benchmarks should lead toward useful scientific contributions.
2. Mathematical discovery can emerge from little external data.
3. Generating worthwhile questions is a key bottleneck.

## About this segment

Jack Rae argues that math benchmarks should shift toward useful discoveries, not just exam scores. He sees generating worthwhile questions as the harder step than solving them.

From “Noam Shazeer and Jack Rae: Scaling Test-time Compute, Reactions to Ilya & AGI”, Mar 17, 2025. [Watch the full episode](https://realalpha.app/v/atMRWzgHEGg/)

## Transcript

Transcribed by machine (Whisper) from the episode’s audio, so a word may be off here and there.

[25:34](https://realalpha.app/v/atMRWzgHEGg/?t=1534) for? I think like, you know, I'll give one example, which is like math. So I think right now math is being treated as a, it's a bit strange and math is often used as benchmarks and they kind of like exams and maybe even like math competitions. There's going to be like a very important pivot from the math benchmarks and to being really starting to become about like actually generating useful math, starting to solve actually important problems that we really care about um i think there are ways like i i think it was very cool this like frontier math uh eval that was created which is trying to provide like a kind of a gradient towards that so maybe like the harder category are basically almost like unpublished math findings the easier category is supposed to just be like kind of harder or trickier you know

[26:22](https://realalpha.app/v/atMRWzgHEGg/?t=1582) i don't know whether that particular eval is the perfect way but having some kind of ramp of evals that like bridges from where we're at now to like actually useful scientific contributions, this is something I'm like especially excited in as, you know, bringing in professors and researchers and saying, okay, use this tool in a non-ironic way to actually accelerate research in this area. What would you do?

[26:42](https://realalpha.app/v/atMRWzgHEGg/?t=1602) What's missing? What do we need to advance? And I think, yeah, I think like this kind of notion of like incrementally harder benchmarks, it might sound like, oh, that's like what AI researchers always say, but I think that's going to basically be my metric of progress. I mean, math is a great example here because, I mean, this is a field that you don't actually need more data. Like, you know, like people invented all this math without this external input or a world up to it.

[27:11](https://realalpha.app/v/atMRWzgHEGg/?t=1631) Yeah, a lot less data. Oftentimes in like a room, just thinking of your things. Yeah, you just go into a room. And then there are examples where, okay, there's some data, but, you know, okay, Isaac Newton like takes a bunch of astronomical observations, like goes into quarantine in his house and then like invents physics or something. So, okay, that's an example where there's data but nobody actually knows physics and then you generate physics and then math is even crazier because you start with roughly no data and invent something useful.

[27:49](https://realalpha.app/v/atMRWzgHEGg/?t=1669) So that kind of could provide a counterproof to the assertion that, hey, this is just learning to mimic people. That, okay, the most we can do with AI is to relearn what everybody knows and what we've... The learning to mimic people critique, I feel, has been around for a while. I feel like Jan Koon said a lot about this. Do you feel like that's entirely disproven at this point? basically the critique that like uh you know novel uh discovery and thinking is kind of impossible in these current model architectures well there's definitely one class of scientific discovery that i think almost no one could argue against which is like actually a lot of science is like if you knew about these two disjoint pieces of information and thought about the intersection For a while, you would realize a new property, like in kind of material science, it might be like, oh, it turns out just like associating things way better means actually, you know, way more about like what may, you know, what new kind of material may be photovoltaic, but also may, you know, etc.

[28:54](https://realalpha.app/v/atMRWzgHEGg/?t=1734) So there's like interpolation already would actually completely accelerate science. And I think I'm guessing then it's always going to be this kind of whack-a-mole of like what is considered actually interpolating known ideas versus like creating a completely novel idea. And for that one, I'm going to go to NAMM. Yeah, I, you know, I don't know, but I guess I'd just throw it back at Jan LeCun to prove that he generated a completely novel idea.

[29:26](https://realalpha.app/v/atMRWzgHEGg/?t=1766) We'll see. I don't actually care about arguing this stuff. Let's, you know, let's just, you know, build AI, you know, greatly increase the level of technology in the world, help people that seems good enough for me. Even if we go back to the math example, like the thing I'd love to see is like, you know, maybe the state of mathematics right now is kind of like the state of kind of geographic exploration in the 15th century or something.

[29:57](https://realalpha.app/v/atMRWzgHEGg/?t=1797) So it's like, there's some known things, there's some like, fuzzy area of like, we don't really know what's like beyond these boundaries. And we have a bit of a guess. And then you send a small number of people to go off in a boat, it's very expensive to try and like, push the boundary of like, what what is known and what is not known. And it feels like some pretty funny looking maps. Yeah, they come back with like a little bit of extra territory, like explored, and then they tell people.

[30:20](https://realalpha.app/v/atMRWzgHEGg/?t=1820) And that's a little bit like what's happening right now in mathematics. You have a very small number of like elite math professors that are able to really ask the right questions and then actually like prove useful qualities. And it kind of grows and it's grown that way. And that's how it's been going so far. right if you if we can train a model that can actually like essentially ask like it can pose the right questions of what you could say is like the space of all uh useful mathematics is kind of an infinite space you don't want this to go and like off like a fractal on on kind of uninteresting questions but if there was some notion of like all the set of like interesting mathematical questions if it can like keep posing new ones and then if it's very very strong and it can solve those, then at some point, you know, maybe like right now we have a pretty strong kind of math

[31:06](https://realalpha.app/v/atMRWzgHEGg/?t=1866) model. And at some point, maybe it will be a professor level. Maybe one day it'll be Terry Tao level. And then you have like a million of them. And then now it's like, now I think then you could hope to maybe complete the map. And then what would like completing the map look like? That could be one of the greatest contributions to kind of science. You would now physics, chemistry, you'd now be able to have a very deep understanding of any useful mathematics.

[31:31](https://realalpha.app/v/atMRWzgHEGg/?t=1891) I think that would be a very, very exciting thing. Whether it's possible, I'm not sure, but I would agree maybe the key crux is can I ask actually novel questions? The question posing thing seems to be the hardest part, in my opinion. The solving, I feel very confident we will get there. But maybe mathematics is infinite. Yeah, I mean, it's definitely infinite.