Welcome to the AI crisis in math

AI in modern mathematics

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1:37Hello and welcome to Decoder. I'm Neal Hyatt Patel, editor-in-chief of The Verge, and Decoder is my show about big ideas and other problems. Today I'm talking to Robert Hart, The Verge's London-based AI reporter, about what AI is doing to the field of mathematics and the existential crisis that many leading mathematicians are having about it. The news here is that OpenAI just published a set of solutions to long-standing problems in math that went off like a bombshell in the field. It's caused a huge debate in the math community, and Rob talked to some of the most accomplished mathematicians of our time about it. It's funny that AI systems are still pretty bad at elementary school arithmetic, but they're getting increasingly good at very high-end abstract math.

2:14All of this raises some big questions for the field of advanced mathematics. If AI can do math of this caliber, does that mean AI labs can transfer those skills to other domains? What good are the academic grants and university programs designed to train new generations of human mathematicians to identify new problems as they try to solve existing ones? If the frontier models simply solve all of the outstanding questions? And perhaps most importantly, what if all this attention to math is just another marketing exercise for the frontier AI labs, who don't seem to care less about what happens to one of the oldest and most fundamental academic disciplines there is?

2:50There's a lot here, and Rob talked to a lot of people with a lot of views on all of it. Okay, Verge AI reporter Robert Hart on what AI is doing to math. Here we go.

The existential crisis in math

3:03Robert Hart, you are a London-based AI reporter here at The Verge. Welcome to Decoder. Thank you for having me. I am very excited to talk to you. There's a lot going on in particular with AI and math that you recently dove into. You spoke to a lot of leading mathematicians about the crisis in mathematics due to AI. It feels like a lot, and also like there's a lot yet to know and discover about the interaction of these two things.

3:36A full existential crisis, which is pure decoder bait. Broadly, tell us what's going on. I think a lot sums it up quite well. I mean, basically, a bit of an existential crisis within what is mathematics, what are mathematicians doing, what is the role of mathematicians going forward. And a lot of that has been spurred by kind of a phrase transition in what AI is capable that has kind of, I think, exploded would be a reasonable way of saying in the last six months to a year. And it's gone from being very terrible to seemingly genuinely quite good at a professional level in a very short space of time.

4:14And so I think it's a lot of what these other fields have been struggling to deal with for the last five years in a very compressed period of time. I would put that next to software engineering. We've been living through the AI crisis in software engineering for some amount of time. But as recently as 2024, even last year, the conventional wisdom was that AI models were particularly bad at math. The famous example is they could not count the number of R's in the word strawberry. Even just counting sort of eluded them. What has happened to make them better at math?

4:46Are they still bad at like general arithmetic and they're good at advanced math or is it something in between? Yeah. I mean, they are still truly, truly terrible at some areas of math. I did check. They can do strawberries now. I think someone's tweaked. I think strawberry is hard-coded. I want to be very clear. My conspiracy theory is that the strawberry thing is hard-coded into all the models. I think so, too. That is a conspiracy I'll buy into. But yeah, I mean, it's still terrible at those kind of things. I mean, it's math. It's arithmetic. It's, I mean, even the days of the week.

5:16My boyfriend was saying the other day, he's like, it keeps thinking it's Wednesday. It's not Wednesday. Or time. I mean, Alyssa Welly for us a few months ago, I think, wrote the chat GPT. Can't tell time. Still can't. That's not all of maths. So there's this sort of disconnect, I think. We always kind of equate. Or to be good at math, you've got to be good at counting or adding or multiplying. And a lot of it is reasoning. Like, I mean, if you look at academic maths papers, a lot of the time you won't see numbers, which kind of sums that one up, I think. So they're still terrible. But they're now also very good at this other part. And as to why, I mean, I think at some point you reach a critical mass of what these systems

5:52can do. And we've seen it, as we said, with writing, we've seen it with programming. And they're very good at kind of forging connections between different areas or applying old methods in new ways or those kind of things. And it appears that the newer models they're training have apparently reached that level where it clicks. And now it can do maths. I mean, it's important to say as well, like it's, we speak of it and especially from the outside as a sort of unitary discipline. But I mean, imagine say biology, you've got something that would range from like literally

6:23watching animals and describing behavior all the way through to like cellular mechanisms and biochemistry. Like maths is not a unitary discipline either. Some bits it's really good at, some bits like counting, still really bad.

6:38And even on the more kind of abstract levels of that, I mean, some experts told me they floated topology as one area that it's apparently still quite bad at. I can't verify that, to be honest. It's beyond my own expertise, but it's still, yeah, it's a bit of a mixed bag. So you're describing mathematics as a huge field, obviously, many, many academic areas of interest. And there are some parts where the models have gotten quite good. Some parts, maybe the basic parts that people think of as math, which is simply counting where they're still struggling. And there's a wide range in the middle.

7:10Is it the wide range in the middle where the existential crisis is? People don't know what's going to happen. Or is it at the parts where it's really good? A bit of both, which I feel is going to be a running theme through this. I mean, no one's really afraid of it being a mediocre mathematician, but obviously there's a huge element of what this field does. And in terms of the research elements, like the cutting edge, as we see with a lot of the results that generate hype, what can it do? There are areas now where it seems to be producing work that is on par with good mathematicians, alongside other parts where, yeah, it can't count.

7:41So I think it's, and all caught up in that is whether it's going to kind of rewrite employment structures, funding structures.

7:49I mean, you also raise the murky question of like, what is mathematical knowledge? And the roles that these workers will be doing as well. So it's kind of all of that wrapped into one. I think that tracks broadly with sort of the rise of AI in every field where you can just add horsepower or compute to a problem. And there's some kind of verifiability. It seems like the models continue to get better. Everything in the middle where you might need some world knowledge or the models might need some actual intelligence about the world itself. They seem to struggle.

8:20The parts of math, at least reported out in your piece and what the labs are talking about, they seem to be almost entirely self-contained theoretical problems where the models can generate a proof or solve a problem that no one's been able to solve and then try to verify that that has existed and they can just run it again and again and again.

OpenAI solves ten hard problems

8:36That brings us, I think, to May of this year where an internal OpenAI model, which we have not really seen, disproved the unit distance conjecture, which is an 80-year-old problem. And then just recently we heard about Astra from OpenAI. Astra is the one where it seemed like the switch flipped and everyone decided it was an existential crisis. What did Astra achieve and why is it a big deal? I'm also pretty sure that Astra was probably behind the earlier one as well. OpenAI just listed it as an unnamed internal model. It's probably Astra. They didn't answer me when I asked, but there we go.

9:08OpenAI a few weeks ago dropped a blog along with a lot of paperwork proving it. I think several hundred pages that they described, they called it 10 advances in mathematics and theoretical computer science. It was basically an array of disciplines that they claimed the newest model Astra had solved in some capacity that ranged from, I think one was in quantum game theory, which I don't know how to begin to explain. And even less how to explain is kind of there was seer packing in higher dimensions, so more on three

9:41dimensions. And there was sort of a lot of other different disciplines as well. And it was, I mean, yeah, it caused a lot of stir in the community. It was, I think, a bit of a bombshell. I mean, as we'd said, there'd been these individual breakthroughs that had happened, but to drop 10 in one go, and they were quite big ones. I mean, researchers sort of told me that, yeah, these were, if a human had solved these, we would be impressed. If a human had solved all 10, we probably wouldn't believe it.

10:09Their problems they actually care about as well, I think, is an important one. A lot of kind of previous ones have been accused of areas that mathematicians didn't really bother with, and these are ones that mathematicians, good mathematicians, have spent a lot of time trying to solve, and had them.

10:28We need to pause here for a quick break. We'll be right back.

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Attribution and academic reception

13:10We're back with The Verge's Robert Hart, talking about AI's math capabilities and what happened earlier this month with an all-new AI model called Astra. Let's talk about these 10. You reported them out. OpenAI did produce some documentation. But they're not all entirely horsepowered out of nothing, right? They're based on previous work. There's some question of attribution. What was the response? Is it, oh, the models did this?

13:42Or was it the response we see to so much AI work, which basically boils down to, well, you stole this and didn't attribute anyone. And you've built on the shoulders of giants without mentioning it. How did the response land? By and large, it was generally one of being quite impressed from the people I spoke to. It was, as I said, these are problems mathematicians cared about. There was one that drew particular attention for how they credited it and also how they kind of announced all of this in their blog post. OpenAI initially, I think, had said that these are 10 problems.

14:12There have been no progress in the last 10 years. And then if you actually read the papers, one of them, it quite clearly says, oh, we build on progress from these two researchers. And so, I mean, that was later changed quite quietly as well. But a few of the researchers I spoke to were quite unimpressed and they did feel it was an element of, well, yeah, you've not credited something that you've used heavily here. And by your own acknowledgement, that said, one of the researchers I did speak to who was one of the ones named was a bit ambivalent on the whole thing as well.

14:43So it was a real mixed bag. But I mean, the general vibe, I'd say, other than this perhaps was oversold in terms of what came before, which was corrected to their credit. I don't think it was anything other than I think the word sloppy was what was described to me by one person. The general impression was quite impressed. Like, these were actual breakthroughs that bothered people. And it did move the field forward in a way that, yeah, as I said, if it was a human mathematician

15:13that had done these, I think, I mean, several researchers actually said that, well, if a researcher had done any one of these problems, they'd probably be set for an academic career. So, yeah, it was impressed with what it did, if not the credit for some of it. Well, it's funny, you know, credit and attribution in academia is like the whole game. And it seems like the AI companies get away with being sloppy in a way that no human would be able to get away with being sloppy. Did the scale of the discovery or the work overcome the sloppiness?

15:46If a human had accomplished the same goals and had been as sloppy, would the reaction be the same? I mean, part of me always wants to lean on the whole, like, oh, it looks like plagiarism kind of element. But like, if you actually read the papers they kind of produced, and I mean, one of the researchers I spoke to said, there's probably about 50 people in the world who are going to bother reading through this in depth. It is very clear. Like, it doesn't attempt to plagiarise. I think it was just a poor press release, to be honest. And as much as I love to go in on it sometimes, I mean, I find that having, I suppose, having

16:17covered science for a decade plus, the press releases are often overselling what discovery has actually been made, and the import of it, and the novelty of it. And I think that's just another case of what happened here. Does this seem repeatable? There's some proof that they provided that they solved 10 problems that were unsolvable. Do they provide any proof that they can solve another 10? That's the question. I mean, it's also, so the big unknown from, oh God, the near dozen people I spoke to for

16:50this was, well, how many did they try to get these 10? Who knows? Um, I mean, they know, but they won't say. But that is the big question here. It's like, it's unclear how, quite how many attempts it took to get these 10. Impressive as it is, it's not like that was, I mean, I would be very impressed if it was the kind of first thing they sort of go and then outcome these 10 impressive results. It's unclear kind of what areas they would focus on next and why. I mean, there are, I imagine, business reasons as to putting together which problems they are choosing to publicise so their models can, can do.

17:22So it's, yeah, and they've, all the AI labs have been hiring a sort of cohort of senior mathematicians, uh, behind the scenes. So it's anyone's guess, I think, as to whether they do it again. But on the question of proof, I mean, maths is, I suppose, a bit, it's an odd discipline in science in that a repeatability is kind of not the same thing like with experimental sciences. A proof is a proof. And if it works, it works. It's the problem here is, well, can people follow through what they've done? Each field is quite highly specialised.

17:53So there'll be individual mathematicians who are in those fields that go through, um, those I spoke to that worked in some of the fields that were covered here say it all looks very legit. There's also, um, in maths, there's a programming language slash computational proving type thing called Lean, where you can basically codify the mathematical proofs and run them through. And it kind of, well, proves it. I keep saying prove a lot here, but it will test the rigor and the assumptions of everything going on there. And they've published that as well.

18:24So it does appear to hold like no one I've spoken to was, they may say that the press release has a lot of hype or there's a lot of hype around it. No one seems to be doubting the kind of essential breakthroughs that they're claiming here.

Verifiability and model transparency

18:36I want to stay on this subject for one more second. There's the mathematical proof. We've generated a proof. And that is, as you say, just repeatable in a way that math is just logic. You can just go through the steps and say this proof worked. And anybody listening to this who had to suffer through writing a proof in calculus in high school probably remembers that process. There's something there that's pure logic. Then there's a part of it that is software code, as you're describing in Lean, where you can take the pure logic, you can express it in code, and you can run it to see if it works, I understand how AI is theoretically good at all of that.

19:08You're just going to run the reasoning and the reasoning is going to generate some code. You're going to run the code. You're going to get some verifiability. We've seen this play out in software engineering where the code runs or not, it's verifiable or not, and the models can just reason out about it. Then there's, to me, the big question that you alluded to. How many times do you have to run this? Can we verify that the models did this and they weren't directed by human mathematicians who've been hired at high rates by the labs in a way that suggests the field is going topsy-turvy? You have a quote here from James Maynard, who has won the Fields Medal, the highest prize

19:42in mathematics, who said he's been soul-searching. I keep looking at the quote. You've got similar quotes from all these other mathematicians in the piece. It seems like they're soul-searching against a thing that hilariously they cannot verify, which is how did the models do this? Is that thing scalable in a way that threatens mathematics? What do we know about how the models did this? I'd say as much as we normally do and do not know about this, I think there are a few issues kind of there. One is the nature of the models.

20:12Well, this is an unreleased model, so good luck to anyone wanting to independently test it. I mean, the same if that goes with anything proprietary, really. That said, I am inclined to kind of almost get the benefit of the doubt that they're not lying in some capacity about the models they're using. As for the other part, I think it's perhaps more noteworthy on the kind of how do we prompt this or how is it being guided and whether that's by a mathematician that knows what they're doing. And I think that's probably a key factor here is a lot of mathematicians I spoke to when

20:47they've tried using these. And this is often the consumer models, but still, it kind of speaks to a broader landscape. And they say that if you know what you're doing and you can kind of point things out, it's good. Or you can use it as a tool in a way that you kind of want and in a way that you wouldn't be able to if you didn't really know how to fact check it. I mean, the same time as if... I mean, I've had it where I've had ChatGPT or saying doing a basic sum and I'm like, that number is not right. It's like, well, I'm so sorry. You're right. It's this and it's still wrong. But that's kind of still needed at this level as well.

21:19I think it does allude to a kind of broader problem. As you said, kind of this almost soul searching of, well, what if we can automate that away? And what if it gets to a point where we don't understand it? And that really cuts to a deeper question of like, well, what is mathematics? Why do we do it? Why do we value it as a field? I mean, everyone will have different answers to that, I think. But a fear of a lot of people I spoke to was that this might kind of move beyond a realm of human interest, in which case, well, maybe they just won't engage with it or it will be something that interested people will go through and then the rest will kind of continue as normal.

21:49You got a quote here from a researcher in Zurich named Johannes Schmidt, who says, we might be headed toward a situation where the math problems get, quote, mowed down by AI, but we don't actually push the field forward because humans are taken out of the loop and they're not either checking or they don't understand it or they don't know what the future breakthroughs might be. How likely does that feel? Is that a big concern? There is an element of that, of the mowing down of the problems, and especially those are used as sort of a training field for younger mathematicians coming up and to kind of cut

22:19their teeth, so to speak. But I also think that kind of this problem solving idea in maths, that that's what maths is, is a very much outsider's perspective of the mathematical endeavour, I think. So a lot of the mathematicians I spoke to sort of found that almost tick box part the least interesting and valuable part of the field, like the areas that are valuable for them aren't that, oh, you've solved something or you've proven something, it's what happens from that. And I think it was James Maynard that said that the most interesting kind of discoveries

22:50in this isn't that you've solved something, it's what evolves from that. So is it like sometimes they open entire new fields of research that no one ever thought was possible? Or, oh, this is a new tool that you can apply everywhere in fun and exciting ways. I think if we look as well about what almost the kind of popularisation of maths, like even kind of what I'm thinking of is kind of those theorems that people have posed, it's the questions that endure, not the solutions. Like, it's always kind of Fermat's last theorem, not like, well, here's the solution to whatever

23:22the last guy proposed. I think the concern here is that, well, they're going to kind of tick off all of these questions that normally in the process of doing so, one would hope would branch out into all of these new exciting areas or pose new questions. But it won't do that. That's the concern. And then that would kind of leave the field quite sterile. And it will have all of these things that have been done and maybe nothing left to pursue. And the general consensus was, well, the jury's out. It's too early to tell. Like, even with human mathematicians, it takes a lot of time to kind of realise the impact

23:52of these kind of things. And it's, as I said, it's kind of exploded in the last six months to a year. Which, I mean, maths is not a fast-moving discipline at the best of times, but it's too early to tell, really, whether that will then be a kind of concern. But it is a concern and a big one. You have another quote from Maynard here saying, if the standard for a publishable paper in maths is something that an AI cannot do, particularly when a PhD is typically four years, the challenge is you're not trying to come up with a problem that AI can't do now. It's an AI in four years' time.

24:22And so this is really related to the rate of improvement of the models. Which, as you say, particularly in math, it seems to be increasing, but not at an even rate across all of the domains in mathematics. That appears to be what is causing the soul-searching, right? If you're a student and you start today and you pick some obscure domain that maybe the AI isn't good at sometime halfway through your PhD thesis or your PhD research, the AI will just solve it and you'll be done. And that is a real problem for you. Is the field reacted to that yet?

Shell shock among graduate students

24:52Or are they just in the shock of, oh, the models can start to do things that we didn't think they were capable of? Yeah, I think it's shock, really. I mean, the little notebook I have whenever I do these interviews, I keep one to the side to just do broad feelings. And I've written like shell shock in it because it just feels that it's, and it's far from universal, but it feels like it's happened so quickly that it has just taken a lot of people by surprise. I mean, even if they kind of knew in theory that, well, this is coming, they've seen all

25:24these sort of AI math startups kind of going. They've seen colleagues being, moving around to different labs or kind of areas of work. But yeah, it's just happened very, very quick. And so it's given them very little time to kind of figure out what, and it's not necessarily even the fields that it might be good at. It's more just like, well, like what, what can it do? Like, it's just, that's how quickly it's happened is that like, if I think like what, six months, I'm thinking of like an academic year in the UK from what it goes from like October through

25:56to October. But I can't imagine how, when I was studying, if something like this had come out and literally in the space of half a year, it just upended what was possible and over the summer as well. So students are possibly coming back to a completely different discipline after a break.

26:17We have to take on a short break. We'll be back in just a minute.

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27:59So why not you? Try Odoo for free at Odoo.com. That's O-D-O-O dot com. We're back with The Verge's Robert Hart discussing why mathematicians are so concerned about what AI is doing to the discipline.

Generalization across other domains

28:19There's some skepticism here in the world. Gary Marcus is a reliable skeptic of AI. And he pointed out that over and over again, what you see is AI accomplishes something in one domain, and then it's used to generalize AI's ability across every domain. Good quote here. As we learned a decade ago from AI's shambolic and ultimately failed attempt to turn jeopardy-witting Watson into a cancer-fighting machine, success in one domain does not guarantee success at all. I can read this two ways. One, there's AI has solved math, which is not true, as you've pointed out, in several ways, all the way down to it's still bad at counting.

28:55And then there's AI has solved math, and that means necessarily it's going to come for everything else. It will come for physics. It will come for law. It will come for whatever you want in the world. You can see if there's any verifiability, AI can solve it because you can just run it in this way. I understand both sides of that argument, right? That obviously success in one domain does not guarantee success in every domain, and then the arc of AI is, well, it keeps collecting domains. And if there is any verifiability, it is more likely to connect those domains than not.

29:28How do you see it? I'm not entirely sure that the people that Marcus is criticizing here have actually said quite what he says they are saying as well. There's a lot to say about the hype. But yeah, success in one domain does not even equal success throughout that domain, let alone other domains. I mean, that said, there has been an undeniable trajectory, I think, in the last few years of a broadening capability increase. And I don't think you need to be on the whole AGI train to acknowledge that and to acknowledge that that will have an impact.

30:00I mean, within mathematics, I mean, it is the case of like, I think it was Andras Juhas, I've probably butchered his name there, but one of the professors at Oxford that I quoted in the story, but something else he'd said to me was that he's been kind of toying around with ChachiBT a bit. And he's like, I don't think it has any geometric intuition whatsoever. And he's like, which might explain why there have been a very kind of limited amount of progress in fields like topology. I'm in no position to verify that claim in terms of the maths of it.

30:31But I think it illustrates it quite well. I mean, it is. It's almost like, what is it? They call it a jagged edge. And it felt like an easy argument for me, the whole, let's, let's criticize the whole, the singularity is near. And I mean, I think that's what Elon Musk said in response to, to the Astra thing, which it's a lot. I also think it's perhaps the least generous interpretation of that argument you can take to argue against. I think if you take a more nuanced element that does acknowledge that there has been clear progress here and quite quickly,

31:02and as you said, it is racking up domains, I feel there's a trajectory there that is like a reasonable one to like consider rather than just dismiss out of hand. One of the bigger arguments about AI in general is that it democratizes access. I was not a great software developer in my days trying to write software code. And now I can vibe code apps at will to do all kinds of dumb stuff in my house. Is there a similar argument here where a bunch of people who had mathematical intuition, but did not have the formalized language or training of academic mathematics can now access a model and push the field forward?

31:35Because that is usually the thing that undercuts the criticism from the professionals is, well, many, many more people now have access to this thing that only you had access to because of your money and your training. Yeah. I mean, annoyingly, I am going to say it's a two-pronged thing again, but yes, I mean, on a broad sense. Yes, it is. I mean, a lot of the mathematicians I spoke to were almost quite weary of this, actually. They love the idea and theory of democratizing access. They're also quite fed up of AI-generated slash assisted papers that are flooding every publication and manageable,

32:07as well as the preprint servers that they kind of use in these fields. I mean, at least two I think I spoke to were like, oh, I got three emails this week alone with people being like, hey, is this legit? Because they thought they told something with ChatGPT or with Claude. And they also don't have the mathematical skills with which to check whether they've actually solved something. I mean, on the flip side, there are parts of where they said, well, we've got a talented undergrad who's done something that a talented undergrad would probably have never managed. And here they are doing grad level work and they've produced a paper that is legit. And on the kind of bigger scheme of things, a few I spoke to said, well, yeah, a lot of these kind of are in the ivory tower.

32:44Having access to this kind of thing globally could really boost access to the kind of things here. I mean, on the flip side, the cost. I mean, these things cost to run. It's, I mean, it's always easy to forget. I think when you use, say, a free version of ChatGPT or Claude or something to the higher levels, these things cost money. And whilst they may not necessarily cost a lot of money, I mean, OpenAI claimed, I think it was 2K for these 10 results, which, again, doesn't factor in literally anything else once they've got these.

33:16So it's a very generous number. But even taking that figure, maths is quite a poor discipline, even at very well-off institutions. I mean, Colva Rooney-Dougall, St. Andrews, who I spoke to, she said, she's like, well, a lot of the time I don't bother getting a research grant. I don't need one. I just have a blackboard.

33:38And so, like, if you're not even getting, say, a research grant, two grand is a lot to put up. And so it could lock out researchers that way, even at quite well-funded institutions. Not to mention that the speed of which this is happening, that virtually no one would have been able to bake any of this into a grant proposal yet, was another theme that I came across a lot.

Labs as advertising playgrounds

34:02Actually, Ronnie Dougal has another great quote in your piece about the nature of the AI labs and how they are talking about math. She said, they're treating our discipline as an advertising playground. A bunch of mathematicians have signed something called the Leyden Declaration, which is an open letter to pledge not to buy into hype around AI. These things are running right at each other. The AI labs are not going to stop using every discipline as an advertising playground. And a bunch of mathematicians saying we refuse to buy the hype certainly does not seem to be stopping the hype.

34:33There's just a piece of this that is organized professional resistance to a thing that is upending a field that has, as you say, been pretty cheap to operate. And now might be getting cheaper or easier to access or easier to upend day by day. Do mathematicians feel that that is going to be effective? Historically, mathematicians are not like savvy political operators. There's a part of me that says, oh, they're just going to get run over. I don't know. The history of maths, actually, I think a lot of them were quite savvy. Isaac Newton is the one that always comes to mind for that. Although quite a petty political operator as well.

35:04But, yeah, I mean, that is the fear. I mean, it's a few that I spoke to and one really comes to mind as they say that there's often this belief that maths is kind of the pinnacle of knowledge.

35:18We're not live, so I can be free on this one. But he was like, well, that's bullshit. Because it is, and he wasn't alone in kind of illustrating that sentiment, but it is good for showcasing. And it's a lot neater as a discipline and a lot cheaper as are than, I mean, you mentioned with Marcus saying IBM's Watson is this cancer curing thing. Like, well, that involves lots of messy experiments, including on people. You don't need that in this. So it's a really easy discipline to kind of come in, throw your weight around, and then move to somewhere more lucrative if that's what you want.

35:58I'm not saying that that's what they are. I mean, a lot of the people at these companies have kind of been hired. I mean, I don't doubt their credentials for sure, and I don't doubt their motivations as well. But it does raise a question long term as to, like, how viable is this? Because, I mean, let's be clear, as a field goes, I cannot imagine them being a very lucrative enterprise customer for these companies. The thing that might be lucrative is pushing a field forward to turn it into something economically viable.

36:30We push mathematics forward as a field that turns into some engineering or physics breakthrough based on that mathematics, and that turns into, I don't know, yet another way to launch rockets. Some circle happens in there that I don't quite understand, but that is the history of innovation, right, from research to engineering to products or services that make money. Is that on the minds of any of these mathematicians, that pushing the boundaries here is upstream of something radically economically lucrative?

37:01The immediate counter that would come to mind here is that a lot are scared that it's closing off the field. So, by definition, those breakthroughs that lead to something surprising and new that you can say, oh, this works here, may not be happening anymore. And so, like, if anything, that kind of lucrative endeavor of, like, applying maths to then this entire new field that may have a lot of money in it, I mean, it remains an open question as to whether anything like that would be possible if we're closing off avenues rather than opening them up. Right. If the economic incentive of solving the unsolved problem is reduced because you personally won't get rich if a computer is just solving every unsolved problem, like, something very fundamental breaks there.

37:41I mean, a lot of it comes down to, though, like, it's not just solving problems. I mean, a lot of these things, as we said, like, it's about what solving that problem tells you elsewhere. And it's those elsewhere's that, like, if these were very lucrative problems to be solving, I imagine more people would be trying to solve them than have to sort of left them for decades. So, like, but it's possible that in and this is the nature of a lot of kind of pure science. And it's, I'd say, a broader criticism of what is going perhaps with the Trump administration's approach to science policy at the moment in that it's very applications focused.

38:15There is something to doing pure research that can yield potentially very big dividends that is by definition utterly unpredictable as well. Like, you cannot plan for it. And the fear is, I think, with maths is that in solving all of these problems and then also in doing so not opening up new areas of research in that sort of, I suppose, that's that open question. Well, what are you left with? Even if it's from a more lucrative kind of, like, what are you going after point of view, if you're not opening up new areas of research and you're just taking off old ones, it kind of just leaves a big sort of question mark as to what might be left in its wake.

38:53And I think the sentiment of almost, even from those I was excited that I spoke to that were very excited about what's happening, they said that even they don't really know what's happening and they're excited from, like, a personal level because, oh, we might be able to do this, might be able to do that. But there was still this lingering uncertainty of, like, well, what, where does this leave the field? Especially for more pure disciplines like research mathematics, it's tougher to say what comes next because in a lot of the other sciences you can say, well, okay, well, they shift onto more engineering problems or applying.

39:23But if you solve all the problems at the ground and there's nothing being built up from that, where do you go from there?

Optimism for the future

39:29One great thing about The Verge is our commenters are vast, they're very knowledgeable, and there was a comment from a mathematics researcher on your story that I just want to read to you and see if you think this is the right framework. Here it is. Quote, I have no doubt these models will bring massive change in the field, but in their current state, they won't yet drive us to obsolescence, just occupy a particularly useful spot in our bag of tricks. My apprehension comes from not knowing where these things will peak, but overall I remain optimistic. I think AI will be a net boon for math when used properly. I feel like AI will be a net boon for X when used properly is just where you land in life in a lot of things.

40:04But that's the most optimistic response that I've heard. If we get it right, it's going to be great. Is that kind of the vibe or is it still more shell-shocked than that? Yeah, I'd say shell-shock is still the overriding impression. I mean, I think perhaps the gut response to that is like, well, it will be a net positive for whom? And what is properly? All of those are quite legitimate questions here, I think. And I mean, some of the bleak responses from graduate students I saw in essays posted online, where's their place in this as future researchers?

40:36Do they have a place in this? Is it as glorified AI proof checkers? That will be quite an unsatisfying career, I imagine. Or maybe not, I don't know. But that's, we will see. I think anything used properly will be a net boon. But, yeah, I think it all comes down to what properly means and for whom we're talking about. I suspect over the next year or so, things will come into focus. Because at some point, OpenAI will have to show people how they did the things of the models.

41:08And perhaps more importantly, the other labs are going to want to either replicate these results or show that they can push farther. Which will necessarily have to lead to a little bit more transparency and yet more mathematicians having a crisis with you. Rob, thank you so much for being on the show. We'll have you back very soon. Thank you for having me.

41:28I'd like to thank Rob for taking the time to join me on Decoder. And thank you for listening. I hope you enjoyed it. If you'd like to let us know what you thought about this episode or really anything else at all, drop us a line. You can email us at decoderattheverge.com. We really do read all the emails. Or you can hit me up directly on Threads or Blue Sky. We're also on YouTube. You can watch full episodes at DecoderPod. We also have a TikTok and Instagram. Same handle, at DecoderPod. And they're a lot of fun. If you like Decoder, please share it with your friends and subscribe where we get your podcasts. Decoder is a production version. Part of the Box Media Podcast Network. Show is produced by Kate Cox and Nick Stat. This episode was edited by Ursa Wright.

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