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Today on Decoder, I’m talking with Robert Hart, The Verge’s London-based AI reporter, about what AI is doing to the field of mathematics and the existential crisis many lead mathematicians are having about it. OpenAI just published a set of solutions to longstanding problems in math that went off like a bombshell in the field. It caused a huge debate in the math community, and Rob spent some time talking to some of the most accomplished mathematicians of our time about it. It’s funny that AI systems are all still pretty bad at elementary school arithmetic, but getting increasingly good at very high-end abstract math. That raises some big questions for the field of advanced math. If AI can do math of this caliber, does that mean AI labs can transfer those skills to other domains? What good are academic grants and university programs training new generations of human mathematicians to identify new problems as they try to solve existing ones, if frontier models simply answer all the outstanding questions? What if all this attention around math is just a big marketing exercise for frontier AI labs, which couldn’t care less what happens to one of the oldest and most fundamental academic disciplines there is? There’s a lot here, and Robert has 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. This interview has been lightly edited for length and clarity. Robert Hart, you’re our 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. A full existential crisis, which is pure Decoder bait. Broadly tell us what’s going on. I think “a lot” sums it up quite well. Basically a bit of an existential crisis within, “what is mathematics? What are mathematicians doing, and what is the role of mathematicians going forward?” A lot of that has been spurred by a phrase transition in what AI is capable of that has exploded in the last six months to a year. AI went from being very terrible to seemingly genuinely quite good at a professional level in a very short space of time. 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 that these models could not count the number of R’s in the word strawberry. Even just counting eluded them. What has happened to make them better at math? Are they still bad at general arithmetic and they’re good at advanced math, or is it something in between? They are still truly, truly terrible at some areas of math. I did check, they can do strawberries now. I think someone’s tweaked it. I think strawberry’s 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, it’s still terrible at those kinds of things — math, arithmetic, even the days of the week. My boyfriend was saying the other day, “It keeps thinking it’s Wednesday. It’s not Wednesday.” Or time. Elissa Welle for us a few months ago wrote that ChatGPT can’t tell time. Still can’t. That’s not all of math. So there’s this disconnect. To be good at math, you’ve got to be good at counting, or adding, or multiplying. A lot of it is actually reasoning. If you look at academic math papers, a lot of the time you won’t see numbers, which sums that one up, I think. So they’re still terrible, but they’re now also very good at this other part. As to why, at some point you reach a critical mass of what these systems can do. We saw it with writing, we’ve seen it with programming. They’re very good at forging connections between different areas, applying old methods in new ways, those kinds of things. It appears that the newer models they’re training have apparently reached that level where it clicks, and now it can do math. It’s important to say as well that we speak of math as a unitary discipline, especially from the outside. But imagine, say, biology. You’ve got something that would range from literally watching animals and describing behavior all the way through to cellular mechanisms and biochemistry. Math is not a unitary discipline either. AI is really good at some bits. Some bits like counting, it’s still really bad at. Even on the more abstract levels, mathematicians have floated topology as one area that AI apparently still quite bad at. I can’t verify that, to be honest. It’s beyond my area of expertise. Still, it’s a bit of a mixed bag. So you’ve described mathematics as a huge field, obviously, with many, many academic areas of interest. There are some parts where the models have gotten quite good. There are other parts, maybe the basic parts that people think of as math, which is simply counting, where they’re still struggling, and then there’s a wide range in the middle. Is 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. No one’s really afraid of it being a mediocre mathematician, but obviously there’s a huge element of what this field does. In terms of the research elements or 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. All caught up in that is whether it’s going to rewrite employment structures or funding structures. You also raised the murky question of, what is mathematical knowledge? And the roles that these workers will be doing as well. It’s all of that wrapped into one. I think that tracks broadly with 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. Those parts of math, at least reported out in your piece and what the labs are talking about, seem to be almost entirely self-contained theoretical problems. That’s 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. That 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 early one as well. OpenAI just listed it as an unnamed internal model. It’s probably Astra. They didn’t answer me when I asked. OpenAI a few weeks ago dropped a blog along with a lot of paperwork proving it, I think several hundred pages. 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. I think one was in quantum game theory, which I don’t know how to begin to explain. Even harder to explain is there was sphere packing in higher dimensions, so more than three dimensions, and there were a lot of other different disciplines as well. It caused a lot of stir in the community. It was a bit of a bombshell. As we’d said, there’d been these individual breakthroughs that had happened, but OpenAI dropped 10 in one go, and they were quite big ones. Researchers had told me that if a human had solved these, we would be impressed. If a human had solved all 10, we probably wouldn’t believe it. They’re problems mathematicians actually care about as well, which is an important point. A lot of previous breakthroughs have been accused of being in areas mathematicians didn’t really bother with. These are ones that mathematicians, good mathematicians, have spent a lot of time trying to solve and hadn’t. 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?” Or 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, the reaction was generally one of being quite impressed, from the people I spoke to. As I said, these are problems mathematicians care about. There was one that drew particular attention for how they credited it and also how they’d announced all of this in their blog post. OpenAI initially had said that these are 10 problems, and there had been no progress in the last 10 years. And then if you actually read the papers, one of them quite clearly says, “Oh, we build on progress from these two researchers.” So that was later changed quite quietly. 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, and who was a bit ambivalent on the whole thing as well, so it was a real mixed bag. The general impression was that it was quite impressive. These were actual breakthroughs that bothered people, and it did move the field forward in a way that, if a human mathematician had done these, 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.” It’s funny, credit and attribution in academia is 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? If a human had accomplished the same goals and had been as sloppy, would the reaction be the same? Part of me always wants to lean on the whole, “Oh, it looks like plagiarism,” element. But if you actually read the papers they produced — and 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. It doesn’t attempt to plagiarize. I think it was just a poor press release, to be honest. And as much as I love to go in on it sometimes, having covered science for a decade-plus, I find the press releases are often overselling what discovery has actually been made and the import of it and the novelty of it. 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. So the big unknown from the near-dozen peop [truncated for AI cost control]