[RADIOLAB INTRO]

SOREN WHEELER: This is Radiolab, and I am Soren Wheeler.

STEVE STROGATZ: Hey, Soren! Hi.

SOREN: I have to apologize for, like, dragging you away from Twitter. Or I guess I should call it X. But ...

STEVE STROGATZ: [laughs] And so it begins, all this teasing. Okay.

SOREN: Have you been out there? Have you been ...?

STEVE STROGATZ: It's been really interesting. My addiction is coming back. It's probably like a smoker who stops and then—I shouldn't say that to you. Are you still smoking?

SOREN: I have my dalliances—like you, I guess. Sometimes something happens in the world and it draws me back in.

SOREN: So that is Cornell mathematician and long-time friend of the show, Steve Strogatz. And the reason I had to drag him away from Twitter was because just a couple days before we talked ...

STEVE STROGATZ: It's really been an interesting few days.

SOREN: ... OpenAI announced that they had solved a longstanding big deal math problem. If I'm honest, I'm not even sure I knew exactly what that meant. But all the mathematicians I was seeing talking online, including Steve, it was almost like they were having an existential crisis.

STEVE STROGATZ: It's a big deal. It was a big deal.

SOREN: But why? Like, why?

STEVE STROGATZ: Because we're on a trajectory somewhere, and it's unclear yet whether it's a happy trajectory or a very sad trajectory, but we're going somewhere. And ...

SOREN: I feel like you have a sad ...

STEVE STROGATZ: You want to know what I think in my heart?

SOREN: Well, I feel like you have a sad—sure. Yes.

STEVE STROGATZ: I'm terrified.

SOREN: Now Steve wasn't terrified about a lot of things we've all been talking about, I don't know, like a big hack or crashed economy, computers taking over the world, or even really losing his job. Instead ...

STEVE STROGATZ: Yeah, I think it would be good to go further back.

SOREN: ... as we talked, it became clear that Steve was reckoning with questions about his own sense of purpose in the world in a way that, trite as it might sound, touched on one of the most fundamental things about being human.

STEVE STROGATZ: So I think we should just talk about it.

SOREN: Yeah. I mean, however you want to start.

STEVE STROGATZ: Okay, so I would start the story in November of 2022.

SOREN: Okay.

STEVE STROGATZ: That's when ChatGPT made itself known to the world.

SOREN: Were you—did you start using it right off the bat? I didn't.

STEVE STROGATZ: I did. I used it right away for gags.

SOREN: [laughs]

STEVE STROGATZ: You know, write this—at first it was all about writing. Write a poem in the style of Malcolm Gladwell about some crazy subject. Okay, so whatever. Then naturally, being a math person, I want to see is it any good at math?

SOREN: Yeah, I was gonna say ...

STEVE STROGATZ: It's not trained to do math. It's just supposed to do language. But you could ask it little math problems. And it was pretty pathetic. It couldn't do elementary school arithmetic. It would make mistakes. It was easy to fool it. But over the years, it went from being inept at arithmetic to then, like, it could do algebra kind of clumsily. And then at some point it was getting good scores on the International Math Olympiad, which is the test for high school whiz kids.

SOREN: Is this all just number crunching, like what a calculator could do, but perhaps ...

STEVE STROGATZ: It could actually solve problems, not just number crunching, no. You could give it logic puzzles, you could give it what looks like a hard math problem for a high school student that involves reasoning.

SOREN: I see.

STEVE STROGATZ: This is the part that's mysterious, and I'm not even sure it's very well understood by anybody. Somehow, by having read all the books in the Library of Congress and ...

SOREN: And everything on the internet.

STEVE STROGATZ: Everything on the internet, including blog posts, news articles, somehow the language itself encodes enough logic and reasoning to do math. They hadn't built it to do math, and this is what we would call an "emergent property." It emerged without being designed.

SOREN: And you were saying it's starting to get better at math slowly, like a child?

STEVE STROGATZ: Yes, it did.

SOREN: Were you sort of noticing?

STEVE STROGATZ: It progressed through all the developmental stages. It got good at high school math, then it got good at ...

SOREN: Did it spend longer in trigonometry than it expected to? Because ... [laughs]

STEVE STROGATZ: [laughs] That's one of the more painful subjects. No, actually, you touch on a really interesting point, Soren, because what they're not good at and have not been good at until recently is anything that's visual.

SOREN: Okay.

STEVE STROGATZ: But the bigger point is that it keeps getting better. Like, as of a few months ago, we were saying it can do research-level math.

SOREN: Well, that—that seems crazy fast. Like, a year ago, you were about as worried as you would be about me taking your job.

STEVE STROGATZ: [laughs]

SOREN: Which is zero. And then ...

STEVE STROGATZ: No, I want to get the chronology right. High school was like 2024.

SOREN: Okay.

STEVE STROGATZ: 2025, it's as good as a really smart college student.

SOREN: Okay.

STEVE STROGATZ: And then in 2026, in the spring, it's as good as a first-rate mathematician, but not the world's best. That was in March or whatever, but by May, it was actually solving problems that the world's best mathematicians had not been able to solve. By May of 2026.

SOREN: What—what problem did it—was it one particular problem?

STEVE STROGATZ: So the first—the first one that really got everybody's attention in my world was called the "unit-distance problem."

SOREN: Okay.

STEVE STROGATZ: I mean, I could describe the problem if you want, but it's ...

SOREN: It gets pretty hard to keep in your head, but the gist is that, like, well, imagine a bunch of pegs on a flat board. And for some number of pegs on the board, the question is like, what's the maximum number of pairs of those pegs you can have that are just one unit apart?

STEVE STROGATZ: That's the idea, because if I—if my job was to make as many pairs of pegs as possible ...

SOREN: You could see how, like, you're doing a—making a computer chip, that seems like a useful question.

STEVE STROGATZ: Maybe. It's not motivated by any practical thing.

SOREN: Oh.

STEVE STROGATZ: It was just a pure question about—you could call it "discrete geometry."

SOREN: Okay.

STEVE STROGATZ: So there was a guess about what the best possible arrangement was for putting down the pegs if your goal was to have as many as possible unit-distance apart from each other.

SOREN: Now for many decades, mathematicians had assumed that the best you could do was basically kind of like a simple grid.

STEVE STROGATZ: That you couldn't really do better than that. But no one was sure.

SOREN: So what everybody was trying to do was one of two things.

STEVE STROGATZ: You could prove it.

SOREN: Prove that the grid was the best solution.

STEVE STROGATZ: You'd have to come up with a logical argument that shows why it's correct. Or you have to come up with a counter-example, which in one stroke shows the conjecture is wrong, that there's a better solution or a better arrangement of pegs in this case. And in May, OpenAI, using one of its best models at the time, they found a better solution. And what was very interesting—and this is the part that really made all of us mathematicians sit up straight like I'm doing right now in my chair—it was very creative. It was not just a number-crunching solution. Everyone who looked at it, all the experts said this is a really beautiful argument. I mean, they used words like that—"beautiful," "elegant." And not only was it very ingenious, but it brought together two subjects that we didn't realize had a bridge connecting them. I mean, it sort of took from way over here and then took something you didn't think was connected at all.

SOREN: Like a different part—a different branch of mathematics?

STEVE STROGATZ: A different branch of math.

SOREN: Okay.

STEVE STROGATZ: We know because these AI models are now using what they refer to as "chain of thought." So a chain of thought is a way for us to see what it's thinking.

SOREN: I see.

STEVE STROGATZ: It doesn't just compute. It actually says, "Oh, I'm gonna try this now. This seems promising." And it literally has output that writes in natural language.

SOREN: Really? Writes it? You can read it like a doc?

STEVE STROGATZ: It writes it like that, including expletives. Like it will say, "Oh shit, this looks really—oh, this is gonna work!" I mean, it uses exclamation points, it swears, it will say any—it acts ...

SOREN: Well, you have given it the whole internet. I mean, so ...

STEVE STROGATZ: That's the point. It's trained. It sort of knows what people would say in situations of great discovery or an epiphany.

SOREN: But we're not even all that—you don't care about the F-bombs.

STEVE STROGATZ: I'm not interested in that topic. All I can tell you—I mean, yes, I am. But let's not go there.

SOREN: Okay.

STEVE STROGATZ: But what I'm saying is it taught us something. And it's sort of like when this guy named Dick Fosbury figured out a good way to do the high jump.

SOREN: The flop.

STEVE STROGATZ: You know the Fosbury flop.

SOREN: Yeah, the Fosbury flop.

STEVE STROGATZ: Right?

SOREN: Just for those who don't, in 1968, Dick Fosbury broke the high jump record. Now 'til then, people would run up to the high bar facing forward and go up, like, over their stomachs. But Dick Fosbury ran to the bar and sort of turned with his back to it and sort of jumped, arching over his back.

STEVE STROGATZ: He showed if you go over with your back going over, it looks dangerous.

SOREN: It looks idiotic. It looks ridiculous.

STEVE STROGATZ: [laughs] Nobody had tried it, but my point was that that taught other jumpers, and you don't see anybody doing it the old-school style now. Everybody does the Fosbury flop.

SOREN: Right.

STEVE STROGATZ: So in the same way, kind of, having seen the machine's brilliant idea on this unit-distance problem, human mathematicians were able to borrow and improve it and apply it to other problems.

SOREN: I see.

STEVE STROGATZ: If a person had come up with this, we would have called that person brilliant, and we would publish that result in the best journal in math. So May of 2026 is when it became clear that there was now a world-caliber mathematician that was not human. And that's—I think that's unforgettable. But of course, we've had many months now since May. So throughout the summer, from May until I'm speaking to you in September, one by one, harder and harder and more central problems have been getting knocked off or solved or mowed down or whatever you want to call it, one by one, all summer long. And it's having a traumatizing effect on a big subset of the math community.

SOREN: And that brings us to September of '26, just two days before Steve and I were talking, when OpenAI announced that it had solved a very important problem in math.

STEVE STROGATZ: Called the Navier-Stokes problem.

SOREN: Okay.

STEVE STROGATZ: That is one of the seven Millennium Problems.

SOREN: So the Millennium Problems are a group of seven problems that some mathematicians got together in the year 2000 and sort of said we should set our sights on these problems.

STEVE STROGATZ: For us to aspire to solve in the 21st century. And not just to solve, but to make the trek.

SOREN: Hmm.

STEVE STROGATZ: These are very cherished mountaintops that we aspire to reach. And this one just got solved. OpenAI announced it two days ago, as we speak.

SOREN: And can you tell me just a little bit about what the problem is?

STEVE STROGATZ: So Navier and Stokes were two scientists from the 1800s.

SOREN: They had come up with this enormously complex equation to describe the motion of fluids.

STEVE STROGATZ: How does water flow, or how does air flow? How does—I mean, more generally, anything that's fluid, like honey, molasses, lava, blood, there's a lot of things in the world that flow. And the Navier-Stokes equations are this simplified description of how things flow.

SOREN: And over the last 150 or so years, these equations have been very useful for us.

STEVE STROGATZ: So we use it for weather forecasting. We use it for thinking about ventilation systems in a room.

SOREN: But mathematicians are interested in these equations kind of for their own sake. And the big question, the big problem was ...

STEVE STROGATZ: Could the Navier-Stokes equations, as a purely mathematical device, could they predict something that we know is wrong? Like, are they fundamentally unsound in a certain way?

SOREN: Could you find a situation where they'll spit out something nonsense?

STEVE STROGATZ: Yes. Is there something fundamentally flawed about the equations? Can they generate nonsense?

SOREN: And this is what OpenAI claimed it did. It found a condition under which these equations start spitting out a bunch of infinities.

STEVE STROGATZ: The machine came up with a really tricky vortex. So it's like a tornado that's getting stronger and stronger at the same time that it's getting smaller and smaller. And it creates a kind of singularity where the equations break down at that point. So it answered the question, and it involved, at least according to the early reports, 10,000 agents. So these agents, this is a whole new thing in artificial intelligence.

SOREN: 10,000. So they spawned 10,000 little individual-ish ...

STEVE STROGATZ: Little genius mathematicians.

SOREN: All right.

STEVE STROGATZ: And they're independent to some extent. They try different tricks on the problem, but they also can collude and collaborate. They can make other computers do stuff for them. Anyway, they spent, it's estimated, somewhere between—OpenAI—somewhere between $15 and $20 million to solve a problem that had a reward on its head of $1 million. [laughs] Which you could see the economics is not so good. They weren't doing it for the money. They were doing it to say our AI can solve a problem that no human being can solve. And also Anthropic didn't solve it, right? I mean, there's this whole big competition between OpenAI and Anthropic.

SOREN: Okay.

STEVE STROGATZ: But they built on ideas of two Spanish mathematicians who came very close to solving the problem themselves: Diego Córdoba and his student Luis Martínez-Zoroa. So these guys figured out a brilliant strategy, and they were following it, but at human speed. They were making progress. They might have gotten there.

SOREN: They might have gotten there in five years.

STEVE STROGATZ: It might have taken five or ten years, and it's possible they would never have gotten there because the calculations are so monstrous that were required.

SOREN: Apparently, it took OpenAI about four days to solve this problem, but if you take into account there was 10,000 little agents working on it, that turns into rough—almost exactly 100 years of working hours, around the clock, day in, day out.

STEVE STROGATZ: And also, I mean, there's a whole controversy and more of a story here, because it looks like there's ...

SOREN: I should just quickly say there are some questions about how much OpenAI used, maybe without admitting, the work of Tristan Buckmaster and Levent Alpöge.

STEVE STROGATZ: And which I don't have any special visibility into any of that, but it's interesting in the public ...

SOREN: But what I wanted to know from Steve was how he felt about the Navier-Stokes solution.

STEVE STROGATZ: Okay.

SOREN: Was it like the unit-direction? Were you also like, "Oh! How cool, how clever, how amazing, how delightful? How ..."

STEVE STROGATZ: Well, not yet. That has not been the community's reaction so far.

SOREN: Why not?

STEVE STROGATZ: Unlike the unit-distance problem, where the—the solution is I would say transparent to an expert, this does not look like that. No one yet knows how the AI solved this problem. We have a 160-page write-up.

SOREN: But the math and the calculations are so incredibly complex and intricate.

STEVE STROGATZ: It's that hard to figure out that even the experts aren't sure what it did.

SOREN: Hmm.

STEVE STROGATZ: It's this inhuman computation that is very opaque and very—honestly to me, very off-putting.

SOREN: Steve says when it comes to, like, these, as he describes them, seven mountaintops of math, just solving them isn't necessarily the point. I mean, of course they want to solve them, but ...

STEVE STROGATZ: Even if we can't get there, we're made better by the quest, you know, by trying and struggling and learning.

SOREN: So if someone—or something—does solve the problem, for Steve ...

STEVE STROGATZ: I want to know why.

SOREN: And he feels like this rapid progress in AI solving all these math problems ...

STEVE STROGATZ: It's pointing in a certain direction. The key question, and what is so disturbing to think about—unsettling—is let's imagine a time where the machines are so good at math that we can't learn from them because they're too advanced, they're so far beyond us that we—we can't understand what we're doing anymore.

SOREN: And then, like, eventually you'll—like, all you'll get is sort of yes/no, yes/no?

STEVE STROGATZ: Right. Exactly. We're gonna start dealing with oracles that are infallible but opaque. They'll tell us the truth, but we won't know why.

SOREN: We're gonna take a quick break, but when we come back ...

STEVE STROGATZ: May I talk about Regina Barzilay now?

SOREN: I'm always gonna say yes.

STEVE STROGATZ: [laughs]

SOREN: ... Steve makes the argument that this is not just an issue in math. And we talk about whether if AI starts solving our problems or answering our questions, does it even matter if we don't understand how?

STEVE STROGATZ: May I talk about Regina Barzilay now?

SOREN: Sure. I'm always gonna say yes when you ask me questions like this. Like, can I?

STEVE STROGATZ: [laughs]

SOREN: Yeah, go.

STEVE STROGATZ: All right. Well ...

SOREN: This is Radiolab. I'm Soren Wheeler, talking to Steve Strogatz about what happens when AI starts answering questions or solving problems in ways that we aren't able to understand. And it so happens that Steve has been working on a book, it's called Big Math, that explores some of these ideas. And for that book, he talked to a woman named Regina Barzilay.

STEVE STROGATZ: Well, Regina is currently a computer scientist at MIT.

SOREN: Okay.

STEVE STROGATZ: But when she was 43, she was diagnosed with breast cancer.

SOREN: Hmm.

STEVE STROGATZ: And this came as a big shock to her. She had no symptoms. She had no risk factors that she knew of. Nobody in her family had ever had cancer, not breast cancer or any other cancer. But she had already had three mammograms, and on the third, at the one at age 43, the radiologist saw something that looked concerning, and it turned out it was bad. And she had to have two lumpectomies, chemotherapy and radiation.

STEVE STROGATZ: Her hair fell out. She had a seven-year-old. She was recently divorced. She had a seven-year-old and she had immigrated, so she is an immigrant to the US. And she had no family, nobody to support her, really. It was pretty bad, and she said if something is gonna happen to me, what's gonna happen to my little son? Okay, so fortunately she did survive and she is alive today. This all happened in 2014. But when she was going through these awful therapies, she talked to the doctors. She asked them specifically, how do people like me tend to do at your hospital? How do women with my specific diagnosis, you know, and mammograms that look like mine, what are my odds? And they said, we don't know because that's a complicated medical study that they hadn't done about ...

SOREN: Because there's too many different confounding factors about your age or your genetics or your diet or your environment or ...

STEVE STROGATZ: Right, we're just doing our best. Like, we don't know, we're just trying to help you. So she thought, well, look, I already had three mammograms. Maybe there was a clue back in my first mammogram that no radiologist could see. Maybe it was missed.

SOREN: I see.

STEVE STROGATZ: And is it possible that the clues are there, but human radiologists can't see them? It's too difficult for the human perceptual system.

SOREN: I see.

STEVE STROGATZ: And she ended up collecting about a quarter of a million mammograms.

SOREN: Ooh.

STEVE STROGATZ: From records at this hospital where the women had been followed up for years afterwards. So they knew who survived and who didn't, and if they died, how many years till they died. I mean, they had all the data, but it just had never been analyzed. And so she was able to train—again, this is around 2014. She used machine learning, she and her team, to build a prediction machine for assessing risk of breast cancer from one mammogram. And it's now the state of the art. It certainly was better than any method that was known at the time. And it has been tested in countries all around the world, hospitals all over. And it really works. But here's the uncanny part: If you ask her what is the machine seeing in the mammogram that enables it to make such a good prediction, she doesn't know, and the machine doesn't tell her.

SOREN: So you can't, based on what she did, say to doctors, "Keep an eye out for this."

STEVE STROGATZ: No.

SOREN: You have to feed it to the machine.

STEVE STROGATZ: Right now, yes. When I heard this, I asked her, does it bother you that you can't understand how the system is doing this? And she said something that has stuck with me. I think about it every day. She said, "Why would we limit the machine to what humans can understand?"

SOREN: Hmm.

STEVE STROGATZ: "We have to save lives here. Why would we limit the machine to what humans can understand?" I found that very haunting because, you know, yes, if it's a matter of saving lives, I get your point. Of course, it would be morally perverse to limit yourself to what—you know, the fact that a radiologist doesn't understand it, we don't have time to wait for that. And medicine is often like that. But I come from this math culture where understanding is everything. If we don't have understanding, we feel like we haven't solved the problem.

STEVE STROGATZ: And this is a point I guess I want to emphasize. It's not just that understanding gives us a pleasurable "a-ha" feeling. Yes, we like that. But I'm actually an applied mathematician, not a pure mathematician, meaning I care about how math meets reality in, you know, bringing an astronaut to the moon and back safely, an ultrasound for a pregnant mother. That's math, that's a lot of math in designing a good ultrasound machine to interpret all those waves bouncing around. You know, we could go on and on about this. This is the story of the past 400 years. Math, in combination with science, has made the world modern, and it's just had innumerable benefits for our health, for our society, for everything.

SOREN: Steve's point is that what you learn in one field or one area, even if it's just abstract mathematics, what you learn by trying and struggling, or by seeing how someone else solves the problem, that can pay off in another domain.

STEVE STROGATZ: That's it. What we have learned over hundreds of years is that understanding is the key to power.

SOREN: And I guess the whole—and you feel like you're running into this sort of like, answers-without-understanding problem, in mathematics you're running into that more and more.

STEVE STROGATZ: Yeah, we are. You know, like, if we solve things too quick—because here's where we are today. The AIs can solve essentially everything that we consider worth solving. They haven't solved our hardest problems yet, but we're—it's a matter of time. I think we're on the edge of it.

SOREN: And that's why Steve—and a lot of the mathematics community—right now they're worried. And not necessarily just about their jobs, but about the whole field of mathematics.

STEVE STROGATZ: A three or four-thousand-year-old discipline and culture, I mean, we will still have the ability to do—we can still do math for fun. It can become a game. Like, people do Sudoku for fun, even if a computer could do every Sudoku. Is that what's in store for us in math, that we're gonna just play math for fun, but we'll never make any discovery that matters?

STEVE STROGATZ: You know, what about young people who love it? Can they be mathematicians in the future? We don't know. Maybe we'll under—well, it's unclear. We might—we might be—I mean, I would want to argue against myself just for a minute. We might get a golden age of understanding. It's possible that the computers will teach us a lot, they'll be the best—not only the best mathematicians, but the best teachers. And so for those of us who love the subject, we might be entering the happiest time ever in history. Like, our problems are getting solved, there's magnificent methods. It's like listening to, you know, Pavarotti singing the opera. Like, nobody has done math better than these fucking machines.

SOREN: [laughs]

STEVE STROGATZ: And they're singing—they're singing better.

SOREN: You're undercutting yourself with the F-bomb.

STEVE STROGATZ: Well, but you see I'm all conflicted. I'm very conflicted.

SOREN: So I actually talked to Steve a couple different times since that first conversation, in the days that followed, a week later. And he really did go back and forth a lot about what this is gonna mean for math. But it was clear that he couldn't totally shake the feeling that he himself was losing something and being sidelined in a sort of a way.

STEVE STROGATZ: And if we're gonna end up like the people in Wall-E, in the movie Wall-E, just sitting on our chaise lounge, you know, plugged in with our Big Gulp and our credit cards, like what does that ...

SOREN: It does feel like being a human being in the world involves some level of—like, currently I'm trying to understand my children.

STEVE STROGATZ: Yeah.

SOREN: And for me, you know, it's fine for math to remain inscrutable. I mean, there's so many things in the world that I don't understand anyway.

SOREN: Also, not just for you. I think most of us live our life not understanding a lot of stuff. I don't understand how my toaster works. But I don't need to, and I don't really care. I just want my bagel.

SOREN: Right. I mean—but I guess I just—I don't think that we should let go of understanding lightly.

STEVE STROGATZ: Yeah. Intuitively, it seems like it's one of the things that makes us human, that being able to understand is helpful.

SOREN: It feels fundamental, yeah.

STEVE STROGATZ: It does feel very fundamental. I really—unfortunately, I think that we're getting now a little bit outside of our scope to the question of what's the purpose of a human life?

SOREN: That is never outside of our scope.

STEVE STROGATZ: Right, this is Radiolab.

SOREN: That's actually the only thing we're ever talking about.

STEVE STROGATZ: That's the only question. [laughs] I kind of wonder, you know? I feel like that's what we're talking about here is what are we doing? What do we want out of our life? We want to love our kids. We want to be—you know, have a meaningful time. We get to be a little blip of atoms, you know, organized into consciousness for maybe 80 years or 100 years if we're lucky, and then we're dust. So what are we gonna do with ourselves? And for me, part of the answer is I love being curious, I love learning, and I'm not gonna get to do it in the same way if this future comes while I'm still alive. But look, I don't want to dismiss the possibility that these will always be tools. If we can make it so that we're in charge, we can tell them what to do, we can unplug them as needed, they're like brain prostheses. So this year, 2026, will be remembered either as a miracle year, an annus mirabilis, or a horrible year, annus horribilis, for the history of mathematics. And I don't know yet which one it's gonna be.

SOREN: All right. I'll let you end on that.

STEVE STROGATZ: [laughs] Okay. God!

SOREN: This episode was reported and produced by me and also my producer, Maria Paz Gutiérrez. Big shout out to her for putting me onto this whole thing, talking to so many different mathematicians, knowing what was going on. It just wouldn't have happened without her. It was also edited by Pat Walters. Jeremy Bloom did our dialog mixing, and our fact-checker for this one was Diane Kelly.

SOREN: Also, Steve's new book, which hits on many of these issues rather presciently, is called Big Math. He wrote it together with his colleague, another mathematician at Cornell, Alex Townsend. It's set to be released on November 10, but you can preorder it wherever you do your preordering.

SOREN: Now if you happen to like hearing a little bit of math, or me and Steve talking about math or whatever, we actually had an episode from a couple years ago called "The Middle of Everything Everywhere," in which Steve and I try to figure out in real time what the average-sized thing in the universe is. It's a fun one. Go check it out if you like. Until then, this is Radiolab. Thanks for listening, and we'll see you next week.

[LISTENER: Hi, I'm Maia, and I'm from London, and here are the staff credits. Radiolab is hosted by Lulu Miller and Latif Nasser. Soren Wheeler is our executive editor. Sarah Sandbach is our executive director. Our managing editor is Pat Walters. Dylan Keefe is our director of sound design. Our staff includes: Jeremy Bloom, W. Harry Fortuna, David Gebel, Maria Paz Gutiérrez, Sindhu Gnanasambandan, Matt Kielty, Mona Madgavkar, Alex Neason, Sarah Qari, Natalia Ramirez, Joanna Strogatz, Anisa Vietze, Arianne Wack, Molly Webster and Jessica Yung, with help from Maia Appleby Melamed, Laura Karpas and Olivia Rose Greco. Our fact-checkers are Nora Belblidia, Hilary Elkins, Rachel Gross, Diane Kelly, Emily Krieger, Natalie Middleton and Sophie Samiee.]

[LISTENER: Hey, Radiolab. Michael, Tacoma, Washington. Leadership support for Radiolab's science programming is provided by the Simons Foundation and the John Templeton Foundation. Foundational support for Radiolab was provided by the Alfred P. Sloan Foundation.]

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