‘Big Math’ shines a light on the hidden math that runs our world

Mathematician Steven Strogatz discusses the unexpected math in daily life, and how his field is picking up the pieces after AI disruptions.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Speaker 00

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• 0:14Flora Lichtman?

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• 1:03Ira Flatow?

  Hey, I'm Ira, and you're listening to Science Friday. Math is the talk of the town in a way that it hasn't been before, thanks to recent AI news, of course. And some mathematicians, like my next guest, Steve Strogatz, are using this moment as a reminder of the invisible ways that math is embedded in our daily lives. That's the focus of his new book, Big Math: The Hidden Codes That Run Our World. He wrote it with mathematician Alex Townsend. Steve, welcome back to Science Friday.

• 1:35Speaker 03

  Thanks a lot, Ira. Great to be here with you.

• 1:37Ira Flatow?

  Are you tired of talking about AI and math?

• 1:39Speaker 03

  Yes. Well, can I answer honestly?

• 1:43Ira Flatow?

  Yes, go ahead. That's what we like on this show.

• 1:46Speaker 03

  Yeah, it is a little exhausting, but it is the talk of the town, so let's do it.

• 1:51Ira Flatow?

  Okay. Where are mathematicians now, then, in terms of trying to figure out the next steps for the field, then?

• 1:58Speaker 03

  It's definitely a work in progress. This summer and fall, you know, of 2026 is one we're never going to forget. There's people sometimes phrase it in terms of grief, going through five stages of grief. Other folks are very optimistic, think that, look, this is a fantastic new tool, so powerful. It can help us ease calculations, do some proofs. And there have been remarkable advances with the help of AI this summer. So I have colleagues who say it's like a new telescope or a new microscope for us, and we just have to figure out where to point it.

• 2:32Ira Flatow?

  What is the grief part? Explain that to our audience. I don't think they really understand that.

• 2:36Speaker 03

  I'll try, but I worry if I make it too convincing, I might discourage young people. Seriously, I mean, that's been the concern. Yes, no, seriously, to the extent that we wallow in the grief reaction, if it discourages the next generation from going into our beautiful 4,000-year-old subject that really has changed the world, that's a bad thing. We don't want that outcome. So we want to put as happy a face on this as we can while still telling the truth. That said, many people go into math because they like solving puzzles. It's fun. It really is fun. You have companionship. I mean, there's nothing like working with another mathematician or a student. You're both stumped on the same puzzle or the same problem, and then somebody sees the light.

• 3:20Speaker 03

  It's a really thrilling moment and very joyful. So we live for those aha moments. And if the AI can take shortcuts, and we never have those moments of discovery anymore, for many people, that would be discouraging. They like that part of math. That's the concern.

• 3:38Ira Flatow?

  That's not satisfying.

• 3:39Speaker 03

  It misses one of the most attractive parts, the pleasure of discovery, the thrill of the struggle, and then the eventual success when it happens. But, you know, the counterargument is, well, math is not just problem solving. There's also teaching. There's explaining to each other. Like, you know, I've been on the show with you in the past talking about Archimedes. And that's, you know, he's 250 B.C., and I still get overjoyed thinking about that genius in ancient Greece. So we would still have that, you know, and we would still have the great discoveries that the AIs make. So maybe that's what we become math appreciators rather than math discoverers. Is that the future? We'll see.

• 4:22Ira Flatow?

  Yeah. You know, while AI has dumped out these hundreds of math problems, solved them in the past couple of months, they don't really tell you how they got there, right? Because I remember when I was taking calculus, the professor always said, "Give me the answer and show your work."

• 4:38Speaker 03

  Yes, show your work. Well, this is a complicated one to answer, so let me try to tell the truth. It is true that AI writes some kind of document that we can read when they've solved. Like recently, it was, I think, October 6th. OpenAI announced a solution to something like 300-plus problems, really hard problems at the frontier of math. Some of them very longstanding for decades. So then what? I noticed your word "dump." That is a, that's a word with a certain valence to it. They dumped the problems on us. They deliberately didn't explain them in great detail. They, OpenAI. I mean, they do show their work. It's just that their work is so inhuman

• 5:23Speaker 03

  in that they spend a lot of time on obvious things, and some of the hardest parts, they go too fast for us. So they're not really super well-calibrated to human understanding. Nevertheless, some of my friends who are digging through these proofs, who are experts in the various areas, are saying the proofs are very, very clever. When you understand them, it may take two or three weeks to work with a group of other mathematicians to figure them out. In every case that has been figured out, they're really marvelous proofs. So it's not the case that it's totally opaque. It's really top-flight math that the machines are coming up with.

• 5:59Ira Flatow?

  My geometry teacher in high school used to talk about his proofs as he liked them to be elegant. Are these elegant, would you describe?

• 6:08Speaker 03

  So elegant to us in math. And your teacher was right. Elegant means something like there's a surprise, yet once you see it, it feels inevitable. And then you slap your forehead and say, "I wish I had thought of that." Now, is it the case that the AI proofs look like that? Sometimes, yes. We've had some where they combined different parts of math in novel ways, and afterward, people thought, you know what, we really could have done that. Now, on the other hand, the Millennium Prize that was announced in September, that problem, the Navier-Stokes fluid mechanics problem, showing that those equations could predict a so-called blow-up, some velocity becoming infinite in a finite time. That one does not look like something human beings would have thought of.

• 6:53Speaker 03

  That looked truly superhuman.

• 6:57Ira Flatow?

  You know, we've had a lot of mathematicians come on the show in the past year, including Terence Tseau. And they've all said, "One of the main joys of math is the social aspect of collaborating with others to solve the puzzle." And now that AI is basically promising to take those away from math, do you think the joy part will shift to another part of the process? Maybe to reverse engineering the AI solutions?

• 7:21Speaker 03

  Yeah, maybe, maybe. It's a very, this is what's so mysterious and what is such a lively topic of discussion these days. What will be left for us? Is it possible there will be a part of math that will be for us? That will be human math, and we'll still have all the same pleasure, and we kind of don't let the AI tell us the answers. You know, it'd be like not looking at the back of the book in high school. So maybe we can still have the joy of math that way. But, you know, a lot of people would say, "Come on, that's rinky-dink. I wanted to be the first to climb the mountain." And so if that's going to be our role in math, if we're going to still hope to be heroes, maybe the answer is, how about helping us cure cancer? Or how about helping us work on the climate problem

• 8:04Speaker 03

  or new kinds of energy, you know, storage systems? Well, that's my world, that's applied math.

• 8:09Ira Flatow?

  Can math actually help us do those kinds of things?

• 8:12Speaker 03

  Oh, of course, absolutely. Math has been doing this for thousands of years, that there is such deep math in the laws of nature in every part of, you know, whether it's physics, astronomy, chemistry, even biology and the social sciences. There are deep patterns that can be expressed in the language of math, and we gain insight into them through manipulating equations and all of that. So I happen to think that it may be the golden age of applied math coming up. But pure math, the math that looks inward at itself and enjoys its own harmony and symmetries and patterns, that is sort of too easy for the AI. That's the problem. When you're in this hermetically sealed world of pure thought, like chess was, or like software coding,

• 8:58Speaker 03

  the AIs are really good at that. But what the AIs are not great at is asking new questions. I mean, that could be another role for the people, right? If we, our curiosity, they don't, as far as we know, have curiosity yet. So it's really unclear.

• 9:12Ira Flatow?

  So you could be like the prime mover and just hand it over to, you know, solve this problem because you haven't thought about that one yet.

• 9:18Speaker 03

  Solve it, and then explain it to us, and then we get to sit around and argue and think, oh, actually, you know, what has sometimes happened is after the AI explains it, like this happened recently with a problem called the quasi-Riemann hypothesis, which is getting very close to the biggest fish in the sea, the great white whale, the Riemann hypothesis. So the quasi-Riemann hypothesis was considered Fields Medal-level work that the AI did recently in that list of 300-plus problems that it solved. And after we saw the AI solution, human mathematicians improved on it. So it's not just the case that anything you can do, I can do better. In fact, there's still a place for us, and the mathematicians, human mathematicians, have beaten the AI at its own game, once given a hint.

• 10:02Ira Flatow?

  We have to take a break, but when we come back, I want to get into some ancient math history with you. Stay with us.

• 10:15Speaker 00

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• 11:03Flora Lichtman?

  Science Friday is supported by Audible. Presenting Exoplanet. From executive producer Andy Weir, number one bestselling author of Project Tale Mary and The Martian, comes a new interstellar audio thriller with an all-star cast led by Anthony Mackie, Ariana DeBose, and John Leguizamo. When the starship Wild Blue Yonder is torn apart by a quantum anomaly, each surviving crew member crash-lands in a different era on the same hostile planet, hunted, alone, and running out of time. To survive, they must find a way to communicate across time and work together to stop a relentless alien intelligence that feeds on human technology and could consume humanity. Listen along as their stories weave in and out.

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• 12:13Speaker 04

  I'm Kevin Roos. And I'm Casey Newton. And together, we've been tech journalists for decades. Now, we're your hosts of Machine Gods, a new podcast from NPR that makes sense of what AI means for your work, your life, and all of our futures. Twice a week, we'll be exploring the biggest moves in tech and give you unmatched access to the real titans of industry. Listen to Machine Gods from NPR on the NPR app or wherever you get your podcasts.

• 12:42Ira Flatow?

  Steve, there's always a place for you because one of your many talents is the ability to explain math to people like us. And that's what's so delightful about your latest book, Big Math. Let's get into that because there's some really fun stuff and elegant stuff in there. Tell me first, what drove you to write such a book?

• 13:02Speaker 03

  That was a matter of friendship, I would say. Alex Townsend, my co-author, is about 28 years younger than I am. And when he first arrived at Cornell as a new professor, I was invited to be his mentor, you know, help the young guy learn the ropes. And I would talk about his research with him and his classes. And one of his courses was called Top 10 Algorithms of the 20th Century. Isn't that an appealing title? Top 10 algorithms of the 20th century. What are those top 10? And how do they work? And what have they done for the world?

• 13:35Ira Flatow?

  Drumroll, please.

• 13:36Speaker 03

  Yeah, drumroll. I said, you ought to really write a book about that. And that got us talking. Now, our book, Big Math, is not exactly that, but it's some kind of combination of our interests. I mean, Alex is really very expert in how computers can handle problems so much bigger than the math we can normally fit in our head. When you're dealing with, let's say, Facebook, which has 3 billion active users, you know, Facebook will tell you the network of who's friends with who. My wife loves using it that way. She'll say, when she meets a new person, she'll say, I didn't realize that we had these mutual friends. Well, that's a giant network calculation that Facebook is doing for you using graph theory. That's big math.

• 14:19Ira Flatow?

  Well, let's talk about, for example, the hidden math behind something like the Netflix algorithm.

• 14:25Speaker 03

  So the problem for Netflix, back when they were still mailing out their DVDs in those red envelopes. Remember those days? We're showing our age here. Well, they would, of course, love for you to keep coming back and keep your subscription. So it's in their interest to recommend things you're going to like. And they wanted to have a better algorithm, and so they created a contest to try to improve on their recommendation system. And people, hobbyists, computer people from all over the world, joined this contest. And if you think about what the data are like that goes into this, if you want to think about it mathematically, there are a lot of people who are the subscribers, and

• 15:07Speaker 03

  those people have only watched a tiny fraction of all the possible movies that Netflix offers because nobody could watch the whole. All right. So if you imagine like a big table of numbers that says, you know, which movies has Ira watched, which movies has Steve watched, what ratings would they give them, thumbs up or thumbs down? Mostly, that big table of numbers, that's what we would call a matrix, you know, users and the movies and the ratings they give them, that matrix is mostly empty because you and I haven't watched anything near the whole library. And the same is true for all the users. So you're trying, what you would want to do is fill in the matrix with all the correct numbers, whatever that means, to predict what you would rate a movie that you haven't seen yet. And it sounds impossible.

• 15:52Speaker 03

  How could you fill in all those blanks? Well, big math can do that through something called the singular value decomposition, which is a linear algebra idea that grows out of our understanding of matrices.

• 16:03Ira Flatow?

  What areas of today's world do you think people would be surprised that there's complicated math involved?

• 16:11Speaker 03

  Maybe something like building a skyscraper. You know, you think, yeah. So like, the example we mentioned in the book is the Burj Khalifa, which is the world's tallest building. It's in Dubai. It's unbelievably tall. It's about twice as tall, not quite, but almost twice as tall as the Empire State Building. I mean, how is that thing going to stay upright? So the engineering challenges were incredible. And the way that the engineers at one of the world's leading firms approached it, well, they're going to build a model of it in a computer first. And so what's involved in that model is a ton of math. You have, the jargon is finite element analysis, which means you try to break the imaginary

• 16:55Speaker 03

  building into lots of components and think about all the forces, all the deformations, all the deflections. And you use Newton's law. I mean, it's a lot of force equals mass times acceleration and related things about twisting, torque balance. But it's an incredibly big calculation that engineers know how to do, but that uses matrices. Like I just mentioned, the matrix that comes in the Netflix challenge, the same math, more or less, matrix theory is getting used to study the stability of the Burj Khalifa.

• 17:26Ira Flatow?

  Let's talk about, let's go into our wayback machine for a second, Steve. Because I know, I love, I love the history of science and math, and I know there's a lot of math history in this book, too. What do you think is underappreciated about ancient math?

• 17:43Speaker 03

  Well, one thing that surprised me and that I didn't appreciate is we did a lot of research, so we learned a lot in writing the book. I didn't realize that the contrived word problems that bedevil so many students in high school algebra classes, they were doing them 2,000 years ago, too. I could give you a puzzle from some ancient Chinese manuscripts. It's an exercise to help you build your mind, and teachers have known forever that this is a good way to train students. And so there's a puzzle in there about three different grades of rice paddy, like poor quality, medium quality, and excellent quality. Anyway, they describe three scenarios, and you combine the three grades of rice in three different ways, and you get a certain amount of edible rice.

• 18:27Speaker 03

  And then the question is, how much edible rice does each grade produce on its own? So in the jargon of today, this would be called solving a system of three simultaneous linear equations. But the crazy thing is that in 200 B.C., in ancient China, they were solving that problem using a board, a wooden board, that was, had lines ruled on it. So it looks like a table with grid lines. And then they put sticks, bamboo sticks, inside each cell on the board, which represented numbers. And then someone would physically manipulate the sticks to do the process that we call the method of elimination, to eliminate the variables in this problem one by one till there's only one variable left.

• 19:10Speaker 03

  And then you solve it, and then you can substitute that and solve the next variable.

• 19:13Ira Flatow?

  So sort of like a different kind of abacus.

• 19:16Speaker 03

  It was sort of like an ancient abacus, right. And this is the thing, that humanity has been externalizing math forever. We're not that great at holding big problems in our head, but we've learned to use machines like the Feng Cheng, the name of this wooden board, or today, supercomputers.

• 19:34Ira Flatow?

  Wow. And you started your journey writing this book. Do you look at math or present research from any sort of different perspective after you finished writing it?

• 19:46Speaker 03

  Yes, I would say so. Because in thinking about what has happened as the computers that are so essential to big math have gotten more and more powerful, I started to, and Alex, too, I think, would agree, we've come to realize that humanity inadvertently made a kind of Faustian bargain. I'll just remind your listeners that Faust wanted unbounded knowledge in the legend from the 1400s, 1500s, an old folklore story from Germany. There's also a happier version that Goethe wrote, a couple hundred years after Christopher Marlowe wrote this really scary version. And Goethe's version has Faust being redeemed at the end, being saved by some angels who

• 20:29Speaker 03

  say, he whoever strives with all his might, him we can redeem. Meaning, what does that mean for us? That we've made this deal with computers and AI that are now getting so, so advanced that we are at risk of losing our ability to understand them. They're outgrowing their creator. And, and so, will that lead to a golden age with all diseases being cured and wonderful things for humanity? Or will we be dragged to hell? We don't really know yet, and we have to be very careful. This is, I'm sure you must have had guests on who talked about AI safety and that sort of thing. It's very tricky to control a system that may end up being more intelligent than we are.

• 21:12Ira Flatow?

  Well, Steve, we're so happy you're here to explain all of this to us who really have trouble understanding it. And thank you for taking time to be with us today, and good luck with the book.

• 21:21Speaker 03

  Thanks very much, Ira.

• 21:22Ira Flatow?

  Steve Strogatz, author of Big Math: The Hidden Codes That Run Our World. And you can read an excerpt from Alex Townsend and Steve's new book at sciencefriday.com/bigmath.

• 21:42Ira Flatow?

  This episode was produced by Dee Peterschmidt. I'm Ira Flatow. Thanks for listening.