A person requires surgery to correct a congenital malformation of the skull. To prepare for the operation, the surgeon rehearses the procedure virtually, using an extremely detailed mathematical model of the head, packed, as it is, with hundreds of miles of blood vessels, nerves, muscles and tendons. The entire surgery is planned with millimeter precision - and with math equations, lots of math equations, which are solved by computer - all before the patient goes under the knife.
Welcome to the world of Big Math. For years now, we've all been living in it.
In their new book, "Big Math: The Hidden Codes That Run Our World," published Nov. 10 by Little, Brown and Company, Steven Strogatz and Alex Townsend crack open this algorithm-driven world and reveal the history of mathematical concepts that undergird, and often control, modern life.
"This kind of math is not just recommending what movie to watch tonight. This is changing people's lives very directly," said Strogatz, the Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics in the College of Arts and Sciences (A&S). "There are millions of examples, and people have no idea. They think this is Big Tech or this is just modern medicine, but it's totally math under the hood."
Strogatz and Townsend coined the term Big Math to describe the kind of mathematics that can only be calculated - and perhaps only comprehended - by computer. And Big Math is everywhere.
"It's on your iPhones. It's deciding whether you get a mortgage. It's letting you sit in an MRI machine for half as long as you should. It's why TikTok is so addictive," said Townsend, associate professor of mathematics (A&S). "It's the math that actually is in the public, just quietly."
The book began to germinate five years ago during Strogatz and Townsend's weekly lunches in Risley Dining Hall, where the two would bat ideas back and forth. Maybe they could write a book about matrices. How about algorithms? They eventually settled on the topic of math and computers, and the publisher accepted their pitch, but they still weren't sure of the story.
"We've learned from over the years of trying to write for the public that there's this genre: narrative nonfiction," Strogatz said. "It doesn't come easily to academics. We often tend to think thematically, because our courses are organized around this topic built on that topic, and it's based on logical organization rather than narrative or dramatic tension. And readers like stories."
At the suggestion of their editors, Strogatz and Townsend began to incorporate historical examples to help narrativize the concepts - call it the Malcolm Gladwell effect - and they tried to frame the math in a way that the general reader would find relatable.
The process of collaboratively drafting the book began to resemble their lunchtime discussions.
"For almost every single section of the book, there's this back and forth between Steve and me, reacting to each other's work," Townsend said. "In the end, we had such fun writing this together. It really brought in both of our areas of expertise: the way Steve thinks about explaining and teaching mathematics to different types of people, and for me, it was a lot of stuff that is core to my research in numerical linear algebra and AI."
'When math scales up … everything changes'
The resulting book traces the full arc of mathematics, both big and small, from the ancient use of linear algebra in Islamic inheritance law, up through the nonlinear dynamics and chaos theory that are Strogatz's area of study, to Big Math's current collusion with modern computing. Along the way, the book introduces people like Regina Barzilay, who used machine learning to predict a woman's risk of breast cancer, and Stanisław Ulam, whose insights into fission were pivotal for building the hydrogen bomb.
"It's very easy to write a white male Eurocentric math book. Pretty much all math books read like that," Strogatz said. "But it's no accident that our book starts in China, then goes to the Arab world. And you've got women flying through clouds, discovering the laws of how they move and affect the weather. It's really an adventure story of men and women, with a lot of unsung heroes."
Steven Strogatz, right, and Alex Townsend hatched the idea for their new book, "Big Math," while discussing mathematics and computers during their weekly lunches in Risley Dining Hall.
Each chapter title poses a practical question: "What Does Chutes and Ladders Reveal About Internet Searches and American Politics?" "Why Do Your Photos Still Look Perfect After You Shrink Them?" "Can a Machine Read Your Mind?"
As the book progresses, the math grows more complex and Strogatz and Townsend pose serious questions about where the field is heading - and if we are prepared to go there. As they write in the book: "When math scales up with the help of computers, everything changes."
"Of course, we're afraid of what AI can do. But in the book, we're kind of telling people what AI is inside, what is it made of," Townsend said. "We can understand the mechanics of how AI works, but what we don't understand is why it's doing such a good job, why those numbers end up doing what they exactly do."
The timing of the book's release is fortuitous. The past summer has been a challenging - and sometimes terrifying - one for mathematicians, with AI solving a swath of classical math problems, which has raised existential questions for the discipline. But Townsend draws a distinction between those kinds of equations and Big Math.
"Those problems have some consequences for Big Math, but often Big Math is a bit messier," he said. "It has to deal with the real world. It has to deal with data. It has to go and sample and build. Right now AI is answering questions that other great mathematicians have asked, which is extremely impressive, but it's not yet an oracle."
Strogatz and Townsend see Big Math as something, well, much bigger than AI.
"This is really high-stakes stuff. I feel it is a saga of something that humanity has done over thousands of years, and we're now at a climactic moment, some kind of crisis. If you just look at the headlines, you'll be disoriented. It's so confusing, and I feel it," Strogatz said. "But it's also a very transcendent story. It's the story of one of the great monuments of human creativity."
