Mathematician Aims to Keep It Simple

John Baez PhD ’86 Pioneers New Way to Address Complexity

Mathematical physicist John Baez PhD ’86 has spent his career working on problems few people have heard of and even fewer understand—quantum gravity, n-category theory, and a unified theory of networks. Yet, what he loves about his field is its simplicity.

“A lot of the math that I do—that pure mathematicians do—there’s something incredibly simple about it. You can delineate what the problem is,” says Baez, a professor of mathematics at the University of California, Riverside.

What he means by simple is not easy, of course. He means clear and uncomplicated, noting that knotty mathematical problems can often be worked out just by thinking them through. (At least, that method works for him!)

Plus, they’re fun, says Baez, who has gained attention over the years for his playful side. In 1992, he created the Crackpot Index for rating unorthodox theories of physics. (“A key step in becoming a crackpot is becoming unwilling to accept corrections,” Baez says. “Anyone who wants to get good in a field has to get used to being wrong. You’re wrong often.”) Earlier this year, Baez was also spotlighted in the New York Times for a rectangle puzzle that took off on the social media site Mastodon.

Fun with Physics

Yet, it was physics that first caught Baez’s attention as a child. Growing up in Washington, DC, Baez was inspired by his uncle Albert Baez (father of the folk singer and songwriter Joan Baez), a physicist and science educator. On visits, his uncle “would always have in his suitcase different experimental projects and goodies,” Baez says. “He’d pull out some project or other and show it to me, and it was really exciting.” 

Advancing the field of physics, however, seemed to require a lot of equipment, such as huge particle accelerators—which to Baez seemed to limit his ability to contribute. “Over time, I got interested in mathematics because I could do stuff in math in my own bedroom,” he says.

Ultimately, Baez combined his interests by pursuing mathematical physics. After earning his undergraduate degree from Princeton and his PhD from MIT, both in math, he joined the mathematics faculty at the University of California, Riverside, in 1988 and spent many years researching quantum gravity.

The field focuses on a problematic gap in our understanding of the physical world: The rules that explain the way gravity behaves at the macro level—such as in the movement of the planets—don’t seem to work to explain behaviors at the quantum level—such as the movement of electrons around a nucleus. “It’s an extremely frustrating problem,” Baez says. “I enjoyed working on it, but I’m glad at some point that I stopped working on it.”

That point came around 2002, when Baez narrowed his attention to n-category theory, a type of algebraic structure that could provide a conceptual framework for quantum gravity.

Then, in 2010, Baez took a visiting professorship at the Centre for Quantum Technologies in Singapore and used the opportunity to make another research pivot—this time, to focus on what he sees as the existential crisis of our time: climate change.

Hoping to put math to work, Baez dove into climate modeling but quickly discovered the complexity level was outside his comfort zone. “With Earth’s climate system, there are so many variables!” he says. So, drawn again to the simplicity of pure mathematics, he began searching for a unified theory of networks. In this work, he is pioneering math that’s useful for working with flow charts, circuit diagrams, and complex interdependent models such as those used by climate scientists and epidemiologists.

Addressing Complexity

Baez is now working with friend and fellow MIT alum Nathaniel Osgood ’90, SM ’93, PhD ’99, a professor at the University of Saskatchewan, to improve the usability of dynamic models for public health: Osgood used these to help plan the public health care response to Covid in Canada. And while that might seem totally unrelated to climate modeling, Baez points out that, for the mathematics he is doing, the particular application isn’t really important.

“It’s like the guy whose job it is to run the power line to your house,” he says. “The math that I’m doing is really just about how you hook up these models to other models and how you modify these models. It’s not about the details.”

As ever, Baez is working to keep things simple. His goal is to make it possible to break huge, complex system models down into small portions (which individuals can comprehend and manipulate), then easily reconstruct the larger model to see how changes affect the whole system. “Part of the reason we need these abstract mathematical ideas is to make it easier for people to deal with these models and not get overwhelmed by the complexity.”

Having retired from teaching in 2021, Baez now spends his time lecturing and writing (in 1993, Baez started one of the world’s first blogs, This Week’s Finds in Mathematical Physics, and he continues to write about math and physics today).

He is also taking time to quietly think about whatever deep mathematical questions interest him. “I feel more like a student now again, more irresponsible,” he says.

Photo illustration: Gretchen Lambert; photo courtesy of John Baez.