Marie Claire Chelini, Trinity Communications
Mathematics Professor Jonathan Mattingly has been selected as a Simons Fellow in Mathematics. The award provides a salary and funds for leave-related expenses that allow faculty to extend their sabbaticals — which typically last one semester — by up to six months.
Mattingly has a broad and highly collaborative research program, often applying complex mathematical solutions to practical problems that span from cellular homeostasis and the spread of the common flu, to fluid mechanics and gerrymandering. The latter gained national attention, and his subsequent appearances in court cases led to the replacement of North Carolina’s legislative and congressional maps in 2020.
A native of Charlotte and graduate from the NC School of Science and Mathematics, Mattingly came back to North Carolina to join the Duke faculty in 2003, after a B.Sc. at Yale, a year at the École Normale Supérieure de Lyon, an M.A and a Ph.D. from Princeton and four years as a professor at Stanford.
We sat down with Mattingly to better understand the importance of sabbaticals, the nature of his research collaborations, and the research he is planning to conduct while away from Duke.
This interview has been edited for clarity and length.
What is the goal of this sabbatical?
Sabbaticals are a period when faculty are relieved of our teaching and administrative obligations, so we have a moment to think, not just a complete sentence — which is sometimes all I aspire to — but entire paragraphs, pages or even chapters.
The Simons funding gives me the opportunity to spend a whole year immersing myself in problems, like a postdoc or a graduate student. The grass is always greener, so faculty look with starry eyes back at the time when we were postdocs and think, “Oh, those were the good days, now we don't have time to learn new things.” Of course, when you're a grad student or a postdoc, you are constantly upset and worried about getting a job! But sabbaticals are about being able to think deeply and learn new things. That's one part of it.
Another part is that there are people I want to work with. And, you know, we see each other at a conference, you visit them for two or three days, then we try to pick that up on Zoom. But there's something different about being at a blackboard with someone, having lunch with them every day, and just popping into their office to discuss whatever idea I just had. It's also good to shake yourself out of your normal. I have wonderful colleagues and we have one of the best Mathematics departments in the country. Still, it's nice to have your mind broadened and be exposed to other perspectives and traditions.
It's nice to have your mind broadened and be exposed to other perspectives and traditions.
You're spending the bulk of your sabbatical at the Courant Institute at New York University, then Lausanne and Leipzig. How did you choose these places?
I wanted to actually go somewhere. I've always spent my sabbaticals here. The Courant Institute was a good balance: It’s a place with a long tradition of applied mathematics, with a huge number of people with whom I’ve written papers or had long term discussions, and the Simons Institute for Data Science is nearby. But being in New York, I can easily come back here every couple of weeks, talk to my students and see my spouse.
Then in Lausanne, I get to work with Martin Hairer — a Fields medalist — with whom I've written some of my most cited papers. And Lausanne is a beautiful place, and I always enjoy speaking French, so it's fun to have a bit of a refresher, spend some time dreaming in French again. In Leipzig I will visit the Max Planck Institute for Mathematics in the Sciences and the Center for Scalable Data Analytics and Artificial Intelligence, where I have colleagues with whom I've talked a lot, but never collaborated with, and colleagues with whom I have ongoing collaborations — one of my four ex postdocs is now in Leipzig. In all these places I’m excited to have time to find a problem where our interests overlap. If we find it, then we can find lots of interesting things to do.
Your proposal covers more than one of your research areas. What is the common thread between them?
My thread is what I call stochastic dynamics. Let me unpack that a bit: when we think about dynamics, what we mean are things that evolve with time. Take the weather, for example: you're starting where you are today, and you want to look at it over time. Or fluid mechanics: if you start the fluid in a certain state and then you run a stick through it, how does it change?
I also do a lot of work with gerrymandering, which is also a problem of scale structure. North Carolina has about 3,000 district precincts, but you could also think about the Census Blocks, and that's 80,000. As you try to go finer and finer, what happens with the scaling? The Bayesian statistics algorithms we use for sampling in gerrymandering, how do I understand their evolution in time? Those are all systems that evolve in time with constant influences.
Now, sometimes those influences are easy to predict, but sometimes they're constantly changing. One way to model their effect is to see how small randomness is organized by this dynamic, this evolution over time. Colloquially we talk about things being random or not. Well, the truth is that they’re not dichotomous, there's a whole gray area between them.
Colloquially we talk about things being random or not. Well, the truth is that they’re not dichotomous, there's a whole gray area between them.
You have pure randomness, like white noise on a speaker, and then there is randomness that follows a structure. And one of the ways that this structure develops is by evolution in time. So, a common thread of my work is how randomness evolves in time and is shaped by dynamics, whether that's fluid mechanics, a biological system or algorithmic questions.
Your work is extremely collaborative. Which comes first, the mathematical model or the real-world problem?
They happen together. One of my mentors always says, “Beautiful problems lead to beautiful mathematics.” Sometimes you solve the applied problem your collaborator cares about, but you keep digging and keep looking, and that leads you to think about just the mathematics. To hell with the problem, right? You just think about the mathematics for a while, and that leads to questions you never thought to ask. And then somebody else will use that mathematics in a different way for a different problem.
Just look at the way you and I can communicate complicated, nuanced ideas in this interview. That’s because we have some cultural overlap, we share a language, we have shared metaphors. People have to build those languages, those metaphors, those scaffoldings, to be able to conceptualize things.
People have to build those languages, those metaphors, those scaffoldings, to be able to conceptualize things.
You build it for one thing, and you build three of them, and someone says, “Oh, wow, I can put these all next to each other. And look, I learned how to connect them, and now I've built a new edifice in an area that we've never been before.” They use our understanding, our poetry, our metaphors and our perspectives to see into this new part of the problem. So it's both, right? It's both.
Will the research you conduct in your sabbatical come back to your students in some way?
Absolutely. When I do something new, there are always spin offs I can give students. My students are constantly wanting problems to work on, and they often surprise me and find a completely new direction based on the idea we started from.
What is a misconception you’d like to dispel?
I think we're in an interesting time where mathematics is everywhere. The language of mathematics is being used to model all these computational things, and ideas that have been developed for quite a while are being leveraged in really surprising ways. Mathematics has been driving change and progress in our society, it's both the engine and the navigator of many of our conversations.
Mathematics, not applied math or computational math, just mathematics, has been a license to follow my curiosity and be well trained no matter where I go. I could go off and get a job in lots of different companies, the government, consulting, aerospace, biomedical, Google, those are all places where my knowledge and skills are incredibly relevant. And I think students sometimes don't understand how versatile mathematics can be.
Mathematics is the artful obfuscation of facts.
Mathematics is the artful obfuscation of facts. It's the abstraction of facts to only capture the important part of the problem, and that can bring intense clarity to something that was buried in the noise of all the details of the system.
We're often the early arrivers in problems. Mathematics isn’t how to calculate the tip at the end of a meal. The math you did in high school is like spelling is to literature. Spelling is useful, right? But it's not the conversation that people have when they think about literature. Same thing for math. Get into the upper-level mathematics classes. Instead of trying to guess what the next big thing will be, train so that you are ready for the next big thing, and the next big thing, and the next big thing and so on.