Massachusetts Professor of the Year
Polymath prof finds beauty in chaos — in classroom, on Broadway, under sail
Robert Devaney’s office is neat, orderly, and, fittingly, chaotic. A CAS professor of mathematics and statistics, Devaney studies dynamical systems, or phenomena that are always changing and thus impossible to predict using mathematics. He’s decorated his walls and shelves with colorful posters representing various forms of disorder: patterns called Mandelbrot and Julia sets that swirl and twist and defy easy geometry. As if to offset all the uncertainty, Devaney has neatly arranged on shelves a massive collection of coffee mugs, one from each of the some 200 universities he has spoken at around the world.
A 2003 winner of a Metcalf Award for Excellence in Teaching, Devaney was recently named the 2004 Massachusetts Professor of the Year by the Council for the Advancement and Support of Education and the Carnegie Foundation for the Advancement of Teaching. This fall he’s teaching courses on differential equations and chaotic dynamical systems, and according to one of his former students, he “is able to make every lecture entertaining and understandable: he renders jaw-droppingly difficult mathematics simple and fun.” Another student says, “The brilliance of Devaney’s instruction lies in his ability not only to present complex theory so that it can be clearly understood, but more important, appreciated. Mathematics is an art form.”
The B.U. Bridge recently visited Devaney in his office.
Bridge: Do you have any guiding philosophy in your teaching?
Devaney: One thing I enjoy doing is bringing contemporary mathematics into the classroom. In the typical high school math classroom, you see 4th-century bc geometry and 11th-century algebra. If the kids stick with it for a long enough time, they see some 17th-century calculus, but nobody ever touches this incredible math that’s going on now. I think that’s something we should be doing more of in mathematics.
Bridge: What attracted you to dynamical systems?
Devaney: In the late 1970s, people realized that most of these systems — such as weather patterns and the Dow Jones average — are chaotic, or totally unpredictable. That’s interesting, but how do you study chaos? Luckily the computer arrived around then, and how do you study a system like this on the computer? You draw a picture of it, and these beautiful fractal images emerge. Even though you can’t understand anything from the numbers — they just go crazy — when you stand back and take a viewpoint from afar, you see this very distinctive pattern. What it means remains to be decided, but it was a very different and exciting way of looking at mathematics.
Bridge: How can technology improve the teaching of mathematics?
Devaney: When I started teaching, I would walk into the classroom, pick up some chalk, and immediately turn my back on the class. We didn’t have computer graphics, and we didn’t know about chaos. We’d start each class with a differential equation, and demonstrate all kinds of mathematical tricks to solve very special problems. Now I go in, turn on the computer, and immediately draw solution after solution. We can see the chaotic behavior changing. It’s just a totally different environment.
Bridge: You’ve been a “chaos consultant” in the theater?
Devaney: There’s a wonderful play by Tom Stoppard called Arcadia that involves a lot of mathematics. He writes so beautifully about mathematics that I think a lot of people in the play are intimidated by it. My son is an actor in New York City, and he told a director that I was a chaos person and that I could help him. Next thing I knew I was coaching the actors, showing them what this mathematics means. The director had these crazy ideas that had nothing to do with what Stoppard was saying, so when he saw how beautiful chaos is — the way it can be used to make pictures of leaves, mountain ranges — he changed his plans pretty quickly.
Bridge: What’s the most challenging aspect of teaching math?
Devaney: In mathematics, we’ve got to be absolutely rigorous, but we also need to keep the material interesting for the students. So there’s this problem: you could shave off a little bit of the complexity here and make it a little more accessible and interesting, but you also want to be thorough and rigorous.
The most rewarding part is seeing students get excited about the mathematics. Some kids are just born to be mathematicians — they’re going to be excited no matter what you do. But to have other students encounter contemporary mathematics for the first time and get just as excited — that’s amazing.
Bridge: Can I ask you about that photograph of the sailboat? Are you a sailor?
Devaney: Oh God, yes, I’m a fanatic. My wife and I keep our boat, Cygnet, down in a beautiful harbor in Buzzards Bay. We went up to Maine for a couple of weeks last summer, then down to New York City, and all over the place. I do a lot of single-handed sailing — this particular boat is easy to single-hand; you don’t have to be changing the lines all the time. When my wife’s working, I’ll just sail wherever the wind’s blowing, and sometimes I look up and say, geez, I’m in Nantucket! Now I gotta get back for dinner. But it’s great because I can do math the whole way.
Bridge: When are you not thinking about mathematics?
Devaney: When I’m listening to opera. I’m a fanatic about that as well. I’ll drive all the way down to the Metropolitan Opera in New York for a Saturday matinee with a CD playing of the opera I’m about to see. I’ll watch the opera all afternoon and then get in the car and drive back to Boston listening to the next opera I’m going to see. It’s a little strange.