Robert L. Devaney

Boston University
2002 DTS Award

Robert L. Devaney
Professor of Mathematics
Boston University

NSF Award Recognition


Jeanne L. Narum, Director, Project Kaleidoscope, interviewing Dr. Robert L. Devaney

If a visitor were to come into your classroom/lab-the environment in which you work with students-what impression would s/he leave with?

A visitor to the mathematics courses I now teach would probably marvel at how different these courses are from the way they were in ancient times (pre-1985). Now, with the computer at my side, I can have my sophomore level students tackle the kind of real-world differential equations that were impossible to solve in the old way-when all we had were very specialized analytic tricks and the only differential equations of interest were usually linear. Now I can give my students a glimpse of what is new and exciting in mathematics, instead of confining my attention to seventeenth century ideas from calculus. Finally I can introduce very simple-sounding questions that relate directly to the course content, tell students that nobody knows the answer to the question, and then challenge them to get involved in contemporary mathematics.

What brought you to an interest in "advancing the frontiers of education" and to connecting your research to that work?

There was a pivotal moment in my research and teaching career. Back in the mid-eighties I realized that certain dynamical systems undergo what we now call "explosions." The crude computer graphics of those days showed that the chaotic regimes or Julia sets of simple mathematical expressions-like the sine or exponential-could change shape in dramatic fashion as parameters vary. These Julia sets are extremely beautiful fractal images that are quite interesting to look at, even if you are not a mathematician. In order to investigate these explosions, several undergraduates prompted me to make a movie of these changes. It took us over 200 hours using the largest computer we could get our hands on in those days to compute a two minute film. To my amazement, the movie was incredibly spectacular both visually and mathematically; indeed, it has motivated much of my subsequent research.

At that time I was teaching a large freshman calculus course. The lecture hall I taught in was part of a theater complex. In fact, it was used in the evening as a movie theater. One day, I had a few minutes left at the end of class and decided to show the movie just for fun. The reaction of the students stunned me. I had never seen so many students so excited about anything I had ever told them before. They were absolutely amazed that they were seeing mathematics-not done by Euclid or Newton-but rather by their own professor and his undergraduate students. From that day forward, I have always tried to give my students little glimpses of what is happening in mathematics. For many students, the reaction is always the same. "Wow," they say, "This is cool!" (Or "awesome," or whatever the current jargon is for "exciting").

Were there risks in doing this? What made you persevere?

I see no risks whatsoever in exposing students to contemporary ideas in mathematics. In fact, I cannot understand why we in mathematics have built our curriculum so linearly that very few students ever see the incredibly beautiful things that we encounter in our research all the time. Why is it that many mathematics majors never see any twentieth century (not to mention twenty-first century) mathematics during their undergraduate years? I cannot imagine this happening in the sciences or engineering. Why is this culture so pervasive in mathematics? This must change.

What connections have been of most value in pursuing these efforts, within your campus community as well as in the broader professional communities to which you belong?

Unfortunately, there are very few connections within the mathematics community that have helped me pursue these efforts. Most of my efforts have been either on my own or with a very small group of committed faculty and students.

For faculty at an early career stage, it is difficult to figure out how to balance responsibilities for research and teaching while having a personal life; any advice - for them and for faculty at any stage?

What kind of institutional culture needs to be in place to nurture careers of faculty actively seeking to integrate their research and education?

I hear senior faculty and administrators telling junior faculty: If you want tenure, make sure that your research comes first. Yes, you must teach well, but your research is most important. You can do the educational things later.

This is troubling, especially given the situation in the mathematical sciences. For centuries, all we have had at our disposal in the classroom was a blackboard and a piece of chalk. Now, in many areas of mathematics, the computer is creating a whole new research and educational environment. Mathematics now has a truly experimental component. In my mind, these changes need to be brought into the classroom. For the most part, it is not the older faculty who are poised to implement these changes. It is our younger colleagues who have the most to offer in this regard. It concerns me deeply that they are not encouraged or rewarded for their assistance in these matters. Indeed, punishing them for this service is bizarre.

What can be done at the national level to encourage and support efforts?

The efforts of the National Science Foundation regarding the integration of research and teaching are visionary. I know of many students who have opted to continue their careers in the mathematical sciences thanks to an early exposure to research in an NSF REU program. NSF has pushed for the "Vertical Integration of Research and Education" through the VIGRE program. This program seeks to make a radical change in the prevailing culture at top research universities by blurring the lines between research and education. While this program is quite controversial, I applaud NSF for having the courage to stand up and say to mathematicians: It's time to change your ways. If I had a dream, I would love to see NSF extend this integration to the high school level, thereby bringing all segments of the mathematics community together in an effort to make everyone-students, teachers, the general public-aware of the importance and relevance of contemporary mathematics.

What is the project you are undertaking as part of your DTS award? How can others be involved?

I currently direct the Dynamical Systems and Technology Project at Boston University (http://math.bu.edu/DYSYS). This project attempts to bring contemporary ideas in mathematics into the classroom at all levels, from high school through graduate school. The DTS award will assist me by providing the means to create additional online activities for students to pursue. These activities involve contemporary topics in mathematics drawn from the areas of chaotic dynamics and fractal geometry.