*A native Californian, **Frank A. Farris** is associate professor of mathematics at Santa Clara University, where he has taught since 1984. He did his undergraduate work at Pomona College and received his Ph.D. from the Massachusetts Institute of Technology in 1981. **Farris completed a five-year term as editor of *Mathematics Magazine* in 2005 and serves again through 2009, aspiring to continue the journal's tradition of challenging and inspiring teachers and students of mathematics at the undergraduate level. He received a **Trevor Evans Award** for his article "**The Edge of the Universe**" in *Math Horizons* and Santa Clara’s David E. Logothetti Teaching Award. *

Ivars Peterson: You have a long California history.

Frank Farris: I'm a native Californian. In fact, it was my mother's grandfather—my great grandfather—who brought the family to California in 1852. I was born in Santa Monica, and my family, soon after I was born, moved inland 20 miles to Covina, a suburb of Los Angeles. I went to college just 15 miles further inland at Pomona College.

My mother was born in San Jose, which is where I ended up living, just by coincidence. I have lots of dead relatives up on the hill in San Jose.

IP: How did your interest in mathematics arise?

FF: I usually say that I was converted by an NSF summer science training program in 1972. That was a program, I'm sure in response to the whole Sputnik thing, to enrich mathematical talent in America. This was at San Diego State, run by Ed Deaton. There were 50 of us, and I was 15 years old. It was the first time I was among my cohort in some sense. Deaton ran a Moore method style development of geometry, starting with the Hilbert axioms. He presented us with the axioms and said, "Tomorrow you will be called on to prove theorem one." I was hooked. It was a marvelous experience.

But, in thinking back to my childhood, my mother had been very interested in mathematics at UCLA. I'm the youngest of four children, so I certainly benefited from the education of my older siblings. And I just flashed on a memory of my sister Patty, who I think was learning about negative numbers in perhaps her fifth- or sixth-grade class, and she explained it to me and asked, "So, what's four minus seven?" And I replied, "Negative three." And she ran off exclaiming, "Frank's a genius! Frank's a genius!" My ability to impress my sister, I'm sure, had a positive influence on my affinity for mathematics.

We were a musical family, and we would perform together. We had a Weavers-style folk group in the late 60s and early 70s. Ideas about rhythm are very deeply ingrained in me. And, of course, that is connected to mathematics.

IP: How did you end up doing math in the NSF summer training program?

FF: I applied to a variety of these enrichment programs right after my junior year in high school. I was interested in an astronomy program; I was interested in a variety of things. But I had liked mathematics and had been successful at it, so I applied to that one too. And that happened to be the one that accepted me.

I have to say that the mathematics in my education until then was just one of many subjects that I was good at, and interested in.

FF: I went to Pomona saying that I wanted to be a pre-med major because that's what people in my high school were doing when they wanted to be well-to-do. But I would do that by being a math major, because I was told that that was possible, because I loved mathematics since that summer science training program. The pre-med idea lasted maybe one year. I'm extremely glad I took chemistry. That was a dazzling experience. But mathematics very quickly took over.

The community at Pomona College was a very happy mathematics community. It was fun to study mathematics. I got involved with the Putnam competition, and did okay. It just seemed very natural. After my sophomore year at Pomona, I was able to do a summer research project with Rick Elderkin, who became quite a mentor to me.

After my junior year, it was the bicentennial year, and we did an NSF-funded undergraduate research project (URP), so that was the bicentennial undergraduate research project, or BURP. That had to do with an age-dependent model of malaria.

IP: What was it about mathematics that attracted your attention?

FF: I think some deep part of my personality has a Platonic idealist in there, so it was just the beauty of this system that was real and true and beautiful.

IP: You went on to graduate school.

FF: I went to MIT. That was quite a transition for me. Culturally, I am very happy that I spent seven years on the east coast—four years at MIT and then my first job was a very nice postdoctoral position at Brown University.

I did suffer from some culture shock. Whereas Pomona was a happy and nurturing environment, MIT was a nurturing environment in a different way. It was much more vigorous. There was much more a feeling that one must take care of oneself. The students who had been undergraduates at Princeton were already involved in mathematics at a much higher level that I was. So some of us from the west coast formed a little support group. It was definitely a difficult transition for me.

IP: On what area of mathematics did you begin to focus?

FF: I've always known that I liked geometry, which is my field, but I went into graduate school saying that I wanted to be an applied mathematician, because as an undergraduate I had studied differential equations, though studied from a geometric viewpoint. So the geometry was always there, but it was in service of differential equations and applied mathematics.

MIT took my application to their applied mathematics department and put it in the pure mathematics pile. So, in some sense, I was informed by MIT that I really was a pure mathematician, and I think that's an accurate assessment. I'm a pure mathematician who has a great love for seeing mathematics of service in other fields—seeing mathematics come true in the real world. But at heart I'm a pure mathematician.

IP: Who in particular helped you along your path?

FF: My thesis advisor, Richard Melrose, was a very influential figure, and Sigurdur Helgason, James Munkres, Daniel Kahn running a topology seminar.

Looking back, I don't think I took the best advantage of my time with those people. I was struggling with some personal issues. I could have learned so much more.

IP: How important was teaching to you?

FF: I had not really taught a class at MIT. The most I had done was run a problem session. I was at MIT on an NSF graduate fellowship, so I wasn't obligated to teach, and nobody seemed to think it was important for me to teach except to run little problem sessions. At MIT, I did grade for a course in analysis, where I read students' proofs. That, in some way, was the beginning of my love for helping others with their mathematical exposition.

But I had never taught calculus, and at Brown my first assignment was to teach calculus. I was teaching second-quarter calculus at 10 o'clock. I attended Eva Kallin's 9 a.m. class and saw what she did, and then did that at 10 o'clock for 125 students. But I have had a lot of performing experience. I, in some sense, consider myself a natural performer, so it was not difficult for me to figure out what to do with my performing instrument to be helpful to those people who presumably wanted to know something that I know.

I'm sure there were some bumps in the road, but I took to teaching. I loved it. The students at Brown were wonderful. They gave me quite a variety of courses to teach. I did the beginning calculus as well as ODEs and PDEs—a full-year course—and a graduate course in differential geometry. So I got some nice assignments.

But I also got a grant from the Lilly Foundation to develop a course on writing geometry. I wouldn't say that the course was a great success, but it laid foundations for a course that I think has been a success for me, which is "Writing for the Mathematical Sciences." I've taught it maybe four or five times at Santa Clara. I didn't develop the course. Others did, but I've taught it many times. Next fall, I plan to teach this course at the University of Minnesota, visiting for a semester.

IP: How did you end up at Santa Clara?

FF: My three-year position at Brown was a terminal position, which had a lot of positives. You wouldn't be involved in departmental politics. I applied for perhaps 70 jobs all over the country, interviewed at several places, but it was Santa Clara that made me the job offer first. It's been a perfect place for me in many ways. It is that department at Santa Clara that connected me to the MAA.

Jerry Alexanderson was the chair of the department who hired me. He completed 34 years of service as chair of our department a few years ago. It may have been in 1985 or 1986 when Jerry asked me to consider joining the MAA. Looking back, I wonder why no one at Pomona told me that. I understand why people at MIT and Brown did not tell me that, although I think they were wrong. But I was glad Jerry got me involved.

That led to assignments refereeing for *Mathematics Magazine*. Paul Halmos had brought the *Monthly* to Santa Clara about 1984. I gradually became more and more involved with the MAA. I’m very grateful for that involvement. It was a great source of help for me.

IP: How was your experience as editor of *Mathematics Magazine*?

FF: I learned a lot. My mathematical horizons were broadened. There are large fields of mathematics that had been left out of my education, for instance, number theory. I have now become much better educated in those fields. It’s wonderful.

I appreciated the chance to use what I think is one of my strengths, which is to help mathematical ideas find their clearest expression. I received many papers whose authors had wonderful ideas to share but perhaps through lack of experience or personal inclination had not shared those ideas in the most digestible or approachable way. I feel very good about the way I helped various authors over the years to share their ideas in a better way.

IP: Where do you see yourself, say, 10 years from now?

FF: I want to do more mathematical exposition. I feel that this is something that I started to learn how to do in the 90s. That's not very long ago. I hope there is time for me to write many, many expository mathematics articles.

I'm also very passionate about defending the value of this activity in our community. I get hot under the collar when people contrast exposition with research. I say, "No, mathematical exposition is a distinctive kind of mathematical research." It requires the same research methodologies that people in the academy are rewarded for, say, an Emily Dickinson scholar. No one thinks you have to write new poems by Emily Dickinson. People think that you have to find a new way for people of our time to interpret those poems. So mathematics is in constant need of reinterpretation for the thinkers of today.

What I think happened in the 20th century is that everyone went off into their little corners and proved the hardest new theorems from their own small corner without making as much effort as they could have made to communicate across these little branches. I think the 21st century can represent a great coming together when we try to learn about one another's branches of mathematics. If we will only place value on the expository efforts of people who try to communicate across disciplines, I think that our area of mathematics will be much better off.

I'm most interested in explaining mathematics to mathematicians. I feel that that's my niche. I would like to see the efforts of people to popularize mathematics respected more than they are. Then there is this other category of explaining mathematics to scientists and engineers. I think that's valuable. I don't think that's my strength.

IP: Are you thinking of writing a book?

FF: I've been thinking about that. Currently, I'm more attracted by the article format. It allows me more variety. So if I write a dozen articles, they could be about a dozen topics. Whereas if I tried to write a dozen chapters in a book, that would have to be about one thing. That's not where I'm headed right now. Ten years from now, I would love to write a book.

IP: Any regrets about your career path?

FF: Many mathematicians are doing research that grew exactly out the research they were trained to do in graduate school, following rather closely, or even loosely, in the footsteps of their PhD advisors. At a time in the 80s, I became disenchanted with the idea that my obligation was to prove the hardest theorems in one narrow area. I stopped doing that kind of research, and in the 90s I needed to find a way to continue forward. Mathematical exposition was one way. I also developed some new projects with Tom Banchoff.

I've paid a certain professional price for not maintaining this one thread of mathematical research. But I wish that our community offered a greater variety of opportunities to get involved in research projects, including expository research.

IP: Publishing and communication are changing, and online material plays an increasingly important role. How are you reacting to these changes?

FF: I love being able to pull up articles that are connected to other articles through JSTOR. Although I own an almost full backlog of *Mathematics Magazine*, if I'm in a hurry, if I quickly what to find out what so-and-so said in the '78 issue, then I'm going to pull it up on JSTOR. That's a great richness. I hope people know that there is an amazing treasure house in that backlog of the *Magazine*, as well as the *College Math Journal* and the *Monthly*. I love the convenience.

I fear the people are wanting to learn in 140-character messages. I was very interested by the recent popular reporting on the failure of multitasking because for me there's nothing like a long period of quiet time to focus on one thing. Our modern means of communication are antithetical to that.

When I was a child, there were lengthy times when I was taken to my family's place in the Sierra Nevada that my father started building in 1947, for six weeks at a time for many summers. There was no phone, no radio, and if you wanted to be entertained you entertained yourself. That, I think, developed me in a very important way, and I just wish that kind of developmental period for other young people today. I think it's huge to not always have something to look at but to be invited to look at the things around you.

Read about Frank Farris's Distinguished Lecture

"Visualizing Automorphic Functions" (with Jeffrey Hoffstein)