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An Interview with Bernd Sturmfels

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An Interview with Bernd Sturmfels MAA FOCUS January 2008 “Mathematicians Have a Different Perspective” An Interview with Bernd Sturmfels By Joe Gallian and Ivars Peterson After receiving his PhD from the for very focused studies; students tend University of Washington in 1987, Ger- to reach a higher level rather quickly. man-born Bernd Sturmfels held positions In the traditional German system, the at Cornell University and New York first degree was called the “Diplom,” University before landing at the Univer- and one obtained this degree after about sity of California at Berkeley, where he five years. It used to be a rather rigorous currently teaches. Sturmfels has received program, comparable to a strong Masters numerous honors, including the MAA’s Lester R. Ford Award for expository writ- program with a written thesis. ing in 1999 and designation as a George Pólya Lecturer. Sturmfels served as the In the last 20 years, there have been Hewlett-Packard Research Professor at many changes in the university systems MSRI Berkeley in 2003/0, and was a in Europe, not just in Germany, and now Clay Institute Senior Scholar in Summer most schools offer Bachelor and Masters 200. A leading experimentalist among Degrees more similar to the system in the mathematicians, Sturmfels has authored States. Not everyone is happy about these eight books and about 10 articles, in changes, needless to say. the areas of combinatorics, algebraic geometry, symbolic computation and FOCUS: How do you describe your their applications. He currently works research area? on algebraic methods in statistics and of Washington and the University of To- computational biology. ronto, so I was told to go to one of these Sturmfels: I work in combinatorics two schools. He was absolutely right: and algebraic geometry, with a special MAA FOCUS: Did you become inter- Victor Klee, a former MAA president, emphasis on applications outside of ested in mathematics at a young age? turned out to be a most wonderful thesis pure mathematics. Recently, I have been advisor for me. especially interested in applications in Bernd Sturmfels: I was a pretty good statistics, optimization and computational student in school, interested in almost I obtained a fellowship from the Ger- biology. Computational biology offers all subjects. There was never anything man government to study for one year fascinating opportunities to mathemati- special about mathematics, no competi- in Seattle. Three months after arriving, cians, and can ultimately lead to new tions or Olympiads or any such in my I fell madly in love with this wonderful and unexpected developments within high school. After graduating from high undergraduate English major from Korea, mathematics. school, I was in the German army for 15 and I just had to stay awhile longer in months to do my compulsory military Seattle. That’s why I ended up getting FOCUS: Which mathematicians have service. It was during those lonely eve- my doctoral degree at the University of had a large influence on you? nings in the barracks that I tried to figure Washington. My now-wife and I stayed out what I was really interested in. That together all those years, and, after mov- Sturmfels: Victor Klee, my advisor turned out to be mathematics and the ing around for many years, we finally in Seattle, ranks first. Others that have emerging field of computer science. returned to the West Coast in 1995. influenced me greatly include Louis Billera, Richard Stanley, I.M. Gel’fand FOCUS: You came from Germany to at- FOCUS: How does mathematics educa- and Bill Fulton. tend graduate school at the University of tion at the college and graduate school Washington. What drew you there? level in the U.S. differ from that in FOCUS: You have been involved in Germany? “experimental mathematics.” What, to Sturmfels: My German advisor sent me you, is experimental? What are the ex- to Seattle in 1985. I was interested in Sturmfels: The main difference is that periments that you are doing? spending a year abroad, but I was think- in Germany, students declare their major Sturmfels: Well, computer experiments. ing of France or England, something before entering university. There are few I can experiment by hypothesis testing or closer to home. My advisor strongly breadth requirements, so once someone it could be just plain old exploration, just urged me to go to North America. His is a university student most of the classes to see what happens. “Gee I wonder what contacts were primarily at the University taken are in mathematics. This makes January 2008 MAA FOCUS properties the following mathematical who has many of these diploma students; learned over the years the value of com- object has.” Actually, that’s often the first that setting lends itself more easily to munication skills. Of course you have to step. I think you can use computation as a maintaining software. So the software in be good in math, but I think when I was tool to form hypotheses, or to test. my field is quite difficult for an academic younger I wasn’t as keenly aware of how math person to develop and even more important social skills and communica- I don’t trust humans a lot. You know, difficult to maintain. That’s a real chal- tion skills are. One doesn’t think about it people think that a written proof is the lenge. I admire anybody who does it and in the math context, but that’s something gold standard. I think many mathematical hope they get a lot of support. that I also pay attention to. So if there’s papers and arguments contain errors and a student I feel would have a very hard gaps and the only reason we don’t find FOCUS: Now that you’re at Berkeley, time communicating in either writing or them is because they don’t get read. On a prestigious institution that attracts verbally, then I’m more cautious. the whole, the building of mathematics very good students, how do you find the is sound, but if a mathematical state- students and their capabilities? FOCUS: Have you had any significant ment works out in a computer test, then involvement with undergraduates in I believe it a lot more. So I would say Sturmfels: I think the students are won- research? exploration, verification, and falsifica- derful, but of course we have a large tion. And then the last stage is once you program in Berkeley. Compared to some Sturmfels: Some, but not as much as have the conjecture or hypothesis then of the smaller private schools we compete I would like to. Lior Pachter and I are you can sort of go case by case and see: with, we have more of a spectrum, simply teaching an upper division undergraduate Is it true for n=8? And so on. because our program is much larger and course on mathematical biology at Berke- also because we try to be open. We have ley, where the students work in teams on The design of experiments is very im- a tradition of letting in students that might specific projects. This replaces the final portant. I think that’s where I sort of see not otherwise make the cut, so there’s a exams, and some interesting research my strength. Just like a lab scientist, a lot spectrum. But I would say that the stu- projects have sprung out of that. In fact, of work needs to go into creating a well dents I worked with are wonderful. I’ve thought out model system and model learned a lot from, and with, them. I just taught that course in the spring organism, to design the experiment, to of 2007, and I think that three or four pick a range of test problems that are FOCUS: And it sounds like you work a students have continued their research not too easy and not too hard, which lot with them. over the summer and beyond. However, will reveal the right phenomenon. That’s I must say that supervising undergraduate the challenge that distinguishes a good Sturmfels: Yeah, it’s the best part of research in mathematics is challenging, experimentalist from one that’s maybe the job. and essentially impossible for me, if and not so good. when it requires very regular one-on-one FOCUS: I’ve known faculty who take meetings. A laboratory setting, where FOCUS: Is that influenced by changes the approach of identifying the gradu- undergrads learn from graduate students in technology? ate students they want and approaching and post-docs, always works better for them. Is that similar to your approach? the problems of interest to me. Sturmfels: Definitely! Certainly now you can do a lot more than when I Sturmfels: Yeah I think that’s probably FOCUS: What about the sense of doing started. But I would say that experiments similar. It’s a little bit like dating. It helps mathematics in a broader context, for ex- in mathematics are not as technology- to be proactive. But finding a good match ample in biology and so on. Do students driven as in, say, molecular biology. Our is a two-way street. I think it helps the come in with that kind of interest or do technology is not progressing at the rapid student along if this relationship is built they develop it? rate it is in molecular biology, where it’s early on, so I try to play as active a role crucial to have the latest equipment just as possible, both in recruiting when they Sturmfels: It works both ways. I had to compete… It’s a little less crucial in come to Berkeley, and also in the first some students who were very pure and mathematics.
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