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 2003/04, and was a in Europe, not just in Germany, and now Clay Institute Senior Scholar in Summer most schools offer Bachelor and Masters 2004. 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 140 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. You don’t need the biggest year, to identify who might be a good then found it interesting. There’s a good computer! fit. example of a student I work with. He just finished his first year in graduate school. FOCUS: What about on the software FOCUS: Has the kind of student you He was an undergraduate at Harvard, and side? want changed over the years? he had a very strong undergraduate math background: a very pure, typical Harvard Sturmfels: The software side… that’s Sturmfels: That’s a good question. Since math undergraduate background. Then he actually quite hard because developing I have become a bit more of an applied went back to his hometown and worked and maintaining software is extremely mathematician, I would also expect my in the biotech industry for a while. So he difficult in an academic math environ- students to be open to engage with people got a job and worked for a small private ment. It’s a little bit easier in the old Ger- outside of math. Also, I want them to company that was involved in the Grape man system where you have a professor have good communication skills! I’ve Genome project, so they got funding from

5 MAA FOCUS January 2008 the province of Trento in Northern Italy ics are very different subjects, and that FOCUS: I think Dick Karp and others and they sequenced the pinot noir grape. statistics, computer science, theoretical have spoken very strongly about the That was a two and a half year project physics, and mathematics are very very computer side of these things and how and in the course of that work he picked different subjects. To a typical biologist important those questions are. Are there up a lot of statistics, genetics, and com- these are indistinguishable. similar things on the math side? putational biology. Then he wanted to go back and get a math PhD, so he ended up So I think we have a lot of educating to Sturmfels: I think so. I think math- working with me in Berkeley and it’s a do and to explain that there are different ematicians have a different perspective. very good fit, because he has the biology areas of mathematics like there are dif- Mathematicians can contribute a lot by background but he’s now interested in ferent areas of biology, and they have dif- clarifying the notions and helping to pure algebraic geometry studies. He has ferent points of view. Partial differential gain precise definitions of the objects the option to go both ways. equations can do this while combinatorics and concepts involved, and that’s kind of will do that. And so I think that is very where I see my role. In the conversation, FOCUS: How did you become interested important to explain just what it is you do as a mathematician, I think I’m trained to in mathematical biology? and what techniques you use, and it’s a give precision and rigor to the concepts long process, but an interesting one. and to the discussion, while computer sci- Sturmfels: It all started with my ju- entists thinks more about the large scale nior colleague Lior Pachter. Lior is a FOCUS: In terms of say, computational model and the complexity of carrying computational biologist who ended up biology, what do you see as the important out a certain computation. A mathemati- in Berkeley’s mathematics department. questions and the places where progress cian would ask “what’s meaningful?” or Four years ago, we started talking about is possible? “what is it we’re really computing?” A phylogenetics, and we soon discovered mathematician would say: “suppose we Sturmfels: that the combinatorial structures he was I think in evolutionary biol- had a suffiently powerful computer, what ogy there are key questions. How does would you do with the output?” using for problems such as gene predic- evolution really work for biological tion or sequence alignments are very systems? What drives it? What’s the no- FOCUS: What kind of questions can similar to things I knew about. We started tion of fitness landscapes? I think for the biology suggest for mathematicians? a joint seminar in the fall of 2003 and it first time people have serious data, so has been a fascinating journey for me there’s statistical genetics. Evolutionary Sturmfels: I wrote an opinion piece on and my students ever since. Last year, theory has existed for 80 or 100 years, this for the Clay Institute called, “Can bi- we published a book called Algebraic going back to Fisher and Wright and ology lead to new theorems?” and I high- Statistics for Computational Biology. other people in the early 20th century, lighted four examples of such theorems. but I think for the first time we really see One that I was involved in was compu- FOCUS: When there’s a need for com- a significant amount of data and I think tational algebraic geometry and the study munication between mathematicians, there’s some really interesting problems of certain families of algebraic varieties and for example, biologists, what kinds we can now address. Basically, how does that come from phylogenetics. It turns out of barriers are there? What makes it dif- evolution work? that statistical models for evolution can ficult? be described by algebraic varieties (in the FOCUS: Some recent genome com- sense of algebraic geometry). These are Sturmfels: The language and the back- parisons were showing that there isn’t ground are both very difficult and very that much difference in the genomes of different. First of all, people don’t un- related species, and that more and more derstand that mathematicians will speak important is the significance of what parts about biology as a single discipline. But are turned on and off. That whole process the concept of biology being one field is changing. makes no sense to biologists, because obviously there are a thousand different Sturmfels: Exactly, the networks and the branches that are vastly different from regulatory mechanisms are what really each other. And conversely! At this differentiate cells, and differentiate or- stage most serious senior researchers in ganisms and species. I think the amazing molecular biology in particular realize variety we see in living systems cannot that they have massive data sets and that be explained by a static sequence which they need quantitative help, so often is relatively short. The human genome is they will say “we are really interested in less than 3 billion base pairs. If you see working with mathematicians,” but they the complexity of us, that’s not enough don’t quite know what mathematics is. to explain it. As mathematicians, we think that partial differential equations and combinator-

January 2008 918937_MathFin.qxp 11/19/07 2:27 PM Page 1 MAA FOCUS generalizations of classically known varieties, but very interesting new objects. In the last couple of years, we’ve seen four or five really interesting papers. So BOSTON UNIVERSITY I think biology and models for studying biological systems can suggest new and MATHEMATICAL FINANCE PROGRAM interesting mathematical objects that gen- eralize known objects that have already been classically studied in math. Earn a Master of Arts degree in FOCUS: On a side issue, one of the things mathematicians feel compelled Mathematical Finance in less than one year to become involved in are issues about math education, especially at pre-college levels. Do you have any interests or If you have an affinity for logical thinking and analytical reasoning, are concerns in that way? highly motivated, and aspire to a fascinating and rewarding career in the

Sturmfels: Many concerns. My kid is in world of finance, we invite you to find out more about Boston University’s school right now so I can see it from that Master of Arts in Mathematical Finance Program at www.bu.edu/mathfn. end, but I have not done much with that. I feel that it is more important to build What distinguishes us? a continuous spectrum of research. We now have K–12 and education research programs, and I feel it is all a little dis- � Intensive one-year M.A. program connected from the mathematics research � Focused and interdisciplinary cutting-edge curriculum community. I think there should be a dedicated to mathematical finance layer in between; maybe the MAA could play a big role. Maybe also high school � Rigorous treatment of the subject based on stochastic calculus math teachers who are very interested in � Integration of advanced, abstract theory with practical applications more advanced issues can help bridge the gap. For instance, there is the Park � Faculty dedicated to the field of mathematical finance City Mathematics Institute, the summer program where they have a high school program and a college program, and that The next program will begin on June 30, 2008. Applications accepted I think overall works pretty well. They until April 30, 2008. have some joint activities that I think are pretty good. I personally don’t see myself diving into the deep sea and the deep waters of K–12 education. Mathematical Finance Program 143 Bay State Road, Fourth Floor FOCUS: You were saying before that Boston, MA 02215 your impression is that too few MAA members participate in NSF and institute programs. An equal opportunity, affirmative action institution.

Sturmfels: And conversely, I think the NSF and the institutes could do a better Sturmfels: Yeah, I don’t necessarily have The institutes, for instance MBI at Ohio job in reaching out to the MAA commu- the ideal answer; I think that should be a State, could help find a way to facilitate nity. And in fact I just discussed this with discussion… which format works best? this. Perhaps they can bring in people, Peter March and he agrees, so I hope that Workshops could work, but maybe other give people a chance to speak about Peter and Joe Gallian will get together formats too? As a Pólya Lecturer, I’ve research results, to learn new things. I and have a chat about this. seen a lot of faculty at four-year col- don’t have the answer, but I’d like to leges interested in doing research with raise it as a question. I feel that MAA FOCUS: Is it just more participation in undergraduates to stay connected to the members are amazing and that they are a the actual programs? That means taking research community, maybe to engage in slightly underrepresented group at these time off to spend time for workshops and interdisciplinary research with faculty at institutes. that kind of thing. their college in say, biology for instance.