Chicago Workshop Highlights Opportunities in Industrial MathematicsJanuary 22, 1999
Robert Grossman of the University of Illinois at Chicago organized the workshop, at which the focus was on exciting opportunities not in academia, but in the boardrooms, offices, and factory floors of business and industry.
Barry A. Cipra
You're smart. You're educated. You're a problem solver with analytic skills. You've got a degree in mathematics. What more do you need?
Better yet, a good job.
Ideally, a career.
Traditionally, mathematicians have tended to put academia at the top of their employment wish list, often without a second choice. But as speaker after speaker pointed out at the SIAM Midwest Regional Mathematics in Industry Workshop, held October 2-3 at the University of Illinois at Chicago, some of the most exciting opportunities today lie not in academia, but in the boardrooms, offices, and factory floors of business and industry.
"There are lots of problems out there where mathematicians could make a huge impact," says Robert Grossman of the UIC mathematics department, who organized the two-day workshop. (Grossman is also director of the National Center for Data Mining at UIC, which hosted the meeting.) The participants---130 students, professors, and representatives from industry---spent the two days swapping stories about their experiences with industrial mathematics and exchanging ideas about the creation of programs to expose students to the opportunities in industry and prepare them for the special demands of nonacademic careers.
Armani & Money & Math
Alex Lipton, a former professor at UIC who is now a vice president at Bankers Trust in New York, described some of the mathematical aspects of pricing derivatives in the foreign exchange market, where trillions of dollars change hands daily. It's very dangerous to have a mispriced derivative," he warns; Wall Street is "full of very smart people" who will jump on each other's mistakes. When individual trades are measured in billions of dollars, a discrepancy as seemingly small as a hundredth of a percent translates into a tidy sum. The Black-Scholes formula and related analyses for bond pricing have become indispensable--no one today can trade (successfully, or for very long) on gut instinct.
One of the major unsolved problems, Lipton says, is the pricing of what's called an "American put": an option that can be exercised at any time (as opposed to a "European put," which can be exercised only at a prescribed future date). The underlying mathematics is a free-boundary problem for a nonlinear partial differential equation.
Wall Street has a yen, so to speak, for experts in partial and stochastic differential equations, Monte Carlo methods, and functional analysis. There's just one catch, Lipton says: "You have to learn how to wear business attire."
Paul Brown, also of UIC, agrees that a business suit can be an important element in a nonacademic career. In a talk titled "What I Did with My Summer Vacation," Brown described his recent experience getting started as a mathematical consultant. Last April, he "put on a suit for what was then the sixth time in my life" and interviewed with a small, entrepreneurial technology firm in the Chicago area. "Two weeks later, I was in the same suit in a board room in Atlanta, gathering information to plan a technology-based workflow re-engineering for a large business."
The key, Brown says, was persistence. He spent months looking for potential clients, with help from a friend who works as a headhunter. "It's important to be open to possibilities," he says. Small, entrepreneurial firms are good places to start a quest for consulting jobs, he adds. By definition they tend to be risk-takers, and their smallness often requires them to seek outside help. Also, "people like having an academic person around," Brown says. "As long as you speak their language, they're happy to deal with you."
Learning the language of business and industry is the single biggest step for mathematicians to take, speakers at the workshop stressed. "Communication skills are of the utmost importance," says Tony Evans, a consultant with McKinsey and Company, which specializes in management consulting. Problems in industry rarely come in the well-defined form that mathematicians are accustomed to. Even when there seems to be a clear-cut mathematics problem, a lot of work often goes into identifying the "real" problem. That requires not only the mathematician's familiar analytic skills, but also keen listening skills. As Steve Keeler, a mathematician in the geometry and optimization group at The Boeing Company, puts it, "We try hard not to say very much."
Solving the "real" problem as opposed to hunkering down with an elegant mathematical idealization is perhaps the greatest challenge for mathematicians considering a career in industry. Companies couldn't care less about mathematical aesthetics; their chief concern is getting answers that will improve their product lines. "If you don't impact the product, they're going to be looking for ways to get you out the door," says Philip Fleming, a mathematician at Motorola.
That doesn't rule out a place in industry for traditional, "pure" mathematicians. Fleming himself did his PhD in algebraic topology. Brown's background is in geometric group theory. Michael Benedikt of the Chicago-area branch of Lucent Technologies, who spoke in a panel discussion on hiring practices, did a PhD in logic. ("I had no credentials" for the job at Lucent, Benedikt says, crediting a summer internship for starting him on the way to the position he now holds.) David Rocke of the University of California at Davis, who spoke on collaborative opportunities within the university, began in group theory. As Brown puts it, "It's a maybe unique illusion among mathematicians that mathematics is the only thing we can do."
A growing number of schools are trying to give students a taste of industrial mathematics. At St. Olaf College, in Northfield, Minnesota, for example,the mathematics department offers an intensive, four-week "mathematics practicum" during the January interim of the school's 4-1-4 academic schedule. Steve McKelvey described the unique program at the workshop. Each fall, two faculty advisers make calls on local businesses, often relying on a "latent network of St. Olaf graduates" to find three problems for four- or five-member teams of students to work on in January. The teams spend three weeks working on the mathematics of the problems and then devote the final week to rehearsing for presentations to the problem sponsors.
"Everything is done by the students," McKelvey emphasizes. The faculty advisers "actively don't work on the problems," limiting their role instead to making sure the students don't just give up in despair. This approach, he says, gives the students a real sense of "ownership" of the projects they work on. "Failure is a genuine possibility in this course," he points out, adding that the teams invariably work hard to avoid such a fate.
Dan Maki described a similar hard-working attitude among students tackling industrial problems at Indiana University at Bloomington. "The motivation of the students is much higher" when they're working on what they think of as real problems, he says. They also derive "tremendous confidence" from the projects, often taking the reports they've written on job interviews.
Maki fondly recalls the first student project in the Indiana University program, a forecasting and scheduling problem for a credit union. The problem was to help the credit union decide, for example, how many teller positions to have open on a given day. The students did an outstanding job of analyzing a range of factors affecting such decisions, Maki says. "Better than that, it worked!"
Several schools now have graduate programs specifically geared for industrial mathematics, offering students not so much a taste of the subject as a full-course menu. Floyd Hanson described a master's program at UIC that includes a course in communications in the first year. The program, called Mathematics and Information Sciences for Industry (MISI), gets many of its projects from UIC's National Center for Data Mining. Projects have included "MediMine," aimed at building predictive models from medical data records, and the "Data Object Warehouse" for atmospheric data from NASA satellites.
Fadil Santosa and Avner Friedman described the ambitious Minnesota Center for Industrial Mathematics at the University of Minnesota, which currently has 16 students in its master's program and three students in a PhD program. A central feature of the students' experience is an internship with one of a growing number of companies not only in the Minneapolis-St. Paul region, but throughout the U.S. Among the participants are large companies, such as Honeywell, 3M, Lockheed Martin, Seagate, Ford, Medtronic, Motorola, and Lucent Technologies, as well as a growing list of smaller firms, including XOX Corporation, LORAM, and Manufacturers' Services. PhD theses are to be based on industrial projects, Friedman explains, but must be publishable in mathematics journals. It's important to stress that industrial mathematics programs don't cut corners on quality, he says: "Without strong core mathematics, mathematicians have nothing to offer."
Setting up a graduate program in industrial mathematics isn't easy, Friedman adds. "There must be at least one faculty member totally dedicated to such a program." The department must be convinced to allocate resources. And "the chairperson's full support is a must."
Threats and bribes usually work, jokes Max Gunzburger of Iowa State University, adding "I was the chair, so I was able to do that." The department now offers an applied mathematics option at the bachelor's level, and a master's program in industrial mathematics.
Jeehyun Lee, however, may wind up doing an industrial PhD at Iowa State. A student of Gunzburger's, Lee spent last summer at Lucent Technologies in Murray Hill, New Jersey, working on an optimal control problem related to flow processes in semiconductor manufacturing. The immediate summer project was to develop computer code for the numerical solution of the differential equations describing a new kind of chemical vapor deposition process. More recently, Lee has proved an existence theorem for the equations. "It may well turn out to be her thesis, or some aspect of it," Gunzburger says.
"It's really nice to have the experience in industry," says Lee, who knew before working at Lucent that she wanted to do applied mathematics, but hadn't thought about industrial math. "Now I'm thinking about both."
Barry A. Cipra is a mathematician and writer based in Northfield, Minnesota.