American (Mathematicians) in Paris

Study abroad historically has catered to the liberal arts undergrad, immersed in art and history and language, not graduate students in mathematics.

But that's not the way it should be, according to the organizers behind a new program that will send graduate students from Brown University and a campus of the University of Paris (VI) back and forth across the Atlantic to learn how approaches to mathematics problems can vary depending on the research environment and even the national culture. Unlike other graduate courses, the partnership between the two highly ranked applied math programs (and their pure math counterparts) encourages students to navigate between two distinct academic cultures instead of treating the community of scholars as a totally cohesive, global whole that shares similar methodologies and approaches.

"We wanted to teach the students that although we might be doing similar things, we might be addressing the problems in very different ways. It’s very beneficial to know the different cultures, even within the same topic," said Jan Hesthaven, a professor of applied math at Brown who maintains ties with the campus in Paris at the Université Pierre et Marie Curie, and travels there often.

The joint program, between Brown's applied and pure math departments and the various math departments at Paris VI, will allow Ph.D. students from either university to graduate with a diploma that cites the other institution, where they will be required to spend at least three semesters, or 18 months, out of up to six years of study.

What students will likely discover, the professors spearheading the program suggest, is that the conventional wisdom about American culture, as opposed to the European outlook it differentiated itself from, has some truth to it -- especially when it comes to that most American of approaches, pragmatism.

Hesthaven, who is Danish and studied in Europe before coming to teach in the U.S., called the American approach more "problem-focused." "If you’re cutting some corners now and then, that’s OK to begin with as long as you get the problem solved," at least until it can be revisited, he suggested.

"European culture is the complement of that -- you do it right the first time, and if it takes a very long time, then so be it. You haven’t solved the problem until you do it right," he continued. "Both of them have their own strengths, but ultimately I think the American culture is a little bit more pragmatic. And I think it’s very important for the students to see both of them."

Yvon Maday has experienced the advantages of both approaches first-hand. Maday, the chairman of the applied-math Laboratoire Jacques Louis Lions at Paris VI and a visiting professor at Brown, emphasizes that math -- especially the applied kind -- is a collaborative venture by definition. Since such problems require a broad knowledge of the discipline to which the analytical approach is being applied, working with others within the field as well as in unrelated areas of study is key.

At the Massachusetts Institute of Technology, where he taught for a time after receiving his Ph.D., Maday collaborated with a student working in the mechanical engineering department. That collaboration allowed him to make use of expensive equipment that allowed him to test and implement a solution that until then he'd only worked out on paper.

"The point is that when we work in our field, to try to make numerical simulations, to mimic what exists in real life ... you have to invent new algorithms," Maday explained. "And the possibility to implement this directly and very rapidly, the answer that the computer gives makes you think completely differently." So rather than work out a solution completely before testing it in simulations, he was able to continually tailor his approach by testing it using MIT's equipment. "For this particular collaboration, there was a combination of the pure math side and the part that was more close to the implementation and to the machine that was from this side of the Atlantic Ocean."

With the joint program, it is precisely this kind of cooperation between students who are used to differing approaches to common problems that Maday and Hesthaven hope to encourage. But they won't rely solely on traditional (and decidedly low-tech) face-to-face interactions. The professors plan on organizing regular trans-Atlantic videoconferences so that Ph.D. students can share their work and learn from each other's research.

Maday, for instance, said he still works with colleagues he originally met as a graduate student. By broadening students' scope, they would theoretically be prepared for a wider range of problems down the line -- in either language. (The courses in Paris are taught in French, except for possibly a few special recitation courses offered in English. Students at Brown will have to complete intensive French before traveling abroad, if they aren't proficient already.)

The program will begin officially in the fall, although the two universities have historically had ties for years, with professors bringing students from one institution to another to present research and meet with colleagues. But as is the case with most formalized study-abroad programs, cost will become an issue for some students.

"It's expensive to live here," admitted Hesthaven from Paris, where he was on one of his many research visits. Because of that fact -- the sources of the funding have not entirely been secured at this point -- and the special focus of the program, he acknowledged that not every graduate student studying math is going to want to spend part of their time abroad. International students, specifically, he suggested, might not find it convenient to relocate to a third country after coming to the States to study.

Still, the program's organizers think it's only the beginning for cross-cultural exchanges in an increasingly globalized and educated world.

"General reaching-out to other institutions between countries is really, really important, and there’s bound to be more of it. I’m really excited about this because I think it’s a model for something that I think we will see much more of in the future," Hesthaven said.