Fields medalist stresses intl experience

Wang Hong, who last month became one of the first two Chinese nationals to receive the Fields Medal — often referred to as the "Nobel Prize" of mathematics — believes young mathematicians should embrace opportunities to study and work in different countries, a practice she says is widely encouraged in China, France and the United States.

"Moving to different cities and schools is a very common practice, and people generally believe it is good for one's growth," Wang said in an interview with Peking University's School of Mathematical Sciences.

The 35-year-old mathematician, a tenured professor at the Institut des Hautes Etudes Scientifiques, or IHES, in France, and a Silver Professor at New York University's Courant Institute of Mathematical Sciences, has experienced such moves firsthand.

Looking back on her time at Peking University, where she transferred into the mathematics department, Wang recalled that students typically built a solid mathematical foundation while also getting an early start on graduate-level coursework.

She also emphasized the collaborative learning atmosphere. Many students were keen on research, often discussing which textbooks to read outside class and organizing seminars together. That peer support, she said, helped her develop good study habits that later proved invaluable.

Wang later pursued a one-year master's program at Universite Paris-Sud, where she took a course on harmonic analysis taught by Pascal Auscher. She was struck by the lecturer's deep command of the subject — he never used notes and wrote fluently on the board. But what left the deepest impression were the tutorial sessions.

She also noted that although only a handful of students at her French school pursued pure mathematics — about five or six out of 500 — professors were very willing to engage with those who did.

When Wang moved to the Massachusetts Institute of Technology for her PhD, coursework took a back seat. The most important part, she said, was conducting research with her adviser.

Her adviser, Larry Guth, had a profound influence on her. During their meetings, she had to anticipate every possible question he might ask and prepare answers in advance — a discipline that has shaped how she communicates with collaborators to this day.

Guth also gave each of his doctoral students a book upon graduation. For Wang, it was a French book titled School Blues, an educational essay about a former struggling student who became a teacher. She found it deeply meaningful.

Wang acknowledged that struggling with difficult problems for long periods is part of every mathematician's life. Her advice is to work on smaller problems with collaborators and write them up well when stuck on a big problem. Even modest contributions can be useful and help build momentum.

She compared her approach to solving a large problem to piecing together a puzzle. Each piece comes from working out examples and special cases. Once you have thought about a problem long enough, you know where the real difficulties lie.

Wang said China now has many outstanding professors and a strong research environment, and encouraged students to make decisions about studying abroad based on the opportunities available to them.

For those pursuing mathematics, her parting advice was simple: "Follow your own pace and work on the problems you love."

zoushuo@chinadaily.com.cn