Math-Loving Freshman a Whiz at Getting to the Root of Problems

March 22 is one day that Yale freshman Xiaosheng Mu is not likely to forget.

That morning, he solved a mathematics problem that first drew his attention two years ago and had challenged him ever since. Later, he learned he was one of the top five individual winners in the William Lowell Putnam Mathematics competition — a prestigious intercollegiate contest for U.S. and Canadian students administered by the Mathematical Association of America.

The top five individual finishers in the competition are named Putnam Fellows and receive a $2,500 cash prize. Many Putnam Fellows have gone on to become renowned mathematicians, and some have later earned the Fields Medal, known as the “Nobel Prize of Mathematics.”

When he learned of his accomplishment, Mu pounded his desk — which is exactly what he did when he solved a difficult geometry problem in the 2008 International Mathematical Olympiad (IMO), where he represented his home country of China and won a gold medal with a perfect score.

Mu recently spoke with the Yale Bulletin & Calendar about his accomplishments in mathematics. Here is what we learned.

No mistakes: Mu began showing an interest in math when he was just four years old. His parents remember him taking their bills and adding up the totals to make sure they were accurate.

When Mu was in elementary school, his father, a math tutor, encouraged him to solve mathematical problems. By the time he was in middle school, Mu began participating in math competitions in China. In high school, his aptitude for mathematics was so pronounced that Mu was allowed to focus his study almost exclusively in the field.

One of his main objectives in high school was to make the Chinese national team that would compete in the IMO.

“In China, there is a fierce competition to be selected for the national team,” Mu says. “There are basically three rounds of competition. I had to do tons of math problems to prepare for that. I was mostly just enclosed in the library preparing for those rounds.

“I didn’t make the team as a sophomore because I failed to solve a geometry question correctly,” he continues. “So in my junior year, I trained in geometry. Every week, another student and I would talk about math on the phone. What he is good at is exactly what I was poor at and vice versa, so we complemented each other.”

The young mathematician made the national team in his junior year and says all of his preparation in geometry paid off when he competed in the IMO in Madrid in the summer of 2008, because the hardest question on the test happened to be a geometry problem.

“I got very lucky,” says Mu. “The area of math that had previously led to my failure ultimately led to my success.”

Problems galore: Mu devoted much of his senior year of high school and his first semester at Yale preparing for the Putnam competition.

“In China, we don’t have the opportunity to learn advanced mathematics such as calculus and linear algebra like U.S. high school students do,” he says. “Instead, we study more elementary math in order to prepare for the college entrance exam, which tests our ability in Chinese, math, English, physics, chemistry and other general subjects. It is a more demanding test than the SAT. I was afraid I would be behind American students in calculus and linear algebra, so I focused on those areas. I did many problems from previous Putnam exams and spent most of my Thanksgiving break at Yale just doing lots of problems so I would be prepared.”

The Putnam competition, which is held the first Saturday in December, draws over 3,000 undergraduates, who can compete individually or represent their college on a team. There is only one team per college, each comprised of three members. About 24 Yale students, including a team, competed this year.

Mu is the first Yale student to be a Putnam Fellow since 1989, when two Yale students placed in the top five. (The most recent top five team finish for Yale was in 1991).

The Putnam exam consists of 12 questions, covering concepts in geometry, calculus, algebra and other areas. Competitors have three hours to complete the first half in the morning and another three hours to finish the test in the afternoon.

“It was fun for me and not at all stressful because I’ve taken so many tests,” remarks Mu. “I had to come up with solutions to each problem in no more than 10 minutes, and then spend the next 20 minutes on each writing out the proof.”

Reaching the peak: The young mathematician says he often fails when trying to explain to others the “beauty and intricacy” that he sees in math.

“I feel that challenging myself with a math problem is like climbing a mountain,” he says. “Sometimes you get stuck and you can’t find a way to climb upwards, so you go in a circular way to see if there is a way up, or you go back down to try to find another way.

“Math is essentially based on a small number of axioms,” he adds. “Its beauty lies in the fact that you can ask any mathematical question and its answer in many cases can be derived from those axioms. I have heard a quote that describes it perfectly: ‘If mathematicians ever prove something, they can proudly claim it’s proven forever.’”

Less is more: Mu intends to major in math at Yale, but says one of the reasons he chose to come here is because he also wanted to expand his horizons beyond that subject.

“I applied to several U.S. universities and finally narrowed it down to two — Yale and MIT. I chose Yale, in part, because I heard that to do well academically at MIT you have to sacrifice either friends or sleep. I didn’t want to have to make either sacrifice.”

He also felt that Yale’s diversity would make it the ideal place to learn from other people. “Even in math, I have learned more from fellow classmates and mentors than I learned from books,” Mu says.

While preparing for the Putnam competition, he also found time to participate in intramural badminton and billiards, as well as to sing in the Chinese a cappella group Pentatonic.

This summer, Mu will go back to China, where he will be an intern at a financial company, and he looks forward to seeing the 2010 World Expo in his hometown of Shanghai.

His long-term goals include working in finance and later earning a graduate degree in mathematics, sometime in his late 30s or early 40s.

“I may not achieve anything great in mathematics, but I do want to do academic work in the field,” he says. “I see beauty in art, literature, history and other subjects, but I haven’t found anything that is as appealing to me as math.”

— By Susan Gonzalez