In the United States the IMO process starts in December with a test taken by over 250,000 of the best mathematics students in America’s high schools. In April 2006, 440 of these students qualified to take the United States of America Mathematical Olympiad (USAMO) test. We meet six of them on April 19, 2006 as they wrestle with the very demanding problems on the USAMO during the second day of testing administered at the Harker School in San Jose, California.
Through interviews with parents, teachers, and the students, we learn why these teens are so talented in math, and what drives them to compete in ever more rigorous tests against others who are equally good or better. Although there are early hints about who will make it, and who has to wait until next year, we don’t know if any of the six taking the test at Harker will go on to compete in the Team Selection Test (TST) that decides the final makeup of the U.S. IMO team.
Several of the best math students in the country study with U.S. team leader Zuming Feng at Phillips Exeter Academy in New Hampshire. Dr. Feng has handpicked his students over the years, and develops their skills at solving competition problems through frequent exercises. We see him at work at one of the seminars. Three of the students in his class are among the 12 to win the 2006 USAMO awards.
The top twelve receive the USAMO awards at the State Department a few weeks later. By now we have met several students and their parents, learning why they are passionate about mathematics, and how they have climbed through the increasingly difficult series of tests to the top.
Most of the USAMO winners take the Team Selection Test (TST) to see who will make the U. S. team that will go to Slovenia to compete at the IMO. Another two-day event, the TST is given at the headquarters of American Mathematics Competitions (AMC) on the University of Nebraska campus at Lincoln.
The graders, former math Olympians, immediately evaluate the answers. The names of the six IMO team members are announced as soon as the test is graded.
Students who take the TST end up staying for Lincoln’s intense three-week Math Olympiad Summer Program (MOP). With former Olympians as teachers and graders, MOP is the closest the students ever get to formal training before the IMO. The six IMO team members are placed in an advanced group called “black MOP.” Even after three classes a day, the students spend almost every spare minute working on problems, alone and together. For many of them, this is the first time they’ve felt part of a community, making friends who are truly their equals.
The MOSP program at Lincoln is anything but a haven for lazy students. With up to three classes a day, the students spend almost every spare minute working on problems, alone and together.
The highest scoring students at the USAMO, Brian Lawrence and Sherry Gong, have opted to pursue summer research programs instead of competing this year. Not one member of the 2006 IMO team has been on a team before. Team leader Zuming Feng is wary of handicapping his team. He thinks a third place finish behind Russia and China would be a stellar performance for such a young and inexperienced team. While several team members are veterans of MOP, Zuming is intrigued by Zeb Brady, who came out of nowhere with scores high enough to make the team. “He has never been to MOP. I always hope that one of my six students, one or two are like this,” he says.
The International Mathematical Olympiad (IMO)
The American team arrives in Ljubljana, Slovenia on July 10 in the middle of the night. With only one day before the first day of testing, they have little time to settle in and recover from travel and jet lag.
At the IMO opening ceremony on July 11 the students get a sense of scale as teams of contestants from 90 participating countries parade before the audience.
Their team leaders, who have spent the last two days selecting the six problems for this year’s contest, are then sequestered at a resort on the Adriatic coast 90 miles away so that none of them can leak the questions or answers to their students during the contest days.
The key to a successful IMO lies in the problems that are selected—how original and imaginative they are, and how challenging they are for the students. Selecting the problems involves finding some that will be difficult for students at the very highest level, and others that are within the range of students who will score low. Problem selection is a two-day process that takes place in the host country immediately before the students arrive. See the six 2006 IMO questions here.
The IMO Test
July 12 and 13, 2006
The test is administered in four large halls. Contestants are given four and a half hours to work on three problems each day. By now they are used to the structure of these tests, but there is nothing they can do to prepare for the questions themselves.
Following each day of testing, Alex Saltman, the U. S. Deputy Team Leader, goes over the questions with his students. They discuss how each student constructed his answers, and find the flaws.
Saltman collects information that will help him and team leader Zuming Feng fashion arguments that might help raise a student’s score if there is a disagreement with the Slovenian coordinators during the coming days.
July 14 and 15, 2006
Each of the six problems is assigned different coordinators. Coordinators and country team leaders must agree on a score between 0 and 7 for each student’s work on every problem. Coordination of problem six requires three sessions before the U. S. team leaders and coordinators agree on a score. These discussions are among the most intense in the film.
The students have a good idea of how many points they will get even before the coordination is finished. What they don’t know is where the medal cutoffs will be between honorable mention, bronze, silver, and gold. It is the last question the IMO jury decides once coordination is completed and the scores are in.
The Closing Ceremony
July 17, 2006
Three students attain the highest possible score, a perfect 42 at the 2006 IMO. One of them is Zhiyu Liu from China. When asked why, he says, “I’m very interested in mathematics and I study mathematics using my heart.”
China and Russia are first and second; Korea and Germany, third and fourth. Zeb Brady and Arnav Tripathy win gold medals for the United States. Their four teammates go home with silver, and the U.S. finishes in fifth place.
The exhilaration of meeting others just as passionate about mathematics as they are is often the most rewarding part for students who sometimes feel they are the only ones with the special gift of being good at math. The most important and lasting impact of the competition is to provide these students with a worldwide community of peers.
For Zach Abel, Yi Sun, and Ryan Ko, 2006 was the last year of high school. Yi and Zach went on to be roommates during their freshman year at Harvard. Ryan Ko went into his freshman year at Stanford.
Alex Zhai was considered the strongest member of the 2006 U.S. team. When he narrowly missed getting a gold medal his disappointment was palpable. But being a sophomore he had two more chances.
In 2007 Alex Zhai got on the U.S. team again, and went to Hanoi, more mature, better trained, and ready to win.
Sherry Gong had competed for Puerto Rico in a previous IMO, but in 2006, after winning the USAMO, she opted out to do research. In 2007 she was a USAMO winner again, and this time, joined the U.S. team, along with Alex Zhai, Arnav Tripathy, Brian Lawrence, Tedrick Leung, and Eric Larson.
The IMO leaves students with the sense that they have gone through a major rite of passage. Just participating in an IMO, they have accomplished what only a very few individuals in the world will ever achieve. The series of tests in the United States leading up to it, and the IMO itself were all just a kind of incubator for the great minds they will become. And these students have a very mature understanding of what has happened to them. Once past the IMO experience, they are eager to move on and explore the great unknowns and open questions of mathematics, and to add their contributions.
I like everything about mathematics. I appreciate the elegance of proofs, especially particularly elegant ones, but I also appreciate proofs that are not generally considered very elegant. Just to lay something out by brute force, I feel like just the sheer power of it is also really beautiful.
— Sherry Gong