By Alex Zhai

Gargoyle assistant editor

Posted Friday, Sept. 22, 2006, The OG, features

SLOVENIA IS A small country of only 2 million residents that lies just east of Italy. Europeans occasionally travel there for tourism, but students from 90 different countries visited Slovenia this summer for a different reason: to participate in the 47th International Mathematical Olympiad.

As one of those students, getting to the IMO had long been a goal for me. But having reached this goal, I came to realize that it need not be the end of my endeavors in mathematics.

Six high school students represent each country at the IMO, which consists of a six-question test administered over two days. A long process is used to select the students representing the U.S, beginning with a series of tests. After scoring sufficiently well on these exams, most importantly the national Olympiad, I flew to the Olympiad training camp in Lincoln, Neb., where the top scorers took one last test in early June for the final selection of the six members of the U.S. team.

By the end of the four-week training camp, the IMO team members got to know each other well. After working on difficult problems throughout the camp, we felt ready for the IMO.

The problems of the IMO require proofs and are scored out of seven points to allow for partial credit. Students scoring in the top 12th receive gold medals, those in the next sixth receive silver medals, and those in the next fourth receive bronze medals.

When we arrived with several other teams at Ljubljana, the capital city, we were at first reserved. Teams generally stayed together, still getting accustomed to their unfamiliar surroundings. But in the afternoon, the Canadian team started up a soccer game. Within an hour or two, students from seven or eight teams had joined, all loosening up their minds together with a physical sport before the test.

Staying in a youth hostel without air conditioning, our team was still suffering from jet lag by the first day of testing. Nonetheless, when I walked over to the testing room that morning, the adrenaline from the impending competition kept me sufficiently awake.

I entered the room to discover that it was a gymnasium, filled with an array of desks about two meters apart, each holding an assortment of snacks, a packet containing the day's test materials, and several cards we were required to use when asking for water, more paper, or to be escorted to the bathroom.

A tense and awkward silence hung over the gymnasium as we sat at our desks, waiting for the signal to start. I hoped that my anticipation wouldn't prematurely wear me out. Suddenly, a shrill whistle pierced the air, and all at once, nearly 500 students opened their packets to begin working on the first day of the IMO.

As soon as I saw the problems, I knew that they would be tough for the U.S. team. We were good at geometry, but the geometry problem was the easiest one, and we were expected to solve it anyway.

The second problem asked for the largest possible number of a certain type of triangle after dividing a polygon up into triangles, and the last problem was an algebraic inequality. At the training camp, none of us had fared particularly well with either of those two types of problems.

I finished the geometry problem easily, and the second problem turned out to be easier than expected. I struggled with the last problem, however, finding little of interest. It was clear that I had not found the key step that was the crux of the problem.

Before I knew it, my thinking was interrupted by another sharp whistle; 30 minutes remained. Knowing that I was unlikely to come up with any useful new insights, I started to look through my work, hoping to make better use of an old idea.

When the proctor blew the final whistle, we all placed our papers, including scratch work, back into the packets they had given us. Our team leader and deputy leader would look through our work, hoping to find good ideas to present to the judges that could be worth partial credit.

As we walked out of the gymnasium, the crowd of students quickly clustered into their teams to discuss the test. As it turned out, everyone on the U.S. team solved the first two problems, but no one seemed to have made significant progress on the third.

The next day, the routine was the same, and again the problems were not favorable. I thought I had solved problems four and six, but soon afterwards, a member of the Canadian team, which stayed on our floor at the hostel, noticed a flaw in my solution to number six.

Following some discussion, the general consensus among the contestants was that the cutoff for gold medals would be around 28 points. The amount of partial credit I received on problem six, as well as whether I lost points for two small mistakes, would determine whether I could pass this cutoff or not.

For the next three days, we went on various excursions to see Slovenia, which is a hilly, heavily forested country. The places we visited, including a three-mile-long cave, were a welcome distraction from thinking about the test results, but the uncertainty lingered in the back of my mind.

At last, on the day before the closing ceremony, we obtained the final results. I received three points on the last problem, and I would get a silver medal. (The U.S. team placed fifth overall; China won the title.)

In many ways, the IMO felt like the end of a journey. After all, it was the culmination of so many levels of testing, and it had been the focus of four weeks of intensive training in addition to months of casual study.

At the banquet after the closing ceremony, however, our team leader, Zuming Feng, had a little talk with us. To the three seniors, he reminded them that reaching the IMO was a great accomplishment.

But at the same time, he told them that in a few years, he didn't want to see it at the top of their résumés — he expected to see them continue with the abilities they demonstrated in reaching the IMO to do other, bigger things. Although the IMO may be a milestone, it is not the end.