Posted Monday, June 19, 2006, The OG, news

Uni High rising junior Alex Zhai and five other students have been selected to compete for the United States next month at the 47th International Mathematical Olympiad in Slovenia. Zhai and his teammates were chosen after a final round of testing at the Mathematical Association of America's Mathematical Olympiad Summer Program, held at the University of Nebraska in Lincoln.

Zhai's teammates are:

• Zachary Abel, a 2006 graduate of Greenhill School, Addison, Texas;
• Zarathustra Brady, a rising senior at Magnolia Science Academy, Reseda, Calif.;
• Ryan Ko, a 2006 graduate of Phillips Exeter Academy, Exeter, N.H.;
• Yi Sun, a 2006 graduate of The Harker School, San Jose, Calif.;
• Arnav Tripathy, a rising senior at East Chapel Hill High School, Chapel Hill, N.C.

Zuming Feng, who teaches at Phillips Exeter, is coach.

The U.S. team will arrive in Ljubljana, Slovenia, on July 10. An opening ceremony involving almost 500 students from 90 countries will be held the next day.

The competiton itself will take place July 12 and 13. Three days of sightseeing and group activities will follow as the judges score the exams.

The Olympiad will conclude with a ceremony on July 17, and students will return to their home countries the next day. (Click here for the official IMO program.)

To be selected for the U.S. team, Zhai had to work his way through an elaborate series of math competitions sponsored by the MAA, beginning in late January with the American Mathematics Contest 12, a 25-question, 75-minute multiple-choice exam.

Students who scored 100 or more out of a possible 150 were invited to participate in the next stage, the American Invitational Mathematics Examination, a 15-question, three-hour exam given in March.

Zhai excelled in both exams, earning an invitation to the third stage, the United States of America Mathematical Olympiad. Only 431 students advanced to the USAMO, a six-question, nine-hour essay/proof exam spread over two days in April. The exam followed the same format used in the International Mathematical Olympiad, placing a premium on creative thinking rather than rote knowledge. Zhai, who was participating in his third USAMO, earned the second-highest score in the country, 41 out of 42 points.

But that wasn't enough to qualify him for the U.S. team. He and 11 other top USAMO scorers had to take one more six-question, two-day exam, this time given in early June at the MAA's four-week Mathematical Olympiad Summer Program. MOSP is offered by invitation to 60 of the nation's most promising math students. Zhai is about midway through the program, which began on June 4. He took part in last year's MOSP, but this is the first time he has been selected for U.S. IMO team.

The International Mathematical Olympiad began in 1959; the United States has participated since 1974, when it debuted with a second-place finish. The U.S. has traditionally done well, often finishing in the top three. (Click here for U.S. results dating back to 1974.)

Team members work individually on three problems per day, and they can receive a gold, silver, or bronze medal for their answers. The best U.S. performance came in 1994, when all six members won gold medals and the team placed first in the world. Last year's team won four gold medals and two silvers to finish second behind China. The 2005 top 10, in order, were China, the U.S., Russia, Iran, Korea, Romania, Taiwan, Japan, Hungary, and Ukraine (the latter two were tied).

What will Zhai and his teammates, none of whom have participated in an IMO, encounter when the contest begins? Science writer Steve Olson chronicled the 2001 IMO in a book titled “Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition.” Here's how he describes it:

“On the first day of the competition all of the Olympians receive a sheet of paper containing three problems, and each competitor, working individually, has four and a half hours to make as much progress on the problems as he or she can. The next day they have the same amount of time to solve three additional problems.”

Click here for an archive of all the IMO problems given from 1959 to 2003.

The key to doing well on these problems, as Olson points out, lies in fusing creativity with fundamental mathematical knowledge:

“When most people think about math competitions, they probably envision a roomful of kids struggling to perform calculations faster than the next person. But most of the problems in high-level competitions have very little to do with calculations. Solving these problems requires a sophisticated grasp of mathematical ideas, so that familiar concepts can be extended in new directions. The mathematical procedures everyone learns in school aren't enough. Becoming an excellent problem solver demands creativity, daring, and playfulness. A math competition is more like a game than a test — a game played with the mind.”

If you missed our previous coverage of Zhai's “Road to Slovenia,” here are some links:

• AMC results
• AIME results
• USAMO results
• Akamai Foundation scholarship win