Solve for 'f' and your country gets the gold

No svelte gymnasts? No decathlon specialists with muscles like rock and 100 -watt miles? Not even a flaming torch? What sort of Olympics is this, anyway? The bidding for TV rights to the International Mathematical Olympiad, held last week in Washington, was not spirited. After all, it is difficult to provide color commentary on calculus.

But for teams of high school mathematicians from 26 countries, this was it: the Big One, the chance to battle head to head with the best whiz kids in the world.

This year the United States won, capturing the gold for the second time. West Germany was second, and the United Kingdom third. Four US students rated perfect scores.

"These students like to compete," says Dr. Samuel Greitzer, a retired math professor from Rutgers and chief organizer of the Olympiad. "They like this as much as any kid likes soccer, or basketball, or baseball."

Milling with coaches, competitors, and translators, Georgetown University's Healey Hall began to look like a United Nations for minors. For two days the students were locked in classrooms, factoring and figuring subsets for all they were worth. Allowed to ask questions for the first half-hour, an occasional "mathlete" would burst into the coaches' room with such obvious queries as "is P to be constructed, that is Euclidean or otherwise, or merely described?"

And when the shouting was over, and their coaches were off grading the papers , how did it feel? Were they drained from the effort, like marathon runners after their 26th mile?

"The first day was somewhat easier than we expected," said Jeremy Primer of Maplewood, N.J., a member of the US team. "The second day was even easier."

Jeremy sounded aggrieved, like a worldclass pole vaulter asked to clear a picket fence. His teammates concurred, as did young mathematicians from other countries.

"The second round test in England was harder than this," said Imre Leader of london.

The six questions on the test had been chosen by a conference of team leaders , held before the competition, and then translated into 18 languages. The coaches admitted in retrospect that they should have been tougher. But it is fair to say most of the world would find it difficult to solve: "The function f(x,y) satisfies: 1. f(0,y) equals y plus 1; 2. f(x plus 1, 0) equals f(x,1); 3. f(x plus 1, y plus 1) equals f(x, f(x plus 1,y)); for all nonnegative integers x ,y. Determine f."

"Well, you see, that's an unimaginably large number," said Ian Jackson, a member of the English team. "As opposed to an imaginably large one."

The first IMO was held in Romania in 1959. At the outset, most participants were Eastern European countries, where a young math whiz occupies a social niche reached in US schools only by quarterbacks and those who can catch a Frisbee with their teeth.

Ostensibly the Math Olympiad is an individual competition, but it is imposisible to prevent the coaches from ranking national scores. Nine of the first 20 IMOs were won by the Soviet Union. Six were captured by Hungary, with most of the rest falling to other Eastern European nations.

A US team first competed in 1974, capturing second place in the unofficial national rankings -- even though American math education is spotty by European standards. In 1977, the US walked off with the gold. This year's IMO is the first held in the Western Hemisphere.

Teams are assembled through national Olympiads. The US team, for instance, is made up of the top eight finishers from competitions involving more than 450, 000 students.

"I consider these students a natural resource rarer than uranium," said Dr. Greitzer.

Like all good Olympic athletes, the American team then went into training, isolating themselves in the US Military Academy at West Point and exercising their minds with four hours of class a day.

"The natural condition is important," said Luis Davidson, the Cuban coach, but you have to have training."

But not all countries approached the Olympiad as if they were preparing for the giant slalom. The English team, one of the most respected in the contest, met each other for the first time at the airport.

During the four-day wait between the end of the contest and the official awards ceremonies, contestants were regaled with organized tours of the nation's capital.

"It seems as though this competition is just designed to be nice," said Steve Montgomery-Smith of Petersborough, England, commenting on the easy problems and palatial reception.

"I enjoy going to the Mall. I can't get any Americans to go with me," complained Jeremy Primer of the US team.

Jeremy, 16, will go to Princeton this fall.