Excerpt: Strength in Numbers
|A new book goes behind the scences at the International Mathematical Olympiad.|
For centuries, plays, novels, and films (most recently, A
Beautiful Mind) have characterized mathematicians as misanthropic
geniuses. But Steve Olson, author of Count Down: Six Kids Vie for
Glory at the World’s Toughest Math Competition (Houghton
Mifflin), rejects that stereotype. In summer 2001, the noted journalist
and science writer (his book Mapping Human History was a
National Book Award finalist) followed six high school- age kids to the
42nd International Mathematical Olympiad, which took place that year in
Washington, D.C. Almost 500 participants from 83 countries competed,
and the members of the U.S. team, winners of an intense nationwide
selection process, struck Olson as typical teenagers—with the
exception that they were "rabidly interested in games of all sorts." He
stresses, in fact, that while the complex Olympiad problems "involve
only the mathematics that people learn in high school," they also
demand "creativity, daring, and playfulness." These problem-solvers are
"prodigies," not geniuses, he writes, although they do "share the
attributes of genius in one respect: They employ the same intellectual
tools that history’s great creators have." Fittingly,
Olson’s book often links the Olympians’ lives to
mathematicians of the past.
In January 1657, an unusual letter arrived on the desks of many of the leading mathematicians of Europe. Later referred to as "Two Mathematical Problems Posed as Insoluble to French, English, Dutch, and all Mathematicians of Europe by Monsieur deFermat, Councillor of the King in the Parlement of Toulouse," the letter challenged the mathematicians to solve two specific problems: One involved possible ways of evenly dividing a cubed number; the other, possible ways of evenly dividing a squared number. In spirit, the problems were not much different from the problem that would later become known as Fermat’s Last Theorem.
In the 17th century, personal challenges were common in mathematics. At a point when many mathematicians were still amateurs (Fermat, for example, was a lawyer and jurist), they could make their reputations by solving problems that no one else had been able to solve. Many famous scholars of the time, including Isaac Newton and René Descartes, posed and worked on challenge problems. Many kept their procedures secret to maintain an advantage over their rivals.
Steve Olson: The
Olympians are prodigies, not geniuses.
In the 18th and 19th centuries, mathematicians gradually adopted the more decorous procedure of publishing their results in books, monographs, and journals. Yet the problem-solving tradition remained strong in some parts of Europe, especially as a way for young mathematicians to develop facility. Eastern Europe, in particular, remained a hotbed of mathematical competitions. In 1894,for example, a high school teacher in Hungary named Dániel Arany began publishing a student magazine called KöMaL (an acronym for "High School Mathematics Journal" in Hungarian). Each issue presented 10 to 20 challenging problems that students were invited to solve, and Arany received hundreds of solutions each month in reply. Notcoincidentally, many of the most accomplished mathematicians of the first half of the 20th century came from eastern Europe—including many Jews, fleeing Nazi Germany, who came to the United States and made major contributions to the Allied war effort.
Since the end of World War II, problem-solving competitions as a form of mathematics education have spread around the world. But many of these competitions continue to have an Eastern European flavor. The coach of the U.S. Olympiad team in recent years is a case in point. Titu Andreescu, who in 2001 was director of the American Mathematics Competitions in Lincoln, Nebraska, is a Romanian émigré. He is a tall, stocky bear of a man with a salt-and-pepper beard and eyes so black, they seem bottomless. Andreescu’s mother was born in New York City shortly after her family emigrated from Romania. But she returned to Romania as a child, was raised there, and married a Romanian man. Born in the 1940s, Andreescu was an avid mathematician as a child and was on the Romanian Mathematics Olympiad team in 1973. But the government kept close tabs on him. Because his mother had retained her U.S. citizenship, Andreescu and his mother were viewed as possible defectors. Government officials assumed that if they ever left the country, they would not return.
By the late 1980s, Andreescu had become an assistant coach of the Romanian Olympiad team and was editor of a prestigious mathematics journal in Timisoara, Romania’s second-largest city. But he was restless. Mathematics had given him a way to ignore the numbing repression of life in a Communist country, but outside of his work, he felt trapped. The system found a slot for people and kept them in it. In a society grown rigid with dogma, there were few ways to excel.
Suddenly, in late 1989, the Communist bloc began to collapse, and Andreescu’s opportunity arrived. "My mother and I decided to leave," he says. "The government knew that I would eventuallydefect. I did."
He found a job teaching math at the Illinois Mathematics and Science Academy, a residential high school in suburban Chicago for academically advanced kids. A couple of years later, he volunteered to help coach the U.S. Olympiad team in the summers. In 1994, shortly after Andreescu became an assistant coach, the U.S. team did something that no team from any country had ever donebefore: At the Olympiad in Hong Kong, all six members of the team received perfect scores on all six problems—36 perfect solutions. "The journalists wrote about me like I was the Bela Karolyi of high school mathematics," Andreescu recalls. The next year he became head coach of the team.
Andreescu is the person who oversees the various tests that culminate in the selection of the U.S. Olympiad team. But he also hasa more specific task. Every summer, he directs the Mathematical Olympiad Summer Program, a four-week training camp for the six members of the U.S. team and a select group of other high school students who hope to make the team in future years. For kids interested in competitive mathematics, being invited to the summer program— even if you’re not on that year’s team—is a great honor.
Most summers, the program takes place inLincoln, where the American Mathematics Competitions offices are located and where the students "won’t be distracted by a big city," as Andreescu explains. But the summer before the 42nd Olympiad, the training camp was instead held at Georgetown University, a few miles up the Potomac River from the Washington Monument. For four weeks, the six Olympians and about two dozen other talented high schoolers lived in the Georgetown dorms and worked on math. Between the undergraduates who stay to take summer classes and the high school kids attending camps, a college campus can be a surprisingly busy place in the summer. Amid theaspiring basketball players, ballerinas, and thespians, the math students were fairly inconspicuous—a clump of kids wearing Mathcounts T-shirts making their way to and from the cafeteria.
The group quickly settled into a routine. Each morning and afternoon, they congregated in one of the lecture halls on campus. At precisely 9 a.m. or 1 p.m., Andreescu or one of the other instructors would stride into the room, usually comingdirectly from the photocopy machine. Andreescu sometimes delivered a mini-lecture on a particular subject— combinatorics, for example, or inversions in the plane, or an even more obscure topic. ButAndreescu is not a loquacious person, and his lectures never lasted long. Soon he would pull a sheaf of papers from his valise and pass them through the hall. These were the problems for that session.
The students were not prohibited from working together on the problems. Some preferred to solve as many as they could before seeking help on others, while other students instantly teamed up. Soon the room divided into shifting clusters of bobbing heads as students compared approaches and solutions. Eventually Andreescu began to walk up and down the rows, asking students if they were making progress. Sometimes he offered a few words of advice; sometimes he just listened, nodding his head.
After a half-hour or so, Andreescu returned to the front of the room and asked for volunteers to solve the problems. One by one, the students went to the board and sketched out their solutions. Though it would be hard to find a more competitive group of high school students, they readily praised each other’s work. "That’s nice," they’d say. "I like that." Andreescu was more sparing with his praise. "Good work," he’d say, and the student at the board would blink with surprise.
About halfway through the training camp, a camera crew from the CBS news show Sunday Morning filmed the students for a couple of days. "Just pretend we’re not here," said the producer, even though the cameraman spent the rest of the morning with his lens six inches from the students’ faces. But the kids did a pretty good job of carrying on as usual; maybe a generation raised on cable television is not flustered by the idea of their every move being videotaped.
The next day, the six team members met withthe on-air interviewer, Bob Orr. They endured with good humor the usual goofy questions: "What doesa math wizard do to relax?" "What do you think about people who look at guys like you and say, ‘Hey, these guys are nerds’?" At one point, Orr asked if they knew any math jokes that most people wouldn’t understand, and Gabriel Carroll, a high school senior from Oakland, California, offered the following story:
Two mathematicians sitting in a restaurant are arguing over whether ordinary people know anything about mathematics. The optimistic one says, "Most people know plenty of math." The pessimistic one says, "No, they don’t, people are completely ignorant." At that point, the pessimist has to go to the bathroom, so the optimist calls their waitress over to the table and says, "When my friend comes back, I’m going to ask you a question, and I want you to reply ‘One-third x cubed.’ OK?" The waitress says, "One-third x what?" And he says, "One-third x cubed."So the waitress walks away, muttering, "One-thirdx cubed, one-third x cubed." When the pessimistreturns, the optimist says, "I want to prove to you that ordinary people know mathematics." He calls the waitress over and says, "Excuse me, can you tell me the integral of x squared dx?" And she says,"One-third x cubed." Then, as she’s walking away, she calls back, "Plus a constant."
Everyone on the team laughed. "I don’t get it,"said Orr.
The Sunday Morning segment aired a few days after the conclusion of the Olympiad and was aremarkably good piece of journalism. The students came across as real human beings, not stereotypical nerds. The segment even showed some of the problems on that year’s Olympiad. Yet running beneath the narrative like an annoying hum was a constant, unstated question: What kind of person could possibly want to spend four weeks of the summer cooped up in a lecture hall studying math?
Vol. 15, Issue 6, Pages 56-57
- Reader reviews of Count Down: Six Kids Vie for Glory at the Worlds Toughest Math Competition, have been posted by ScienceBookReview.com.
- Think you know the difference between combinatorics and inversions in the plane? Visit the International Mathematical Olympiad and take a stab at some sample questions. A list of past winners of the competition is also posted.