Count Down Six Kids Vie for Glory | at the World's TOUGHEST MATH COMPETITION STEVE OLSON author of MAPPING HUMAN HISTORY, National Book Award finalist $Z4- 00 ACH SUMMER SIX MATH WHIZZES selected from nearly a half million EAmerican teens compete against the world's best problem solvers at the Interna• tional Mathematical Olympiad. Steve Olson, whose Mapping Human History was a Na• tional Book Award finalist, follows the members of a U.S. team from their intense tryouts to the Olympiad's nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical. In the process he provides fascinating insights into the creative process, human intelligence and learning, and the nature of genius. Brilliant, but defying all the math-nerd stereotypes, these athletes of the mind want to excel at whatever piques their cu• riosity, and they are curious about almost everything — music, games, politics, sports, literature. One team member is ardent about water polo and creative writing. An• other plays four musical instruments. For fun and entertainment during breaks, the Olympians invent games of mind-boggling difficulty. Though driven by the glory of winning this ultimate math contest, in many ways these kids are not so different from other teenagers, finding pure joy in indulging their personal passions. Beyond the Olympiad, Steve Olson sheds light on such questions as why Americans feel so queasy about math, why so few girls compete in the subject, and whether or not talent is innate. Inside the cavernous gym where the competition takes place, Count Down reveals a fascinating subculture and its engaging, driven inhabitants. 0404 count down BOOKS BY STEVE OLSON Mapping Human History Count Down to u n t dow n Six Kids Vie for Glory at the World's Toughest Math Competition STEVE OLSON Houghton Mifflin Company BOSTON N EW YORK FIRST MARINER BOOKS EDITION IOO5 Copyright © 2004 by Steve Olson All rights reserved For information about permission to reproduce selections from this book, write to Permissions, Houghton Mifflin Company, 215 Park Avenue South, New York, New York 10003. Visit our Web site: www.houghtonmifflinbooks.com. Library of Congress Cataloging-in-Publication Data Olson, Steve, date. Count down : six kids vie for glory at the world's toughest math competition / Steve Olson p. cm. Includes index. ISBN 0-618-25141-3 ISBN 0-618-56212-5 (pbk.) 1. International Mathematical Olympiad. 2. Mathematics—Competitions. I. Title. QA20.3.O47 2004 510'.79—dc22 2003056897 Printed in the United States of America MP 10 98765432 MATHCOUNTS® is a registered trademark of the MATHCOUNTS Foundation, 1420 King St., Alexandria, VA 22314. FOR DIANE OLSON contents Introduction • i PART i • THE PATH TO THE OLYMPIAD 1 Inspiration • 15 2 Direction • 38 PART 11 • ATTRIBUTES 3 Insight • 59 4 Competitiveness • 80 5 Talent • 98 6 INTERLUDE: An Afternoon to Rest • 122 7 Creativity • 126 8 Breadth • 149 9 A Sense of Wonder • 167 PART 111 • RESULTS 10 Triumph • 187 11 Epilogue • 199 Appendix: Solutions and Commentaries • 201 Sources • 211 Acknowledgments • 227 Index • 231 count down introduction On July 4, 1974, a bus carrying eight U.S. high school students wound through the narrow medieval streets of Erfurt, East Ger• many. The students were all a bit nervous. In those days of heightened Cold War tensions, few Americans ventured beyond the Iron Curtain. Just that morning, after an all-night flight from New York City, the students had endured a brusque round of questioning by the East German border police. As they stepped from the bus in the center of Erfurt, beneath the spires of the ca• thedral where Martin Luther preached his first sermons, they felt both isolated and highly visible. They were nervous for another reason. These high school ju• niors and seniors were the first team from the United States ever to compete in an International Mathematical Olympiad. In 1974 the Olympiad was already fifteen years old; the first one had been held in 1959 in Bucharest, Romania. But throughout the 1960s the United States had been reluctant to field an Olympiad team. The Olympiad is a competition for individuals in which gold, sil• ver, and bronze medals are awarded. But unofficially the teams always have added their individual scores and compared them• selves country against country. In this informal contest the Olympiad had been dominated by teams from the Soviet Union and eastern Europe. Even as more teams from western Europe began to compete — Finland in 1965 (finishing last), Great Brit• ain, Sweden, Italy, and France (also finishing last) in 1967 — the 2 introduction U.S. mathematics community had no desire to pit America's best high school students against the world's best. "A lot of people were dead set against it," says Murray Klamkin, a renowned mathematical problem writer who coached the U.S. team from 1975 to 1984. "They thought a U.S. team would be crushed by all those Communist countries." In 1971 the mathematician Nura Turner, from the State Uni• versity of New York at Albany, wrote an article that began to change people's minds. She pointed out that several state-level competitions, established mostly since the 1950s, had laid the groundwork for American participation at the international level. She admitted that a U.S. team might be humiliated in its ini• tial attempts but argued that Americans were tough enough to bounce back. "We certainly must possess here in the USA the strength of character," she wrote, "to face defeat and the capabil• ity and courage to then plunge into systematic hard training to compete again with the desire to strive for a better showing." In 1974 the major U.S. mathematical organizations finally agreed to send a team. Two years earlier the Mathematical Asso• ciation of America had instituted a national exam designed to identify the best high school mathematicians in the country. In the spring of 1974 the association named the top eight finishers on the exam as the members of the U.S. Olympiad team. Eric Lander, who is now one of the world's preeminent ge• neticists and the director of the Broad Institute of Harvard Uni• versity and Massachusetts Institute of Technology, was a mem• ber of the team that first year. It was his senior year at Stuyvesant High School in Manhattan, and Lander was captain of the school's math team. "Math team was great," he says. "About thirty kids met each morning for an hour before school in a fifth- floor room of Stuyvesant High School, and the captain of the team was responsible for running the session. This was before you had databases full of math problems, so the captain of the math team, upon his ascension to office, came into possession of introduction 3 what we called 'the shopping bag.' It contained mimeographed sheets of problems and strips of problems and records of the city math contests for a long time. So the captain of the team would pull problems out of the bag and be responsible for leading the group." When most people think about math competitions, they probably envision a roomful of kids struggling to perform com• plex 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 ex• tended 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 com• petition is more like a game than a test — a game played with the mind. The structure of an International Mathematical Olympiad reflects the nature of the problems. The size of the teams has changed over time. In the early years each team had eight mem• bers; since 1983 they have had six. But the format has stayed the same. On the first day of the competition all of the Olympians re• ceive a sheet of paper containing three problems, and each com• petitor, 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. But the competition doesn't begin when the competitors ar• rive in the Olympiad city, because the assembled team coaches first have to decide which problems will be on the exam. In Erfurt the teams had four days to tour the city and get to know one an• other. "It was fascinating — the single team we most resembled and got along with were the Russians," says Lander. "So we hung out with the Russians a lot and got into all sorts of mischief. 4 introduction We were in East Germany, and the Russians figured at that point that they owned East Germany, so they weren't going to get in trouble. I remember very well going up to the top of the dormi• tory at the school where we were staying, and the Americans and Russians throwing water balloons down on the street. The Rus• sians might not do it back home, but they could do it in East Ger• many." On July 8 the eighteen teams competing in the Sixteenth In• ternational Mathematical Olympiad gathered at a local univer• sity to take the exam. All the worries about the U.S. team's abili• ties had been for naught. Lander and his teammates finished second — just a few points behind the Soviet Union. V This book is first and foremost the story of the Forty-second In• ternational Mathematical Olympiad, which took place in 2001 on the campus of George Mason University in Fairfax, Virginia, right outside Washington, D.C.