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Count Down: The Race for Beautiful Solutions at the International Mathematical Olympiad Paperback – July 6, 2005

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Editorial Reviews

About the Author

Steve Olson's Mapping Human History was a National Book Award finalist and won the Science-in-Society Award from the National Association of Science Writers. Olson has also written for the Atlantic Monthly, Scientific American, and Science. He lives in Bethesda, Maryland, where he coaches the math team at a public middle school.

Excerpt. © Reprinted by permission. All rights reserved.


On July 4, 1974, a bus carrying eight U.S. high school students wound through the narrow medieval streets of Erfurt, East Germany.
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 out of the bus in the center of Erfurt, beneath the spires of the cathedral where Martin Luther preached his first sermons, they felt both isolated and highly visible.

They were nervous for another reason. These high school juniors 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, silver, and bronze medals are awarded. But unofficially the teams always have added their individual scores and compared themselves 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 Britain, Sweden, Italy, and France (also finishing last) in 1967 — the 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 former Olympiad coach who now lives in Edmonton, Canada. “They thought a U.S. team would be crushed by all those Communist countries.”

In 1971 the mathematician Nura Turner, from the State University 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 initial 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 capability 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 Association 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 geneticists and the director of the Broad Institute of Harvard University and Massachusetts Institute of Technology, was a member 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 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 complex 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.

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 members; since 1983 they have had six. But the format has stayed the same. On the first day of the competition all of the Olympians reeceive 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.

But the competition doesn’t begin when the competitors arrive 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 five days to tour the city and get to know one another.
“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.
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 dormitory at the school where we were staying, and the Americans and Russians throwing water balloons down on the street. The Russians might not do it back home, but they could do it in East Germany.”

On July 8 the eighteen teams competing in the Sixteenth International Mathematical Olympiad gathered at a local university to take the exam. All the worries about the U.S. team’s abilities had been for naught. Lander and his teammates finished second — just a few points behind the Soviet Union.
_ This book is first and foremost the story of the Forty-second International Mathematical Olympiad, which took place in 2001 on the campus of George Mason University in Fairfax, Virginia, right outside Washington, D.C. The event has grown substantially since 1974. Nearly 500 kids from eighty-three countries competed in the Forty-second Olympiad, compared with about 125 in 1974 (and compared to the 150 or so who competed in 1981, the only previous Olympiad held in the United States).

The Soviet team has splintered into teams from Russia, Latvia, Kazakhstan, and other former republics. Teams from South America and Africa — Argentina, Brazil, Colombia, Paraguay, Peru, Uruguay, Venezuela, Morocco, Tunisia, and South Africa — now compete. So do teams from East Asian countries such as Macau, Hong Kong, and the Philippines.

As one might expect, the competitors at the Forty-second Olympiad had their cultural differences, most notably the more than fifty languages that were spoken. But in general the Olympians were remarkably compatible. Most knew at least a little English, since English has become the language in which most of the world’s higher-level mathematics is conducted. A soccer game immediately sprang up in the courtyard of the dormitory complex where they were staying and continued on and off for the duration of the event. All of the competitors could share CDs and hand-held video games, compare national qualifying exams, and lament the poor quality of the food offered in the college cafeteria.

Into this talkative, energetic, competitive mass of young mathematicians the U.S. team fit perfectly. Its members were fairly typical of those who had been on past U.S. teams. Five had just graduated from high school; one would begin his sophomore year that September. Three had spent at least part of their childhood in the San Francisco Bay area, two were from New Jersey, and one was from outside of Boston. Three participated in other team sports and were fairly athletic; the other three limited their athletic endeavors mostly to Ultimate Frisbee. All had been participating in math competitions at least since middle school.

If you had met the members of the U.S. team in a cafeteria or library or on the street, you wouldn’t think there was anything special about them. They talked quickly and intensely among themselves, sometimes about math but usually about other subjects.
They were rabidly interested in games of all sorts. They liked music, pizza, and movies.

But these kids were special. They were the products of one of the most intense selection processes undergone by any group of high school students. More than 15 million students attend public and private high schools in the United States, and nearly half a million take the first in a series of exams that culminates in the selection of the U.S. Olympiad team. The six individuals who emerge from that process are the best mathematical problem solvers of any American kids their age. Even someone who knew as much mathematics as they do would not have the benefit of the rigorous training the Olympians undergo.

What is it about the members of an Olympiad team that makes them such superb problem solvers? Some people would ascribe their talents simply to genius, saying that their accom- plishments are so remarkable as to be beyond understanding.
This use of the word “genius” as a label for the inexplicable has a long history. In classical Rome genius was the spirit associated with each individual from birth who shaped that person’s character, conduct, and destiny. People sacrificed to their genius on their birthday, expecting that in return the guiding spirit would provide them with worldly success and intellectual power.
In the modern world the term often re...


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Product Details

  • Paperback: 256 pages
  • Publisher: Mariner Books; Reprint edition (July 6, 2005)
  • Language: English
  • ISBN-10: 0618562125
  • ISBN-13: 978-0618562121
  • Product Dimensions: 5.5 x 0.6 x 8.2 inches
  • Shipping Weight: 12.3 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #1,016,276 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 5 people found the following review helpful By takingadayoff TOP 500 REVIEWERVINE VOICE on June 26, 2005
Format: Paperback
Count Down promises to be the story of six students who compete their way to a place on the 2001 U.S. Math Olympiad Team and what happens once they get to the big contest. I was expecting something like the excellent documentary Spellbound, which was about some of the kids who made it to the National Spelling Bee one year. I was a bit disappointed.

Count Down is best when it is about the students, but author Steve Olson often digresses to talk about topics related to math. He discusses what genius is, how math is taught in the U.S., why there aren't more girls on the U.S. team, the history of math contests, and much more. These are all interesting and pertinent topics, but I found that what I really wanted to know more about was the kids themselves.

Maybe a spelling bee is just inherently more dramatic since it takes place on stage, while the math contest takes place at desks and inside the contestants' heads. The whole notion of a math "team" in this case is misleading, since the members' individual scores are added together to determine the team score. They don't solve the problems as a team, although they train together. The top individuals are recognized as well, so I'm not sure what the point of a "math team" is.

Still, I did learn some odd facts, such as that much of the behavior in nature that is considered inborn or instinctive, isn't. Day-old chicks who were thought to eat mealworms instinctively, fail to do so if the chicks' feet are covered. Young chimpanzees who supposedly have an inborn fear of snakes, do not shy away from snakes if the chimps' diet is changed. This sort of knowledge challenges the nature vs. nurture arguments regarding I.Q. and genius.
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Format: Paperback
It is no secret that math and mathematicians traditionally have a bad rap in the States. Part of the fault lies in the great disparity between the math taught in primary and secondary schools and the math that mathematicians actually do. But part of the fault also falls upon mathematicians, who often seem to not care if anyone understands their trade, why it's interesting, and/or why it's important. Whatever the reason, stereotypes about math, scientists and mathematicians tend to be negative, casting mathematicians as socially awkward nerds. Images from popular culture further these stereotypes. The movie A Beautiful Mind, where the protagonist (and perhaps the antagonist) is the schizophrenic mathematician John Nash, was less about detailing Dr. Nash's tragic struggle and eventual pyrrhic victory against schizophrenia and more about aggrandizing Nash's delusions into an action film and conflating madness and mathematics along the way. The widely successful show The Big Bang Theory, a sitcom about three physicists and an engineer, portrays scientists as socially inept, comic-loving geeks whose work is indecipherable to the 'normal populace,' represented by the leading actress Kaley Cuoco as the waitress Penny.

In his book Count Down, Steve Olson tries to rectify these misconceptions. The introduction to the book is about these misconceptions, and about the problems facing the sciences in popular media. My wife happens to have read the book at the same time as me; after she read the introduction, she even told me that she felt a bit guilty for enjoying The Big Bang Theory so much.
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2 of 3 people found the following review helpful By mrliteral VINE VOICE on September 15, 2007
Format: Paperback
A few years ago, the movie Spellbound gave viewers insight into the world of spelling bees, culminating in the National championship. Since then, I've noticed other competitions getting similar treatments, such as bowling (in The League of Ordinary Gentlemen) and crossword puzzles (Word Play). Although it is a book and not a movie, Steve Olson's Count Down fits right into this genre of the competition documentary.

Count Down deals with the International Mathematical Olympiad, in which high school level students from around the world gather together to solve difficult math problems. How difficult? The first problem they are given reads: "In acute triangle ABC with circumcenter O and altitude AP, angle C is greater than or equal to angle B plus 30 degrees. Prove that angle A plus angle COP is less than 90 degrees." This is the easiest of the six questions the Math Olympians must solve.

Perhaps coincidentally, there also six members in the U.S. team, so Olson dedicates one chapter to each member and his approach to a problem (it is an all male team). It is like going from Los Angeles to New York by car: there are a number of different routes, each with its pluses and minuses. Similarly, these math problems can be solved a number of different ways.

Olson goes beyond the Olympiad itself, however, using it as a launching pad for discussions on topics regarding math education. One key theme that runs through Count Down is how Americans look down on math, often treating those who are good at it with scorns and letting people think that being bad at math is okay. This is contrasted with other countries where math is considered much more valuable. The problem is not merely with the education system but the culture itself.
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