Count Down : Six Kids Vie for Glory at the World's Toughest Math Competition
- Book Review,
by Steve Olson
From Publishers Weekly
Geometric figures and equations are relatively few and far between, the nonmathematically inclined may be relieved to know, in this elegant, balanced survey of competitive high school math by science writer Olson (Mapping Human History), who chronicles the progress of the six-member American team that participated in the 2001 Olympiad held in Washington, D.C. In between character sketches, the author examines such issues as whether "genius" is something you're born with (drawing parallels with musicians, he argues that it's those who practice the most who tend to do the best), why certain ethnic groups or nationalities do better than others (traditional rote problem-solving has handicapped U.S. students) and why girls are underrepresented in the fieldâ€"though the book opens with an account of the impressive career of Melanie Wood, the only girl so far to make the U.S. team (twice, in 1998 and 1999). Six problems taken from the Olympiad will challenge math buffs, who will also appreciate a joke about the waitress with a surprising knowledge of calculus. Contrary to the nerd stereotype, Olson portrays the young math whizzes as normal, well-adjusted kids who enjoy other activities like playing the piano and Ultimate Frisbee. Aimed at the general reader, this uplifting book should also draw fans of more technical recent math titles such as John Derbyshire's Prime Obsession or David Foster Wallace's Everything and More.Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
From School Library Journal
Adult/High School–Olson has taken on an always-difficult task: discussing math in a manner interesting and understandable to a society full of math-o-phobics. He succeeds admirably by relegating most of the hard-core problems and solutions to an appendix, and by writing about much more than math. Structured around a chronicle of the United States team's participation in the International Mathematical Olympiad of 2001, the book focuses on such topics as the ambiguities of inspiration, insight, talent, and creativity; the cultural perception of mathematics; and various approaches to math education. The author introduces the key players: the six American teen contestants and their coaches. These portraits are spread out over the course of the volume, as are the problems offered at that year's Olympiad. This arrangement supports an engaging and mildly suspenseful read. Olson's user-friendly presentation of the problems serves to reinforce his argument that the United States is culturally averse to math compared with much of the rest of the world, and that American educators are definitely on the wrong path. The author does an excellent job of showcasing the better side of his subject. Unfortunately, many teens who would enjoy reading Count Down won't get past three words in the subtitle: "toughest math competition." Those who do will be rewarded.–Robert Saunderson, Berkeley Public Library, CA Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
From Bookmarks Magazine
America is not a nation of math-lovers. Olson’s subjects are, for the most part, the kind of kids his readers never were. However, he resists turning the Olympians into curiosities or players in a high-stakes drama. Instead, he uses the Olympiad as a springboard for discussing compelling issues of nature, nurture, and competitive drive. Some of these discussions crowd out the kids themselves; Olson doesn’t describe their lives as fully as he might. Nor does he consider all the questions raised by their success. A longer book might have offered a more complete view of the International Mathematical Olympiad, its role in the lives of its participants, and its place in American society. Still, Count Down is by all accounts an engaging read.Copyright © 2004 Phillips & Nelson Media, Inc.
Book Description
Each summer six math whizzes selected from nearly a half-million American teens compete against the world"s best problem solvers at the International Mathematical Olympiad. Steve Olson followed the six 2001 contestants from the 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 science of intelligence and learning and, finally, the nature of genius. Brilliant, but defying all the math-nerd stereotypes, these teens want to excel in whatever piques their curiosity, and they are curious about almost everything — music, games, politics, sports, literature. One team member is ardent about both water polo and creative writing. Another 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, they are in many ways not so different from other teenagers, finding pure joy in indulging their personal passions. Beyond the the Olympiad, Olson sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate. Inside the cavernous gym where the competition takes place, Count Down uncovers a fascinating subculture and its engaging, driven inhabitants.
Excerpt. © Reprinted by permission. All rights reserved.
IntroductionOn July 4, 1974, a bus carrying eight U.S. high school studentswound through the narrow medieval streets of Erfurt, East Germany.The students were all a bit nervous. In those days ofheightened Cold War tensions, few Americans ventured beyondthe Iron Curtain. Just that morning, after an all-night flight fromNew York City, the students had endured a brusque round ofquestioning by the East German border police. As they steppedout of the bus in the center of Erfurt, beneath the spires of the cathedralwhere Martin Luther preached his first sermons, they feltboth isolated and highly visible.They were nervous for another reason. These high school juniorsand seniors were the first team from the United States everto compete in an International Mathematical Olympiad. In 1974the Olympiad was already fifteen years old; the first one had beenheld in 1959 in Bucharest, Romania. But throughout the 1960sthe 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 teamsalways have added their individual scores and compared themselvescountry against country. In this informal contest theOlympiad had been dominated by teams from the Soviet Unionand eastern Europe. Even as more teams from western Europebegan to compete — Finland in 1965 (finishing last), Great Britain,Sweden, Italy, and France (also finishing last) in 1967 — theU.S. mathematics community had no desire to pit America"s besthigh school students against the world"s best. "A lot of peoplewere dead set against it," says Murray Klamkin, a former Olympiadcoach who now lives in Edmonton, Canada. "They thoughta U.S. team would be crushed by all those Communist countries."In 1971 the mathematician Nura Turner, from the State Universityof New York at Albany, wrote an article that began tochange people"s minds. She pointed out that several state-levelcompetitions, established mostly since the 1950s, had laid thegroundwork for American participation at the internationallevel. She admitted that a U.S. team might be humiliated in its initialattempts but argued that Americans were tough enough tobounce back. "We certainly must possess here in the USA thestrength of character," she wrote, "to face defeat and the capabilityand courage to then plunge into systematic hard training tocompete again with the desire to strive for a better showing."In 1974 the major U.S. mathematical organizations finallyagreed to send a team. Two years earlier the Mathematical Associationof America had instituted a national exam designed toidentify the best high school mathematicians in the country. Inthe spring of 1974 the association named the top eight finisherson the exam as the members of the U.S. Olympiad team.Eric Lander, who is now one of the world"s preeminent geneticistsand the director of the Broad Institute of Harvard Universityand Massachusetts Institute of Technology, was a memberof the team that first year. It was his senior year at StuyvesantHigh School in Manhattan, and Lander was captain of theschool"s math team. "Math team was great," he says. "Aboutthirty kids met each morning for an hour before school in a fifth-floor room of Stuyvesant High School, and the captain of theteam was responsible for running the session. This was beforeyou had databases full of math problems, so the captain of themath team, upon his ascension to office, came into possession ofwhat we called "the shopping bag." It contained mimeographedsheets of problems and strips of problems and records of the citymath contests for a long time. So the captain of the team wouldpull problems out of the bag and be responsible for leading thegroup."When most people think about math competitions, theyprobably envision a roomful of kids struggling to perform complexcalculations faster than the next person. But most of theproblems in high-level competitions have very little to do withcalculations. Solving these problems requires a sophisticatedgrasp of mathematical ideas, so that familiar concepts can be extendedin new directions. The mathematical procedures everyonelearns in school aren"t enough. Becoming an excellent problemsolver demands creativity, daring, and playfulness. A math competitionis more like a game than a test — a game played with themind.The structure of an International Mathematical Olympiadreflects the nature of the problems. The size of the teams haschanged over time. In the early years each team had eight members;since 1983 they have had six. But the format has stayed thesame. On the first day of the competition all of the Olympians receivea sheet of paper containing three problems, and each competitor,working individually, has four and a half hours to makeas much progress on the problems as he or she can. The next daythey have the same amount of time to solve three additionalproblems.But the competition doesn"t begin when the competitors arrivein the Olympiad city, because the assembled team coachesfirst have to decide which problems will be on the exam. In Erfurtthe teams had five days to tour the city and get to know one another."It was fascinating — the single team we most resembledand got along with were the Russians," says Lander. "So wehung out with the Russians a lot and got into all sorts of mischief.We were in East Germany, and the Russians figured at that pointthat they owned East Germany, so they weren"t going to get introuble. I remember very well going up to the top of the dormitoryat the school where we were staying, and the Americans andRussians throwing water balloons down on the street. The Russiansmight not do it back home, but they could do it in East Germany."On July 8 the eighteen teams competing in the Sixteenth InternationalMathematical Olympiad gathered at a local universityto take the exam. All the worries about the U.S. team"s abilitieshad been for naught. Lander and his teammates finishedsecond — just a few points behind the Soviet Union._This book is first and foremost the story of the Forty-second InternationalMathematical Olympiad, which took place in 2001on the campus of George Mason University in Fairfax, Virginia,right outside Washington, D.C. The event has grown substantiallysince 1974. Nearly 500 kids from eighty-three countriescompeted in the Forty-second Olympiad, compared with about125 in 1974 (and compared to the 150 or so who competedin 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 SouthAmerica and Africa — Argentina, Brazil, Colombia, Paraguay,Peru, Uruguay, Venezuela, Morocco, Tunisia, and South Africa— now compete. So do teams from East Asian countries such asMacau, Hong Kong, and the Philippines.As one might expect, the competitors at the Forty-secondOlympiad had their cultural differences, most notably the morethan fifty languages that were spoken. But in general the Olympianswere remarkably compatible. Most knew at least a littleEnglish, since English has become the language in which mostof the world"s higher-level mathematics is conducted. A soccergame immediately sprang up in the courtyard of the dormitorycomplex where they were staying and continued on and off forthe duration of the event. All of the competitors could share CDsand 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 youngmathematicians the U.S. team fit perfectly. Its members werefairly typical of those who had been on past U.S. teams. Five hadjust graduated from high school; one would begin his sophomoreyear that September. Three had spent at least part of their childhoodin the San Francisco Bay area, two were from New Jersey,and one was from outside of Boston. Three participated in otherteam sports and were fairly athletic; the other three limited theirathletic endeavors mostly to Ultimate Frisbee. All had been participatingin math competitions at least since middle school.If you had met the members of the U.S. team in a cafeteria orlibrary or on the street, you wouldn"t think there was anythingspecial about them. They talked quickly and intensely amongthemselves, sometimes about math but usually about other subjects.They were rabidly interested in games of all sorts. Theyliked music, pizza, and movies.But these kids were special. They were the products of oneof the most intense selection processes undergone by any groupof high school students. More than 15 million students attendpublic and private high schools in the United States, and nearlyhalf a million take the first in a series of exams that culminates inthe selection of the U.S. Olympiad team. The six individuals whoemerge from that process are the best mathematical problemsolvers of any American kids their age. Even someone who knewas much mathematics as they do would not have the benefit ofthe rigorous training the Olympians undergo.What is it about the members of an Olympiad team thatmakes them such superb problem solvers? Some people wouldascribe 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 along history. In classical Rome genius was the spirit associatedwith each individual from birth who shaped that person"s character,conduct, and destiny. People sacrificed to their genius ontheir birthday, expecting that in return the guiding spirit wouldprovide them with worldly success and intellectual power.In the modern world the term often retains a hint of the supernatural.To call someone a genius is to imply that he or she issomehow distinct from normal human beings, with apparent accessto experiences or thoughts that are denied to others. Geniusfrom this perspective can seem to be, in the words of Harvardprofessor Marjorie Garber, "the post-Enlightenment equivalentof sainthood."This way of thinking can skew even the most levelheadedanalysis. In describing the achievements of the physicist RichardFeynman, Cornell University mathematician Mark Kac oncemade what has become a well-known distinction:There are two kinds of geniuses, the "ordinary" and the"magicians." An ordinary genius is a fellow that you and Iwould be just as good as, if we were only many times better.There is no mystery as to how his mind works. Once we understandwhat they have done, we feel certain that we, too,could have done it. It is different with the magicians. . . . Theworking of their minds is for all intents and purposes incomprehensible.Even after we understand what they have done,the process by which they have done it is completely dark.Kac"s distinction is beguiling, but it"s really just a modern restatementof the Roman belief in spirits. Are the workings of someminds really incomprehensible? Or do great achievements relyon straightforward extensions of everyday thinking and imagining?Can profound advances in the arts and sciences be analyzedin such a way as to reveal their origins? Or are some realms of ex-perience shut off from us forever, hidden behind the tantalizingveil of "genius"?The varied meanings of the word complicate efforts to answerthese questions. In modern parlance the term is often debased.People say that a politician is a genius at wooing voters.Newspapers label successful football coaches sports geniuses. Interiordecorators, advertising writers, land developers, and countryand western singers are all hailed as geniuses.In middle and high schools, "genius" is usually a term of derision.The word is used to taunt someone who is good at mathor a dedicated writer or simply more interested in schoolworkthan the average student is. Even as adults, many people wouldfeel uncomfortable being labeled a genius. The word seems anunwanted burden, a harbinger of unfulfilled expectations.The kids on a U.S. Olympiad team would not considerthemselves geniuses. They have become incredibly adept at solvingimmensely difficult mathematical problems. In that sense,they are prodigies, in that they have attained very high levels ofperformance at a young age. But they certainly are not geniusesin the sense that Homer, Archimedes, Shakespeare, Rembrandt,Newton, Mozart, or Einstein are so considered.Nevertheless, the members of an Olympiad team do sharethe attributes of genius in one respect: they employ the sameintellectual tools that history"s great creators have. They use insight,talent, and creativity to produce original solutions to baf-fling problems. They exhibit the competitiveness, breadth, andsense of wonder that enable them to achieve at levels inconceivableto most people. By watching the Olympians solve mathematicalproblems, it"s possible at least to glimpse the qualitiesthat have produced humanity"s greatest triumphs._Besides being about extraordinary achievements, this book isabout mathematicians, a group that has received much attentionin popular culture recently. Mathematicians have been theprotagonists of hit movies (Good Will Hunting, A BeautifulMind) and have figured prominently in well-received plays andnovels (Proof, Uncle Petros and Goldbach"s Conjecture). Princetonmathematician Andrew Wiles, who solved a famous mathematicalproblem called Fermat"s last theorem in 1994, was eventhe inspiration for a musical in 2001 called Fermat"s Last Tango.This attention has been a mixed blessing. More than a fewof these entertainments have made mathematicians out to befools, nerds, or madmen. "Many recent works of mathematicalfiction portray mathematicians as insane," says Alex Kasman, amathematician at the College of Charleston in South Carolina,who maintains a Web site that reviews hundreds of fictionalworks involving mathematics. "Certainly there are mathematicianswith mental illnesses, just as there are people of other professionswith mental illnesses. But the high correlation of the twoin fiction both supports and generates an unfair stereotype in thegeneral population that there is some deep connection betweenthe two. When I was watching A Beautiful Mind, and the characterof John Nash was suffering terribly from his mental illness, Iheard a woman behind me say, "I"m glad I"m not a genius.""Other stereotypes plague works of fiction featuring mathematicians,says Kasman. Occasionally mathematicians are depictedas flamboyant and eccentric, like the "chaos theorist"played by Jeff Goldblum in the movie Jurassic Park. In othercases they are boring and repressed, like the husband (who alsoends up deranged) in William Boyd"s novel Brazzaville Beach.Rarely do moviegoers or novel readers encounter mathematicianswith whom they might enjoy a conversation at a party. "Isuppose no author wants to write about people who are ordinary,"Kasman says. "So it"s not surprising that very few fictionalmathematicians are just ordinary people who like mathematics.But because most people do not personally know any mathematicians,they form their opinions of them based on these works offiction. My experience, on the other hand, suggests that mathematiciansare as normal as the people in any other profession."One response to the stereotyping of mathematicians is toobserve that scriptwriters and popular novelists stereotype allprofessions, even their own. But mathematicians have been absorbingabuse for a long time. In the Greek drama The Birds,written by Aristophanes in the fifth century b.c., a geometernamed Meton arrives at a city founded by the Athenian Makedoand announces that he intends "to survey the plains of the air foryou and to parcel them into lots." The populace denounces himas a "quack and imposter," beats him, and drives him from thecity. In the novel Emma, published in 1815, Jane Austen askswhether a linguist, a grammarian, or "even a mathematician"could fail to appreciate the ardor of newfound love.In American secondary schools, the stereotype of kids whoare good at mathematics is somewhat different. They are seenas social misfits, physically uncoordinated, interested only inmathematics and other geeky subjects. Sometimes this stereotypeturns up in television shows and movies as the badly dressed,awkward, computer-programming male who can"t find a girlfriend.The kids on an Olympiad team defy these brutally unfairstereotypes. Not all of them are interested in computers, science,or Star Trek. Some even claim to be not very good at mathematicalcalculations, at least compared with other Olympians. In fact,many of their traits initially seem antithetical to mathematics.They have deep insights into the problems they are solving. Theyare blindingly creative. They perceive the beauty in abstract mentalconstructs with an almost religious passion. And they are ableto combine those traits in such a way that each trait builds on theothers (though in this book I examine a different trait for eachteam member and each Olympiad problem).None of the Olympians fits comfortably into the stereotypeof a mathematician. Each can be understood — and appreciated— only as an individual._Finally, this is a book about mathematics — about its complexities,its unreasonable effectiveness, its stark and breathtakingbeauty. Many people believe that higher-level mathematics isconducted on a plane separate from normal thought, using conceptsand logic that they could never hope to understand. Tomany mathematicians this belief seems misguided. They seemathematics as a smooth continuum from the numbers andshapes everyone learns in grade school to the frontiers of mathematicalresearch. In many professions, acolytes need to makesudden leaps of achievement or skill, as when someone flies anairplane for the first time or teaches a class of boisterous students.Mathematics is not one of those professions.A book about art has to include some reproductions of artwork,and a cookbook has to have recipes. By the same token, abook about problem solving should contain a few mathematicalproblems. For many people, the automatic reaction upon turninga page and seeing a geometric diagram or an equation will be"Oh no, not math!" That reaction is perfectly understandable. Itarises from the boring mathematics classes most of us had to endurein school, the common belief that "I was never any good atmath," and the widespread conviction that only the gifted fewcan hope to understand mathematics.The six Olympiad problems in this book probably should beseen as extended examples rather than as core parts of the story.You don"t have to understand the problems in detail to appreciatethe skills that distinguish the Olympians. And readers whoskip or skim over the problems will be in good company. Whenthe English zoologist Sir Solly Zuckerman was asked once whathe did when he came across mathematical formulas in scientificpapers, he replied, "I hum them."But anyone who can calculate a loan payment or a battingaverage is capable of understanding the problems described inthis book. Olympiad problems are designed to involve only themathematics that people learn in high school. They don"t requirea knowledge of subjects usually learned in college, such as calculus.Coming up with solutions to the problems is very challenging.The reason the Olympiad is generally considered the world"shardest mathematical competition is that high school studentshave relatively few tools with which to solve the problems, comparedwith older students who know more mathematics. Still,many of the solutions the Olympians devise are relatively easyto describe. For the three problems given on the first day ofthe Olympiad, the chapters of this book provide relatively completesolutions, with a few supporting details given in the appendix.For the second three problems, which are more complex,the chapters provide a general description of the solutions,with a somewhat more detailed treatment in the appendix.Working through one or more of the problems may take sometime (though discussions of international relations, political gerrymandering,or the science of dieting are often more complicated),but the effort will be rewarded. As James Newman wrotein his classic anthology The World of Mathematics, "There arefew gratifications comparable to that of keeping up with a demonstrationand attaining the proof. It is for each man an act ofcreation, as if the discovery had never been made before."Just as anyone can marvel at a great painting, a sublimepiece of music, or a thunderous slam dunk without being apainter, composer, or basketball player, so anyone can appreciatethe power and beauty of elegant mathematical problems and solutions.They are products of the human mind, as mysterious andinspiring as are all acts of creation.Copyright © 2004 by Steve Olson. Reprinted by permission of Houghton Mifflin Company.
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