mixedmath

I read a lot of popular science and math books. Scientific and mathematical exposition to the public is a fundamental task that must be done; but for some reason, it is simply not getting done well enough. One day, perhaps I'll write expository (i.e. for non-math folk) math. But until then, I read everything I can. I then thought that if I read them all, I should share what I think.

Today, I consider the book Count Down: The Race for Beautiful Solutions at the International Mathematics Olympiad, by Steve Olson.

It is no secret that math and mathematicians traditionally have a bad rap in the States (see, for example, this sardonically appropriate newspaper clipping at Scientific American). 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. But after the introduction, Olson goes into the main subject matter of the book: following the six student on the 2001 US IMO team through some of the process of preparing for and taking the Olympiad exam, including looking at the six problems and parts of their solutions.

Olson saw a natural bijection between the six competitors and the six problems. The book is structured so that each student has their own chapter, wherein a particular positive characteristic is spoken about, attributed to the student, and somehow reflected in that student's solution to one of the problems. The characteristics are: Inspiration, Direction, Insight, Competitiveness, Talent, Creativity, and Breadth (and A Sense of Wonder, if that counts).

While this is morally equivalent to priming, it is a nice change. Such positive language and barefaced accolades tend to be reserved for sports stars and action heroes. It doesn't hurt to try to cast people who do math in a more positive light. Olson does his best to show that the six kids on the IMO team are largely ordinary teens with a healthy degree of curiosity and enough discipline to sit down and do some real work. He describes the teens as having "casual good looks," liking games of fast wit and ultimate frisbee, having an "easygoing nature" or being "unnervingly calm." A few times, he writes about former IMO competitor Melanie Wood, and he describes her as "an attractive, green-eyed, vivacious blond."

Olson does a great job of talking about tangents related to the Olympians and their pasts, or to the IMO overall. He continually returns to mathematical giants, like Andrew Wiles or Martin Gardner, and ideas about genius and talent. He alludes to and provides further information about a mountain of different sources. Olson is clearly knowledgeable and passionate himself.

Unfortunately, these overarching themes do not always play well with each other. Although the book is purportedly about the six students and their story taking the olympiad, there is so much tangential material that the kids are largely left out. Further, in his struggle to present the olympians as largely ordinary people as opposed to math-geeks, Olson leaves out much of the detail that shows how interesting the olympians really are. At the end of the day, we know that the six American teenagers selected to compete on the International Math Olympiad have some sort of story - many hours of hard work and dedication, some teacher, group of teachers, or mentor who pushed and helped. But we were never privy to this through this book.

Instead, we heard brief testimony from teachers saying that the students were good at many subjects. One of the olympians "was interested in history" and "a good writer." Another teacher said that he "had to think of things to keep him busy." These statements, where a teacher tasked with the education of a precocious young teen realizes that the student teaches him just as much as he teaches the student, are trite. But it would be tremendously interesting to know about the teens, and to see how the teachers actually overcame the task of educating such a quick-learner.

Each student is associated with a particular attribute and a particular problem. While the attributes are generically good, they also seem generic enough that there was no reason for the given associations between students and attributes. Did young Oaz Nir lack talent, or creativity, or competitiveness? Clearly he did not, as he was one of the better members of the team. The more and more I read through the book, the more and more I felt this gimmick detracted from 'the real story.'

When I was in middle and high school, I typically thought that math was boring and easy. My friends and I often finished our assignments early, and in general the teachers had nothing else for us to do. So we did other classes' homework, or played chess, or the like. (This is not completely true - in eighth grade, I had a math teacher named Mr. O'Brien, who kept me engaged with puzzles like the Towers of Hanoi and whatnot. I'm not sure, but I suspect that I would not be a mathematician were it not for him. And my senior year of high school was also different). It turns out that my middle school also had a MathCounts program - a program that Olson frequently mentions as 'an in' into the world of competitive math olympiads - but I never knew about it. There is something to be said for good educators, and I think Olson missed a big opportunity to highlight the teens, their families, and their educators.

Count Down also presented sketch solutions to the six IMO problems, inherently difficult problems; but the presentation is very approachable. There are many times where Olson gives the heart of the proof but decides to omit the computation, and I think he chose the exact right amount of rigor in his proofs. He includes appendices in the back with additional exposition on the proofs, but even they do not include all the computation. For example, in the appendix for Problem 4, a question about a sum over a permutation group, he gives the heart of the proof and skips through the tedium with "... through some fancy calculating, you can show that this sum cannot be evenly divided by..." He uses similar phrases throughout, but in my opinion, he captures the essence of the proofs.

More importantly, the reader comes away with the feeling that he understands the proofs as well. My wife did. This is perhaps Olson's greatest success: challenging math does not feel hard in this book. It's understandable, and feels more like a puzzle. It seems possible that the reader steps away with the idea that math could be entertaining, and does not have to be hard. As a math educator, I see students who have convinced themselves that they will fail before any assignment is assigned because they know that they "are not good at math" or that "math is hard." It is not easy to overcome.

Overall, I thought Count Down was an entertaining read and I would recommend it to others.

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