My own opinion is that the proselytization of mathematics is a bit heavy and is likely to turn off some readers. And, on the other hand, the mathematics presented is too light, and not exciting enough to turn on the readers who will be interested in mathematics.

That is not to say that there is nothing I like about the book. The prose itself is well written and the characterization is nice as well. Even as far as the mathematics goes, there are two places where I think it hits the mark. At one point, Arlen (the "math whiz") paraphrases Galilleo's quotation about mathematics being the language of the universe and I think he is able to make a good point later when he remarks later that some pool players (including Mickey's father) can do pool but can't talk about it because they lack the language. Also, the first introduction of mathematics/physics in the form of the rule that the angle of incidence equals the angle of reflection when a pool ball hits the wall works well.

However, there is a lot more to the mathematics of billiards than this one fact and the notion that mathematics allows communication. I think the book could have been both more interesting and more effective as a promoter of mathematics if this was taken just a bit farther. For example, the term "vector" is introduced, but the power of vectors is not utilized. The thing that makes a vector a vector (as you learn in a good course on linear algebra) is not that it is a line segment, but that they can be scaled and added. These two operations are pretty simple and could easily be explained at the elementary school level. Then, there is a lot more you can do to predict the behavior of billiard balls than simply a single ball bouncing off a wall. With vector addition you can handle many balls moving and colliding and predict the result.

Similarly, I would like to warn readers not to expect too much from the "statistics and probability" that Barbara Montgomery mentions in her comments above. If I understand which part of the book she means, it is merely a reference to the expected lifespan. Mickey should expect to live many more years and so he shouldn't worry, is the basic point. Unfortunately, one doesn't need math to know that a fifth grader should expect to live much longer, and with math one knows that the standard deviation (and not only the mean) is needed to have a good idea of how likely it will be that he will not.

Perhaps I am being unrealistic about what can be achieved in a book for children. (Disclaimer: I am a college professor with training in advanced mathematics. I do not have a degree in childhood education.) However, I cannot help but feel that the book would be better and stronger if the math was taken to the next level.

Another work of fiction that uses billiards to illustrate "real world" applications of mathematics is the popular animated short film Donald in Mathmagic Land.

Also, although this is a much more advanced area of mathematics, I'd also like to point out that billiards forms a branch of pure mathematics as well. In mathematical billiards, one considers the affect of the shape of the "table" on the dynamics of the balls. Although this does not help people play pool better, it has provided some useful information about chaos and quantum physics!