# L.A. Math: Romance, Crime, and Mathematics in the City of Angels

The author James D. Stein, has been involved as a mathematics professor, in mathematics education in several ways. This might explain his engagement in writing popular books on mathematics and sciences. For example in *How Math Explains the World* (2008) he illustrates how mathematics are needed to deal with physics, and hence with our daily lives (from car repair to modern physics as the subtitle states). Another of his books that was quite successful is called *Cosmic Numbers*(2011) in which he discusses the 13 constants that make physics work as it does here on Earth (gravitational constant, speed of light, absolute zero, Planck and Boltzmann constant, etc.). Hence their values are the prerequisites for life forms as we know it

His latest book that is under review here is again illustrating some mathematical problems that sooner or later everybody could be confronted with. In this case, he embeds the problems in 14 episodes of a detective series. This is not the first time this has been done. In such episodes, the hero usually has to solve the whodunit question using logical deduction. Thus, if it is not mathematics, then it is at least the logic that is important.

The format that Stein uses is a fictional part of the 14 chapters that in principle can be read as an independent novel. Also each chapter can be read independently, but the main characters are the same and there is some thread connecting them. At the place where the problem is solved using mathematical arguments, a link is given to the second part of the book. In that part the same 14 chapters appear as appendices that contain the mathematics with extra information, and some more technical details. In principle it is perfectly possible to read on and just skip these appendices, but that would of course be a serious amputation of an important part of the book and destroy the whole setup. Skipping one or two of these appendices or just skimming them if the topic is already familiar, is not harmful though.

Stein turns out not only to be good in explaining these technical parts, but he is actually a quite good fiction writer. In similar books, when written by a non-mathematician, the mathematics are often a bit fluffy, or when written by a mathematician, the fictional characters may turn out to have a flat cardboard profile, and they serve only to frame the technical material. Here however, we get a true story told, and quite well told indeed. The main character is Freddy Carmichael, a New York freelance consultant and private investigator, who has marital problems and is on the verge of a divorce. To provide his wife and himself some free space, he moves to Los Angeles. He is trying hard to make a living, but he is actually some kind of a anti-hero since it turns out that his landlord Pete Lennox, who loves to sleep 14 hours a day and is watching the sports channel on TV when awake, is actually a math geek. When Freddy gets confronted with some problem and doesn't have a clue, he always turns to Pete for advise. So they start a company together. When it comes to the crux of the issue, it is always Pete who finds the solution while Freddy is the one who is always anxious of being paid by the people asking for their help.

As for the mathematics that are involved, these are easily accessible and do not require any advanced mathematical training. The usual suspects (and some less common topics) make their appearence: probability (elementary discrete probabilities, conditional probability, the Monty hall problem etc), logic and set theory, percent computations and usual errors made in calculations, compound interest, arithmetic progression, solving algebraic equations, statistics (normal and binomial distributions), game theory and voting systems (Arrow's impossibility theorem), graph theory (traveling salesman problem) and others. The problems are well intertwined with the fiction, and both are equally important. Some examples: Political parties are mutually accusing the other of embezzling a lot of money which turns out to be explained by wrongly computing percentages. Freddy misses an appointment because average driving speeds were wrongly calculated. Arithmetic progression is needed when Freddy wants to quit smoking by reducing the rate by one cigaret a day. And so on and so further. Several of the problems (mainly towards the end) are related to sports: baseball, (American) football, basket, and horse racing and related betting. Here of course game theory and probability are important. However, the rules of the particular sports and the sports heros that are like semi-gods in America will be very recognizable in the USA, but this might be a stumbling block for non-Americans. Moreover there is also a whole lot of argot needed to understand the bettings. There is an extra (two-page) appendix with some explanation on sports betting and a list of references to read more about them (these are the only references this book contains). For the complete outsiders, this might require much more effort to get used to than the mathematics involved.

Stein, or at least his main character, has also some well defined viewpoints on several controversial topics like being a smoker. He tries to give up smoking, but calls it "the worst forty days since the flood" and he certainly does not approve the way that smokers are oppressed and demonised. When he wants to become a vegetarian and even an animal activist, it turns out not to be such a good idea. Stein also sketches the difference in social behaviour of New Yorkers and L.A. Californians. All these indicate that there is more to this book than just the mathematics.

This is the first book I have read where the fiction and the mathematics are in a 50-50 balance, both in importance and in quality. It is a pleasure reading and warmly recommended.

**Submitted by Adhemar Bultheel |

**9 / Feb / 2016