# Review of “Math Girls” by Hiroshi Yuki

When I have time to kill in a new library or bookstore, I inevitably find myself wandering to the math section — looking not for new textbooks but for decent books aimed at the popularization of mathematics. Sadly, the books I find are usually in one of three categories:

1. Drill books with hundreds of problems for young students to practice certain skills and procedures.
2. Cartoonish books aimed at a young elementary audience.
3. Fact books featuring short paragraphs on various topics in advanced mathematics.

There’s nothing particularly wrong with any of these types of books — and there’s a few that I could recommend from each category — but it’s rare to find a good math book that doesn’t fit one of these molds.

Enter Math Girls, by Hiroshi Yuki, which features conversations between high school students talk about love and talk about math. I won’t write a full review — the one at MAA Reviews does a really good job at describing the book, as well as the one published in the Notices of the American Mathematical Society — but I will list some of the mathematical ideas that the book’s characters discuss:

1. Functions and finding patterns
2. The formula for the sum of the divisors of an integer.
3. DeMoivre’s Theorem.
4. Generating functions and the Fibonacci sequence.
5. The arithmetic-geometric mean inequality.
6. The binomial theorem.
7. The Catalan numbers.
8. The convergence and divergence of p-series
9. Taylor series
10. Vieta’s infinite product for $\sin x$ (see Equation 22 from Mathworld)

What’s unique about Math Girls is that the logical development of all of these topics are present, as opposed a cursory summary typically found in a book of mathematical facts. That said, the logical development is not the clean and sanitized presentation that would be found in a textbook. Instead, the topics are presented as if the young characters were discovering them for themselves, with more than a few false starts and mistakes along the way. In other words, the book feels a bit like the work of real mathematicians, which makes it fairly unique for math books intended for a popular audience.

Again, I’ll defer to MAA Reviews. and the Notices of the AMS for anyone interested in a lengthier review of the book. There’s also a second volume (Math Girls 2: Fermat’s Last Theorem) that I haven’t read yet, but I presume that the style is very similar.

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