Like the author, the character Katya is writer of literary fiction who emigrated to New York City from Russia as a young woman. Katya's descriptions of her interactions with her dying mother, her two children, the husband she is divorcing, the billionaire to whom she is engaged, and the former high school teacher she still loves show her to be selfish and immature. She is in need of the sort of guidance provided by "self-help books", but the guidance she receives turns out to be mathematical.

Katya's mother was an influential math educator, school official, and textbook author in Russia and in her old age decides to write a math-themed self-help book for American adults. The brief notes she was writing for herself in preparation for writing that book are used as the opening of the first 21 chapters of "Divide Me By Zero". For example, Chapter 5 starts with "Do not push too much math on a child or she will rebel" and Chapter 9 says "Fun with graphs: If you can't determine the exact moment of the event, try to find the last defined moment before the event and the first that comes after" (accompanied by the graph of a function of one variable with a local minimum P surrounded by labeled points B and A). These are always intended to resonate with the text in the chapter. For example, Chapter 9 features Katya looking at photos and trying determine the moment that her marriage became a loveless one.

For me, at least, this worked best when Vapnyar was able to build upon the opening mathematical comment of the chapter, using math to say something about daily life and conversely revealing some truth about math itself. For instance, in the chapter which starts with "Higher dimensional spaces occur in the sciences" she writes:

There are some places that the math (or math history) is annoyingly wrong. For instance, on page 266 Katya suggests that "few people outside math circles" know the name of Carl Friedrich Gauss because (unlike the apparently better known Lobachevsky) he was afraid to publish his work on non-Euclidean geometry. And later she says that every function has a limit, or some other such nonsense. But, as is often the case, it is difficult to know whether these reflect a misunderstanding on the part of the author or if she knowingly had the character of Katya mislead the reader.

Divide Me By Zero is not among my personal favorite mathematical fiction novels. Katya's immaturity, her sense of humor, and obsession with sex were not to my taste, and I didn't feel that Vapnyar did much with the math. (The quote above is a rare exception in a book where most of the mathematical metaphors were much less interesting.) However, I do recommend this book to anyone who can appreciate a book for the way it is written. One of the blurbs refers to the "charisma of [Vapnyar's] storytelling". I'm not sure exactly what that means, but I can't quite find the words to describe whatever it is that makes her writing so effective either. The book really is well-written, and is certainly an interesting example of mathematical fiction.