Philip is a mathematician who works in the financial industry, a quant. We also meet his exwife, Rebecca, who is a math professor. But, the main character in this novel is a woman who we only meet in flashbacks and remembrances. She is the Irma Arcuri of the title, an author and bookbinder who left Philip her collection of 351 books before voluntarily "disappearing" from her own life. The books, however, are not just a gift but seem to contain clues and hidden messages in the form of marginalia and even entire chapters inserted into some classic novels. He attempts to follow the clues as he searches in vain for her, and for his missing stepson, Sam, who has also gone looking for her.
Arcuri, we come to learn, is truly alive in a way that others are not. This means living a life without responsibilities, and apparently having lots of sex. Irma not only had sex with Philip when they met as undergraduates, but also seduced his exwives, his friend, his stepson and his stepdaughter! The sexual encounters are described so frequently and so graphically that I would really feel uncomfortable assigning this book for reading by my students at the College of Charleston. (Ironically, David Bajo, the author, teaches at our sister school, the University in South Carolina. Despite the intellectual quality of this book, I doubt that our biblethumping politicians there in Columbia, SC would appreciate the nearly pornographic descriptions...at least not publicly!)
I suppose it is likely that the author chose to make the other characters into mathematicians because of the stereotype that mathematicians are lacking in interpersonal skills and do not know how to really enjoy life, making them better contrasts to Irma Arcuri's vivaciousness. (Consider, for example the following passage: "He cursed his math. He cursed Rebecca's math. He cursed all math and wished he could, just once, delete it from his self. Someone who knew people the way Irma knew people, someone who thought in simple English, would have come directly here to find Sam.") As I find that stereotype to be inaccurate and tiresome, I did not particularly appreciate that aspect of the book.
However, a bigger problem for me in reading this book is that although Bajo has a great appreciation for words (crafting his sentences with care and describing literature with awe), his understanding of math is weak. Imagine, for instance, if an American author and poet tried to write an epic poem about China, with many passages in Chinese. This poem might well appear beautiful and great to an American audience, but completely fail to appeal to someone who is really Chinese. Or, to put it another way, this book also spends a lot of time talking about running. I do not know that much about Olympic track running or jogging through cities, and so I cannot say whether those passages would ring true to someone with actual experience as an athlete, but for a naive reader like me they were just fine. The author's attempt at discussing math, however, was such a disaster that it made it difficult for me to enjoy the rest of the novel. For instance:
 At first Philip is described as being good at numbers, not at "math theory". Aside from the fact that I would not use the phrase "math theory" in this way, this had me thinking of him as a sort of mental calculator, who can do quick computations but not work with other mathematical abstractions. This is supported by an incident in which he multiplies the scores of some angry golfers and finds its square root in his head. However, as the book goes on we see that he models everything as equations (see below for a discussion of this word), that he is an expert on the dynamics of the pendulum (especially the tautochrone), and he also talks a lot about geometry (of ellipses and hyperbolas especially). Is that not "math theory"?
 As my students so often do, the word "equation" here is used incorrectly to mean "some mathematical expression or statement" rather than what it actually means "the statement that two particular things are equal". In fact, at one point he specifically mentions that one equation does not involve an equal sign, which is like a sentence that does not have a verb.
 To figure out why a certain investment is not behaving as expected, he starts by modeling it with Newton's differential equation "F=ma" which he solves using separation of variables. I guess Bajo gets a point or two for mentioning separation of variables, but it makes no sense at all in this context, and neither does the supposed solution.
 In a discussion of the way Cervantes is able to transcend the concept of "point of view" in Don Quixote, we read:
(quoted from The 351 Books of Irma Arcuri)
In math, you often begin booklong proofs by attempting to achieve this type of collective quantification, which must nevertheless remain singular and not rely on omniscience. It is rarely achieved. Einstein could do it. Napier, too.

I have some idea of what he means about Cervantes, but absolutely no idea what he is saying about writing proofs. Perhaps he is being deep and I'm missing it. (Einstein and Napier? Neither of them is known for their skill in writing booklong proofs!) But, more likely, I think he wanted to say something that sounded meaningful about math without caring that it was really vacuous.
 I suppose we could say that math is used metaphorically throughout the book, but the metaphors could be so much better if the author knew what he was talking about. For instance, Philip writes a formula for Irma based on their discussion of the distances between characters in Faust:
(quoted from The 351 Books of Irma Arcuri)
He pointed to the italicized d^{x1}. That, of course, refers to distance. I had to give it an exponent and variable to accommodate the quick and profound changes. Increases and decreases you know. then allowing them to bend according to each person's  I mean each character's  view of themselves and one another.

Like his answer to Irma's question of how long he would search for her (he goes into a spiel about integrating the Taylor series for a function, with inappropriate references to Newton and Fermat, the point of which was supposed to be that it was somehow infinite), this seems particularly uninspired when mathematics contains things that really could capture the feelings he was going for.
Perhaps these seem like small complaints, and they are. Moreover, there are a few occasions in which he gets it right. He plays with the word "eccentricity" as applied to ellipses, he talks about "vibrating lattices" (which struck a nice chord with me, that was destroyed a little later when he changed them nonsensically into "vibrating matrices"). But, there are so many of these small mathematical incongruities that it interfered with my ability to appreciate the other positive qualities of the book. In the end, the overall impression that the book leaves me with is that it is nonsense, and I think that is because the author is trying to write poetry in a language which I know and he doesn't. A quote on the back from Karl Iagnemma suggests that at least some mathematically savvy readers may appreciate this book, but my guess is that many will encounter the same difficulties that I had in trying to read it without being tripped up by the mathematical non sequiturs.
As a contrast to my ``mathematical'' opinion, I offer the following quote from the Los Angeles Times' review of the book:
Contributed by
Tod Goldberg, Los Angeles Times
It's engrossing stuff, there's no question. Bajo uses words and equations to the point of poetry, particularly when he evokes the world created by Cervantes and the theories of pendulum mathematics as they relate to Philip's life. The book is less successful  and borderline pretentious  when Irma's own autobiographical novels are referenced at length, detailing the relationship history of the odd couplings as well as Philip's and Irma's backstories.

Contributed by
miki
Maths is not essential to the book, except for placing the main character a bit above the ground. Probably a bit too much of appreciating The Beautiful Mind or some similar story, but not to the unhealthy level. There is something what still echoes in me from Bajo's book even few months after reading it. Maybe the fact that I am into running recently? It actually aroused my interest in running, not maths (I am an astrophysicist, doing numerical simulations of star birth in nonideal MHD, so I hardly need arousing my interest in maths!). I suspect the fact that it lingers so in my mind is indefiniteness, inconclusiveness of parts of the textin this it resembles Murakami in a way.

