The book was initially released in the UK under the title "White Rabbit, Red Wolf". When I first read a description of the book, it sounded to me a lot like The Curious Incident of the Dog in the Night-time. There are similarities: The protagonist/narrator is a math-loving British boy whose unusual behaviors (he is antisocial, compulsive, overly literal, and apt to recite lists of numbers in times of stress) are a problem for his mother. He unexpectedly gets caught up solving a mystery involving violence. Also like "Curious Incident", although it is marketed as a "young adult" novel, this book seems to be getting a lot of positive press and readership from adults.

So, once I received my copy of the American version (which has been retitled "This Story is a Lie") and started reading it, I was surprised at how different it was. This is much more of an adventure story, involving a secret government spy agency. And, the twins' are able to harness their abilities (fear and mathematical ability for Peter and fighting ability for his sister Bel) as powerful weapons making them almost like comic book superheroes.

I must warn you that Peter is not an entirely reliable narrator. For those of you who would scold me for this "spoiler", I'd defend myself by pointing out that the subtitle of the British version of the book and the title of the American version is "This Story is a Lie", so it should not come as much of a surprise if not everything it tells the reader is entirely true!

Here are some of the mathematical highlights of the book. (I promise...no more spoilers!)

• Peter refers to his sister Bel as his "axiom".
• Peter meets his school friend Isabel when he realizes that they are the only two students in their math class who are already working on the questions near the end of the book (on Lagrange multipliers). They later message each other with user names that reference Kurt Gödel and Georg Cantor. They rank the intensity of their negative experiences using "The Base-Adjustable Logarithmic Scale for Unanticipated Crazy" (a.k.a. "BALLSUC").
• Peter has conversations with the posters of famous mathematicians that hang on his bedroom wall. For example:

  (quoted from White Rabbit, Red Wolf [This Story is a Lie]) I look to the posters on the wall for support. Ten centuries of epic mathematicians stare back: Cantor, Hilbert, Turing. We're all squarely rooting for you, Pete, they say. Maths humor, but you can't blame them. I gaze at Evarizste Galois's pointy face. I feel for you , Pete. I felt the same way before I went into that duel in '32. That duel killed you, Evariste. I think back. You got shot in the gut and died in screaming agony. Good point, he says. Forget I said anything.

• Peter makes an intriguing connection between mathematical recursion (as in the definition of the Fibonacci sequence) and the way we maintain our identity through memory. In fact, he's working on a research project based on this that he hopes will help him understand himself better. This theme runs throughout the book, most obviously in the "flashback" chapters that are titled "Recursion".
• A recurring character in the book is Dr. A, Peter's blind math teacher. Peter uses as a clue the first thing he learned from Dr. A: the product formula for computing the probability that two independent events will both occur.
• On page 175 he talks about the fictions that make life work, like the imaginary number i "that makes bridges stay up and airplanes fly". Then, that same idea (including the bridges and planes) is repeated on page 321 in what I assume is an allusion to the earlier scene and not just an accident.
• Peter uses Euler's topological theory of mazes as trees to get through a physical maze guarding the entry to the spy organization's main headquarters.

I'm also going to complain just a little bit about the discussion of Gödel in this book. First, I do give the author credit for basically getting the math right. There are plenty of complete misrepresentations of the Incompleteness Theorems or their proofs in works of fiction, and this is not one of them. In fact, the title "This Story is a Lie" is used as a way of explaining the proof method based on a paradox, and he even gets into the role of the Gödel numbering system (which is presented here as sort of "code"). Not bad, really. But, Peter reacts to learning of the Incompleteness Theorems the way many other fictional characters do: he decides that if there is no way to know that a proof exists for something he was studying, then he might as well give up! That doesn't make any sense to me, and I'm not aware of any real people reacting that way even though it seems to be rather common in fiction. (Look, most things one would try to prove are really hard to prove, and so it seems more likely that you won't be able to find a proof that exists out there somewhere than that the thing you're working on happens to be undecidable!) In addition, like so many other works of fiction and non-fiction, this book seems to draw some sort of lesson about the pursuit of mathematical truth from the sad tale of Kurt Gödel's delusional state when he died in a hospital as an old man. I am not convinced that this is logical or justified, and it unfortunately has the effect of steering young people away from mathematical pursuits. (Look, lots of people have dementia and delusions when they are old and hospitalized. That's a relatively common occurrence and I don't see any reason to think it was related to his work in mathematics.)

In conclusion, this is quite an exciting tale which includes a good many references to mathematics. If you like violent spy stories with a bit of math and a science fiction twist, then it is worth a look.