|A math professor becomes intrigued with a high school student he meets at an online tutoring site when she presents him with what appears to be a short and very clever proof of the four-color theorem. At first, the plot seems to center on ethical questions, such as whether they should meet in person and whether his feelings for her are appropriate. However, things take a more serious turn when he is arrested for her murder.
It is nice to see a book with mathematical characters (several professors and one prodigy) that avoids the stereotypes and tell-tale errors that plague many works of mathematical fiction by non-mathematicians. So far as I know, the author with the pseudonym "Lior Samson" has no advanced mathematical training, but references to such popular math standards as non-Euclidean geometry, P vs. NP, the Poincare Conjecture, Euler's formula, the Fibonacci sequence, and mathematicians' Erdős numbers all are all accurate, even if they have no deep insights or intimate connection to the murder mystery.
A few brief notes about the mathematical aspects of the book:
- For those who may not know, The Four-Color Theorem is an actual result in mathematics which basically says that if you draw lines to divide a region of the plane into separate pieces (which you can think of as nations on a map, hence the subtitle of the book), then it is always possible to color the regions with only four colors so that no adjacent regions are the same color. This is an interesting result (you might think that a complicated map would require more than four colors), but it is most famous for the fact that the only known proof is both extremely long and relies on the use of computers to check many different cases.
Probably the most interesting mathematical idea in the book is the notion of finding a short and sweet proof of the Four-Color Theorem using a computability approach a la Turing. However, no details are given and I do not really see any way to make sense of this idea, so I think it may have mostly been justification for the pun that this is de-Turing (detouring) from the usual combinatorial approach. In any case, the structure of their discussion of the proof, such as when he finds an error in one of her lemmas and tries to convince her to fix it, seemed realistic even if I do not think the approach makes much mathematical sense.
We see some glimpses of the life of an academic mathematician, with a twist since the character works part time at a number of institutions in Massachusetts rather than having a more standard tenure track appointment at a single institution.
- The least believable mathematical dialogue to me was the discussion of P vs NP. I would not think a mathematician would say that it would be bad for computer science if P and NP are found to be inequivalent. It would be a surprise to many of us if they are equivalent, but not necessarily a good one. True, it would mean that there is some way to do quickly big calculations that must take a long time using current methods. However, it would not necessarily tell us what those methods are (and so we still might not have access to those methods), and furthermore it could also have negative consequences in Internet security since if those "fast" algorithms were ever found it would render all current encryption standards useless.
- A minor side-story seems to be based on the notion that mathematical "genius" is genetically determined. Is there any reason to think so? Although I know of a few instances of famous mathematicians whose children also became famous mathematicians, I am not aware of any in which the children were not raised by those parents, in which case it becomes difficult to tell whether it is genes or environment (or coincidence) that are responsible.
- I have associated this work with the tag "Fictional Mathematics", even though most of the math discussed in the book is real, because the girl develops a new method called "canonical reduction theory" in her attempt to prove the theorem. (In an epilogue we see what becomes of this theory even after its inventor's untimely death.)
As a mystery in the "falsely accused suspect must find the real killer" sub-genre, it was also pretty good. There were a few surprises, interesting sub-plots, and clear prose. Sexuality is a major component of the story, and the situations presented are intentionally (I presume) ethically ambiguous. For both of these reasons, I would hesitate to recommend this book to younger readers, but otherwise I think it would appeal to a wide audience.