| This is a decent but familiar and unremarkable murder mystery, the kind in which an odd assortment of people are trapped together in a house, not knowing which of them is the killer. In this case, they are stranded in the country home of a retired doctor by a blizzard and power outage. The guests include a famous dancer, a gossiping radio host, and a classical pianist (who is suing the doctor for malpractice). There are also two attractive love interests for the protagonist: a flirtatious and rich woman who follows him around and the doctor's strong-willed daughter. The fact that it was written early in World War II (well, early for the US, which had only just entered the war at that point) and is about the importance of cryptography to the Allied efforts is the most interesting thing about it.
Of course, the book would not be listed here unless there was some mathematics to discuss. The main character of the book, from whose perspective the entire book is presented even if it is not in first person, is a young mathematician who arrives at the house to see the doctor just before the drama unfolds. He came because he realized that the doctor, a complete stranger to him, seemed to be ruining his life. For example, the doctor somehow ensured that he did not get hired at universities as a math professor despite his qualifications for the job. Of course, he is angry at first. However, when the doctor reveals to him the important work he is doing on codes for the State Department and convinces him that his mathematical expertise is required, he immediately begins treating the doctor like a revered mentor.
There are a few good mathematical passages in the book. I like the discussion between the doctor and the mathematician about the latter's published papers on the mathematics of cryptography. And, there are quite a few brief mathematical references tossed out throughout the book. Unfortunately, the thing that most sticks in my mind is the book's repetition of a common misconception. At one point, the mathematician insists that the theory of probability is wrong and that he has an alternative approach which is better. His evidence that probability theory is incorrect is the statement that "if a coin is flipped 10,000 times, the theory of probability predicts that you will get 5,000 heads and 5,000 tails", but in practice people rarely get such an even split. In fact, probability does not make such a prediction. (According to theory, the probability of getting exactly 5,000 heads in 10,000 coin flips is less than 0.01. So, the fact that people would not often get exactly that many is hardly a contradiction.) One reason this misconception persists is the fault of those who choose the technical terminology. Probabilists, unwisely IMHO, have chosen to call this number the "expected value", which understandably gives people the impression that the probabilists actually expect to see that come up when the experiment is attempted. But, this is just a poor choice of words and not what they actually mean. For instance, if you played a game in which the score can be 1, 2, 3, or 4 points with equal probabilities (e.g. spinning a fair spinner divided into quarters), then a probabilist would say that the expected value of your score is 2.5. This does not mean that anyone expects you to get a 2.5 when you play it, since that score is not actually possible to achieve with a spin. Instead, this says something about the average of the scores after many, many repeated games. (Actually, about the limit of that average as the number of games goes to infinity.) Similarly, the significance of 5,000 heads is that if you repeat the experiment of flipping a coin 10,000 times over and over again, 5,000 heads is what you'll eventually see as the average number of heads among the many experiments.
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