There is not much said about the mathematics itself. Mostly, the book repeats the idea that he used theorems about permutation theory to work out the rotor positions. The book also emphasizes that something beyond mathematics (especially knowledge of the German psyche that Rejewski gained from having attended German run schools as a child) was also needed to determine the wiring. Marian's love of working on mathematical problems (especially cryptographic puzzles) is portrayed vividly, and sometimes contrasted with his comparative difficulty with words and emotions. (I am curious to know if there is any reason to think that was true of Rejewski, aside from the fact that it is a standard stereotype of mathematicians.) Finally, at the end there is just a little bit about his daughter becoming a mathematician and being able to pursue an academic career, an option that was not available to Marian Rejewski as he was attempting to hide from the communist government in Poland after the war.

I have heard of Rejewski and the work of Polish mathematicians in breaking the Enigma code. (Another work of mathematical fiction to address the same historical events is the film Sekret Enigmy.) However, from those I always got the impression that they had done some foundational work and obtained Enigma machines which helped Alan Turing and his colleagues at Bletchley Park in England to eventually break the code. However, the portrayal in this book is quite different. McGinness leads us to believe that Rejewski really deserves the credit for breaking the code, and that the English basically stole the credit for his work in the 1970s when they first went public with the information that had previously been kept secret. (The book leaves open the possibility that this was not an intentional theft but rather an innocent mistake made possible by the fact that so many of the people involved were dead. However, I think it still strongly suggests otherwise both in the way the procedures have already been given English names at the time that Turing visits Rejewski in Algeria and the way that the Polish cryptologists are not allowed to work on Enigma when they are in England.)

The history presented by McGinness -- a Scottish author living is France -- contradicts what I think I know of history in two ways: by suggesting that the British really do not deserve credit for breaking the Enigma code and by showing Poland to be nothing more than an innocent victim of Germany in World War II, with no blame for the atrocities carried out in their own country. It is always difficult when reading historical fiction to know what parts are known facts, which are speculation the author can support with reasonable evidence, and which are purely fiction created by the author for literary purposes. Unfortunately, the book provides no specific references (aside from a few quotes in the epilogue) that I can check. So, I personally will be consulting reliable non-fictional sources to see whether I really should reconsider my views on what actually happened during World War II. [Update: As of March 2019, I can say that it does seem to be true that the vast majority of the mathematical work on breaking the Enigma code was done by the Polish cryptographers before Turing got on the scene, and that for the past several decades Turing himself has mistakenly been credited with these accomplishments. Of course, Turing did many other great things, but I can't help feeling that this is bad news all around. It is bad for the Polish heroes like Rejewski whose work was not properly appreciated for all of this time, it is bad for Turing whose reputation will surely suffer even though he never publicly made any claims about his role in World War II as it was still classified at the time of his death, and it is bad for mathematics because the idea that Turing's brilliant mathematical ideas for breaking the Enigma code helped the Allies win the war was a good bit of propaganda...but it apparently is not quite true. Oh, well.]

But, regardless of its historical accuracy, I can say that this novel is a well-written and compelling adventure story about a team of mathematicians who played an important role in the allied victory in World War II.