This book takes place in an alternate universe where things turned out slightly differently than they did in our own. The Beatles released a reunion album in the 1980s. The UK suffered a bitter defeat in the Falkland Islands. And, most significantly, rather than submitting to chemical castration and committing suicide, mathematician Alan Turing chooses to go to prison after his arrest for homosexual activity.

The consequences of Turing living beyond 1954 are far reaching. Turing becomes a wealthy entrepreneur (like the famous silicon valley CEOs of today). The internet and associated technologies that we think of as being 21st century inventions are commonplace in the last quarter of the 20th. And, the artificial intelligence capabilities available to people in that world in the 1980s are well beyond anything we have achieved in reality in 2019.

The advances in artificial intelligence are specifically attributed to Turing's mathematical research into the "P vs. NP Problem". For those who may not know, this is a real open question at the intersection of mathematics and computer science about how many steps it would take to answer certain sorts of questions involving n objects, where n some positive whole number. (Think, for example, about factoring a number with n digits or figuring out the shortest path that takes you to n different locations.) In general, increasing n also increases the number of steps required to find a solution, but the open question is whether it always grows like a polynomial in n or whether some problems grow so quickly in complexity that it grows faster than any polynomial. As far as I know, the real Alan Turing never worked on that problem. But, in Machines Like Me, he begins thinking about it while in prison and many years later proves that "P=NP". In other words, he (together with unnamed co-authors) has proved that indeed the number of steps to answer the question can grow at most as a polynomial in n. This, in turn, implies that there is some short and effective way to answer questions that we currently think are too time consuming for a computer to answer in practice. Moreover, his proof apparently revealed how to do these computations quickly, and his ability to create amazing artificial intelligences is a consequence:

For the first half of the book, Turing does not appear as a character but only as someone who clearly shaped the world in which the story unfolds. But, through Charlie, we get to meet Turing on three occasions: a chance encounter at a restaurant, an invitation to Turing's house to discuss the sad fact that many of the artificially intelligent androids are choosing to commit suicide, and one more time (which I won't describe in greater detail to avoid spoilers) at the very end of the book, giving Turing the opportunity to review and bring closure to some of the philosophical themes of the book.

I spotted many ironies associated with Turing, which I assume the author intended. The suicides of the androids whose minds run on the fictional Turing's algorithms are surely some a reference to the suicide of the real Alan Turing. The narrator does mention Turing's role in the Allied victory in World War II (something that is also true in reality, although his role has been diminished in recent years as the contribution of others has come to light), but the book also attributes the British loss in the Falklands to Turing in that the Argentinian weapons used algorithms that he developed and released for free public use. The book never specifically mentions the Turing Test, but there is a scene in which Miranda brings Charlie (her fiancé) and Adam (their android) to meet her father and even after the visit the father is under the misimpression that Adam is the human fiancé and Charlie is artificially intelligent. Charlie eventually realizes that he has been mistaken for a robot and has some fun playing along with the error in a sort of reverse "imitation game".

Alan Turing appears in quite a few works of mathematical fiction (see here), and it is interesting to see where this novel fits in with that specific body of literature. There are some in which he is portrayed as being especially autistic or mentally unstable, with two extreme examples of that being the recent film Imitation Game and the novel A Madman Dreams of Turing Machines. There is none of that here; McEwan's Turing seems quite "normal". It is also worth mentioning that this is not the only work of speculative fiction to imagine Turing somehow living on beyond 1954 in some form or other. (See also Oracle, Tangents and Turing (A Novel About Computation).)

There is a tiny bit more mathematics in this novel than what I mentioned above. Adam, the android, twice explains how he uses Bayesian probability models, not only to improve Charlie's investments but also to make predictions about the outcomes of future events in their own lives. Charlie tries to read about P vs. NP, noting the use of the technical notation "iff" and quoting a Field's medalist, but in the end doesn't really understand it. He briefly ponders going to university to earn a degree in mathematics. And at one point he thinks of Miranda in mathematical metaphors:

This novel masterfully fits together many different pieces, some of which have connections to mathematics, to produce a lovely and thought provoking whole.