The fact that mathematician Alan Turing is name-checked in the title does not make this mathematical fiction. (The "Turing Test" is not really math, IMHO.) Nevertheless, since Minsky has degrees in mathematics, it is not terribly surprising that math gets mentioned occasionally in the course of the novel. Here are some examples, all relating to the aforementioned prodigy, Brian:

• Brian's step-mother recalls meeting his father, a jaded math professor at a small university. (This part is a bit sexist by today's standards. Essentially, she enters a loveless marriage with this man because she was single and 32.)
• As a young boy, Brian independently discovers the properties and importance of prime numbers. (Of course, he doesn't use the correct terminology...he calls them "chunky" numbers.)
• In another part that seems sexist today, he helps a female classmate with her math:

  (quoted from The Turing Option) "In fact it wasn't even your fault anyway," he said. "Old Betser may be a wizard programming mathematician but he doesn't know a gnat's fart about explaining it to anyone." "What do you mean?" She was interested now, reached out and broke off a corner of his sandwich. He noticed that her teeth were very white and neat, her lips red—and that was without lipstick. He pushed the remains of the sandwich over to her. "He's always going off on tangents, getting sidetracked into explanations that have nothing to do with the material he should be teaching, things like that. I always stay a chapter ahead of him in the text so he won't confuse me when he starts to explain something." "Amazing!" Kim said, meaning the thought of reading a text you didn't have to when there were so many other wonderful things to do. "Can you do better than him, Mr. Smartass?" "Run circles around him, Miss Birdbrain. Using the heretofore totally secret Brian Delaney lightning instruction system all will be made clear! In the first place, it's not really so important to know exactly how to solve each problem." "That sounds stupid. How can you solve a problem if you don't know how to solve it?" "By doing just the opposite. You can learn a lot of ways not to solve it. A lot of wrong methods not to try. Then, once you find the most common mistakes, you can hardly help doing the right thing without even trying." He remembered exactly where she had gone wrong and knew at once what her misunderstanding was. He explained it patiently, two or three ways, until she finally caught on. "Is that what my trouble was! Why didn't Beastly Betser explain it like that? It's obvious." "Everything is obvious once you understand it. Why don't you work through the rest of those examples while this is clear in your head?" "Maybe tomorrow. Got things to do, gotta run." Run she did, or at least trotted out of the dining room, and he shook his head as he watched her go. Girls! They were a strange breed.

• A fictional field of mathematics called "excluor geometry" is mentioned, though it does not sound especially mathematical when described:

  (quoted from The Turing Option) Brian read as well, a copy he had printed out of a tutorial article by Carbonell about the new mathematical field of excluor geometry. It was a subject of psychology, concerned basically with the question of why people begin to use diagrams whenever verbal explanations get too complicated. This was because language is still fundamentally serial and one-dimensional. We can say former or latter—but there is no easy way to refer to four or five things at the same time.

• A passage intended to show what it is like for him when memories suddenly appear in Brian's brain uses the field of topology as the topic...but also squeezes in an insult to pure mathematics in the last sentence:

  (quoted from The Turing Option) "Now that is what I call very interesting. Didn't I say when I came in that I knew little or nothing about the mathematical field of topology? Well I must have been very tired or something, just not concentrating. But now I remember my thesis very well. It had a lot of what was new stuff at the time. It started simply by using an algebraic theory of knots based on the old Vaughn Jones polynomial to classify chaotically invariant trajectories, then applied this to various physics problems. Nothing very inspired and I'm sure that it must be pretty old hat now. I'm beginning to understand why I quit pure math and went into AI."

Although it takes the form of a hybrid mystery and science fiction novel, the exposition of the scientific ideas seems to have taken precedence over both the plot and the quality of the writing. According to Minsky, this collaboration came about when Harrison told him that the ideas in his (non-fiction) book "The Society of Mind" would reach more people if it was embedded in a work of fiction. That has not turned out to be the case, at least in part because many readers and reviewers have complained about its literary quality. (See, for example, ‘The Turing Option’: Novel Owes More to Science Than to Art.)

Nevertheless, some readers found it worthwhile to read this book as a way to encounter some cutting edge ideas from artificial intelligence in an entertaining form. That may have been a valid argument shortly after it was published. But now, that it is nearly the year 2023 when the story takes place, it is more interesting to see which of their predictions about the future proved correct and which are (almost laughably) wrong.

Thanks to Vijay Fafat for convincing me to include this novel in this database of mathematical fiction.