When a boy named Sal discovers the burned body of his middle school math teacher, two amateur sleuths try to determine who killed him. One of them is Jake, the volunteer fireman to whom Sal initially reports the grisly crime. The other is Sal's history teacher, one of the few people in town who attempted to befriend the timid and antisocial math teacher since he arrived in this rural Nevada town at the start of the school year.
I suppose I could have guessed from the title that this book would not be a lighthearted comedy, but it portrays a much more depressing view of the human condition than I expected.
The author has an amazing talent for creating tragic and painful tales of misery. Let me give you one example (summarized in my own words) so that you can see what I mean:
Jake was in love with Sal's mother since they were children together. It was love of the unrequited variety, but he was saving himself for her hoping that one day she would come around. Sadly, the first time he went into her home was as an EMT after she had overdosed on heroin. (He cleaned up the scene, hid the drug paraphernalia and reported it as a heart attack.) And, while carrying her coffin at the funeral, he thought about how many times he had imagined walking down the aisle with her in that church, but never in that way. 
Wow, right? But, that's not the only one. Nearly every character in the book  and there are many  has an equally tragic story of woe. There are three fathers in the book who were responsible for the deaths of their own sons and feel overwhelming guilt as a result...all in this same small area in rural Nevada. (I am rarely accused of optimism, but even I don't believe that unbearable sorrow is quite that common.)
I am guessing that the author would also tell us that she is a keen observer of human behavior. The book is filled with details about lies that are revealed by body language, true motivations, and things left unsaid. Sal (short for "Absalom") is described as being especially good at reading people, and some of the chapters are presented from his viewpoint, but this sense of deciphering what people really think rather than what they say runs through the whole book.
Oh, there is also an archeological subtheme concerning the bones of the first peoples in the Americas.
But, aside from the tragic life stories, the details about human behavior, and the archeology, there is also quite a lot about mathematics...and of course the mystery of how the math teacher came to be lying dead beside a campfire with his legs bound by a jump rope.
Before I go into a detailed discussion of the mathematics in the book, let me point out that the mystery is what makes this a page turner. The reader will want to try to piece together all of the information in an attempt to figure out what really happened. The clues are given out slowly, one by one, chapter by chapter, and the final answer will not be revealed until very close to the end of the book. So, if you intend to read this book for enjoyment, you probably want to stop reading this website now.
Spoiler Alert: In the list and discussion below of mathematics in The Distant Dead, I will not be directly identifying the murderer, but I will be mentioning some of the clues.
 Adam Merkel, the murder victim, was an associate professor of mathematics in Reno before becoming a middleschool math teacher in rural Nevada. The book correctly indicates that this is an unusual career trajectory. One of his university colleagues explains his failure to be promoted to full professor as being due to "the usual reasons. Not enough innovation. Not enough publications."
 Merkel fits one of the stereotypes of mathematicians in fiction: he is timid, antisocial, nerdy. His middleschool students call him "Merkel the Turtle" and he tries to ignore it when they mock him openly in class. His one great ability appears to be sharing his love of mathematics in a oneonone situation. He is able to convey the beauty and especially the utility of math to students in that situation. One of the students who likes to hear Merkel talk about math is Sal (who also signs up for Merkel's chess club out of pity). Another student who fell under his spell is his exwife, who took his calculus class when she was in college to fulfill an "interdisciplinary requirement". Finally, there was a brilliant grad student named Lucas who found motivation in Merkel's mathematical soliloquies.
 The reader is supposed to believe that Lucas was so brilliant that he was going to prove the Riemann Hypothesis. The only reason he didn't is that he was arrested for dealing drugs. The university claimed the work he had done on the Riemann Hypothesis was their intellectual property and set some of their professors working on completing Lucas' proof while he was in prison. He blames Merkel for the fact that he is not a mathematician, both because he claims that Merkel was trying to steal some of the glory (and perhaps the $1 million Clay Institute prize money) for himself and because it was Merkel who turned him in to the police.
There is some interesting discussion of this idea that Merkel was trying to unfairly claim credit for the Riemann Hypothesis proof. Merkel would show up to talk with Lucas about the proof, and Lucas saw this as selfish and unhelpful. Sal, despite his youth and inexperience, seems to realize that Lucas may not be giving Merkel credit for the role he played in helping with the proof. In fact, it is not unusual for math researchers to have difficulty weighing the contributions that their collaborators are making and to end up with an impression that they themselves are doing all of the important work while the others are just freeloading.
But, I have some serious problems with this aspect of the story.
For one thing, I can't get myself to believe that Lucas would have proved the Riemann Hypothesis if he hadn't been arrested. All of the characters in the book seem to really believe this without irony or skepticism. In reality, there have been lots of smart people who have thought that they had an approach that could result in a proof but were not able to make it work. You can't be sure that someone can prove it until they have. Either you have a proof or your don't, and Lucas didn't. Since the book gives me no other indication of Lucas' mathematical genius aside from this claim that he could have proved the Riemann Hypothesis if only the law and the university hadn't gotten in his way, I am left with no reason to think that he was as smart as is claimed...but I don't think that was the author's intention.
Moreover, this idea that he was somehow prevented from completing the proof by the university policy is ridiculous to me. I know that universities do sometimes claim that something is their intellectual property, but I think that applies to patents or to data. I've never seen it applied to a mathematical proof and I personally don't think it would hold up in court if anyone tried. (Note that mathematical ideas cannot be protected by either patent or copyright.) And, in any case, they could not have stopped him from working on it while in prison! Number theory research does not depend on having any expensive equipment or data collected from experiments. If he was close to finishing a proof of the Riemann Hypothesis, I would think that a couple of years in prison would be ideal and he'd have finished the proof by the time he got out. Then he would be telling people he had proved the Riemann Hypothesis instead of that he could have done so.
And, if we're supposed to think that the goal here was winning the fame, prestige and money of solving a Millennium Problem prize, then I don't think the university's policy on proprietary research would matter. If the other professors put the finishing touches on Lucas' proof of the Riemann Hypothesis while he was in prison, then as far as the mathematical community and the Clay Institute were concerned, I think the credit would still go (at least mostly) to Lucas!
 Lucas is yet another mathematical stereotype. He's a genius who is not only conceited and obnoxious but also immoral (or at best amoral). Not only was he a drug dealer while working on his PhD thesis, he was also having an affair with his advisor's wife. And, he shows up in the small town where Merkel is working as a middle school teacher with the intention of making him suffer for what he did to him. His plan involves using Sal, and he doesn't mind hurting a child to achieve this goal. It is for these reasons that I've tagged this work of mathematical fiction with the "Evil Mathematicians" motif.
 The book mentions "Pi Day" and Merkel's habit of preparing pies for his students repeatedly, almost to the point that it becomes annoying. While baking pies to bring to school the next day, Merkel defines π for Sal. He describes it in terms of a ratio made from circles which has the same value regardless of the size of the circle and then adds
(quoted from The Distant Dead)
That made it a "constant", which was a special kind of number that helped mathematicians solve equations.

(Note: Although the definition is correct, that last part is not quite right. All numbers are constants, not just the ones that are useful in solving equations.)
 The distinction between pure and applied math is a running theme in the book. It does a pretty good job of addressing that, despite not saying anything particularly novel or interesting. Merkel is said to be mostly interested in the applications of math and the "math stories" he tells Sal mostly involve ways that math helps us understand natural phenomena or even why there are 60 minutes in an hour. In contrast, Lucas is interested in math for its own sake without caring about applications:
(quoted from The Distant Dead)
"No, it's not just a game." Lucas leaned forward, suddenly serious. "It's a beautiful hypothesis. Pure, wicked math, absolutely elegant. And it's true. Everybody knows it's true. But nobody's been able to prove it's true, not even Riemann, even though they've been trying for a hundred and fifty years. How could you not want to prove it, if you could?"

Well, I'm not sure I agree that everyone "knows" the Riemann Hypothesis is true, but I understand his sentiment. (In fact, that's why I find it so hard to believe that Lucas wouldn't have proved RH during his many months in prison if he'd really been able to do so. Read the quote in the box above and ask whether that person would have been deterred by the university's claim that his prior research was proprietary.)
In summary, this is a very sad and dark murder mystery in which the victim is a former mathematics professor, one of the suspects is his former thesis student, and an incomplete proof of the Riemann Hypothesis is one of the possible motives. 