The narrator is an astronomer who has developed a mathematical theory of abductive reasoning and proved something called a "comprehensibility theorem". Although they were developed to help him select interesting hypotheses to pursue in astronomy research, a mysterious billionaire entrepreneur decides they will be useful skills for the team he is assembling to solve the mystery of what happened to the United States of America and so recruits him. (You see, in all of the different universes the USA has been missing for several decades, although most people haven't noticed it.)

There is much fun and excitement to be had as characters bounce between alternative realities, comparing who won World War II, when things were invented, and even personal timelines (as when he and his fiance realize that they disagree about when they met and when their cat died). There is also action as they are pursued by multiple copies of the fearsome rogue police officer known as Billie Beard.

The math gets discussed quite a bit at the beginning of the book especially during the astronomer's "job interview" with the billionaire.

He briefly uses his mathematical reasoning again in the middle of the book, to try to figure out what is going on. And, the word "finity" is used once (without much explanation) towards the end.

However, the math does not end up playing much of a role in the actual plot. In fact, for me, the end of the book did not involve enough of a "pay off" in any way. It was not satisfying emotionally or logically. So, if you choose to read this book, I recommend you "enjoy the ride" and not worry too much about where it's going.