The study of genealogy is full of fascinating discoveries that even “outsiders” appreciate.
I was not a math guy in school, but one of the most intriguing elements of genealogy is simply due to math. The formula for the number of ancestors in a given generation is 2 to the nth power where n is the number of generations back. So if you go back 10 generations to your eight-greats-grandparents, you have a thousand of them (1024 actually). A thousand people in that generation and another thousand people between that generation and you. So 2000 people in your family tree. An excellent chart for reference is here at Diana Gale Matthiesen’s 16,000 page genealogy site.
The related concept of “pedigree collapse” is also pretty wild. If you double the number of people in every generation as you go backward, you soon get to a point where the number of people in that generation exceeds the known population of planet Earth. Pedigree collapse (or implex) is the explanation, sort of whimsically discussed here and given fuller but still accessible treatment here. The two most intriguing corollaries of this are the idea that (1) the number of ancestors alive at any one time reaches its maximum at around the year 1200 AD — not that long ago! — and that (2) some geneticists believe that everyone alive today as it most a 50th cousin to everyone else alive today.
A handy aid in figuring out relationships between distant family members is the Canon Law Relationship Chart. Simple to use, it only requires you to know two things: the relationship of person A to the common ancestor, and the relationship of person B to the common ancestor. The common ancestor is at the tip-top of the diamond, person A goes down one side, person B goes down the other, and you draw your fingers inward to the point where those two lines meet. You have the relationship (cousin) and the generation (times removed) all figured out for you.