There’s a nerd genealogy joke that goes something like this:

At a cocktail party, Person A is going on and on about their family’s history, saying that their roots go all the way back to Charlemagne. He pauses and says to Person B, “How far does your family go back?” Person B responds, “We really don’t know; the records were lost in the Great Flood.”

Despite the first person's vanity, the simple truth is that he almost certainly is descended from Charlemagne, and so are you, and so am I. If you are of European descent, then you are descended from everyone who was alive in the 10th century Europe, except for those whose family lines died out completely at some point. Let’s say that in a different and more precise way . . . of all of the people alive in Europe during the tenth century, roughly 20% have no descendants today, but every individual one of the other 80% is an ancestor of everyone of European descent alive today.

So you’re descended from Alfred the Great, Charlemagne, some Roman emperors, and a few popes. You are even descended from Mohammed, because his descendants were among those who invaded both eastern and western Europe on several occasions.

How can this be so sure? Well, you have two parents, four grandparents, eight great-grandparents and so forth. If we go back a thousand years, that’s about forty generations of doubling. In that generation, you would have about 1 trillion g-grandparents—far more than the total number of people who have ever lived on earth. That number makes it plausible, but more sophisticated mathematical models provide the results I’ve mentioned above.

You can read more about this at:

http://www.theatlantic.com/magazine/archive/2002/05/the-royal-we/302497/