Interesting article in The Atlantic, "The Royal We," talks about a mathematical/statistical approach to genealogy which has some interesting and counterintuitive results: it claims that about 80% of the people in Europe in the year 1000 were each a direct ancestor to every European alive today, and that the other 20% (of people in Europe in the year 1000) have no living descendants.
(The actual year may be somewhat earlier, since the mathematical model assumes that anyone in Europe has an equal chance of marrying anyone else in Europe.)
The article goes on to say:
[A]lmost everyone in the New World must be descended from English royalty—even people of predominantly African or Native American ancestry. . . . Similarly, everyone of European ancestry must descend from Muhammad.
(Presumably "almost everyone in the New World" doesn't include most people whose family immigrated here from places other than Europe in the past couple of generations.)
It seems even more counterintuitive to me to say that all people (of type X) are descended from one specific individual than to say that we've all got a common ancestor or a group of common ancestors. I think that the logical step that's left out of the article is to say that we know that there are some descendants of Muhammad alive today, thus Muhammad must have been one of the 80% rather than one of the 20% who have no surviving descendants, thus he was one of our common ancestors. But I think the article's (and many amateur genealogists' in general) focus on famous ancestors also obscures another important point: saying we're descended from Muhammad makes it sound like a vast downward-branching tree, starting at Muhammad at the top/root and branching out until you reach everyone of European ancestry in the present day. Whereas that model ignores the fact that there were many many other "roots" to that tree, that it's really a vast interconnected tangle, and it's just as accurate to say everyone of European ancestry descended from a peasant named Guillaume somewhere in eastern France who had a lot of kids.
(The article also mentions Nefertiti and Confucius as ancestors of everyone alive today; again that assumes that they have descendants who are alive today, and I don't know whether that's known.)