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According to this article in The Atlantic back in May 2002,

The mathematical study of genealogy indicates that everyone in the world is descended from Nefertiti and Confucius, and everyone of European ancestry is descended from Muhammad and Charlemagne

The article further states (in paragraph 8):

The idea that virtually anyone with a European ancestor descends from English royalty seems bizarre, but it accords perfectly with some recent research done by Joseph Chang, a statistician at Yale University. The mathematics of our ancestry is exceedingly complex, because the number of our ancestors increases exponentially, not linearly.

and in paragraph 9:

In other words, all Europeans alive today have among their ancestors the same man or woman who lived around 1400.

and in paragraph 12:

This constant churning of people makes it possible to apply Chang's analysis to the world as a whole. For example, almost everyone in the New World must be descended from English royalty—even people of predominantly African or Native American ancestry, because of the long history of intermarriage in the Americas. Similarly, everyone of European ancestry must descend from Muhammad. The line of descent for which records exist is through the daughter of the Emir of Seville, who is reported to have converted from Islam to Catholicism in about 1200. But many other, unrecorded descents must also exist.

and in paragraph 13:

Chang's model has even more dramatic implications. Because people are always migrating from continent to continent, networks of descent quickly interconnect. This means that the most recent common ancestor of all six billion people on earth today probably lived just a couple of thousand years ago. And not long before that the majority of the people on the planet were the direct ancestors of everyone alive today. Confucius, Nefertiti, and just about any other ancient historical figure who was even moderately prolific must today be counted among everyone's ancestors.

Has this study or reasoning since been rejected?

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    What about European Jews, aka Ashkenazim? Are they descended from Charlemagne and Muhammad too? I think the answer is pretty obvious. – user6136 Jul 5 '17 at 3:47
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    It's a statistical argument with unfounded assertions that cannot be backed up by research. Sure there's a lot of ancestors in my tree but unless we can measure the degree of mixing, a statistical trick is all it is. I don't need to refute the argument. These guys need to prove it - that's how science works. Probability is not proof. – AdrianB38 Jul 6 '17 at 10:07
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    This is a statistical argument based upon the fact that you cannot double the number of your ancestors every generation without rapidly exceeding the population of the planet. While statistics is not proof, it is not disproof either. A paper from 2004 discusses this and has further links to various arguments: dept.dawsoncollege.qc.ca/finearts/Faculty/AManniste/… – Chenmunka Jul 6 '17 at 12:13
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A very easy way to challenge the article is to highlight that there are still races in the world and not a single mixed race.

What the article tries to demonstrate is that, the more generations moving in the back, the more ancestors and the more likely 2 random persons will have a common ancestor. This is a plausible argument, for example, 10 generations back means 1024 ancestors, which is a significant amount of people, how likely is that those 1024 are not from the same city. Actually pretty likely.

But... one thing is arguing that statistically those 1024 persons are not from the same location and another is saying that one is Asian, 10 of them egyptians, 3 australians...

We are living today in a situation that has not happen before in the world, the transportation means are accesible to the population and the developed countries are having strong connections and not in war constantly. Today the probability that a person mates somebody from a different country is relatively high.

What was the probability that an egyptian was mating a hitite during Ramses II war period? Extremly unlikely.

So, although the number of ancestors will be high, also the chances of those ancestors were mating others based in distant cities was also reducing. There was only one Marco Polo, and I do not know if left descendants in China.

That's essentially why have races. Saying that, biologically is demonstrated that we all have common ancestors, which is basically called mithocondrial Eve and Y-Adan.

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