Henry T. “Hank” Greely was interviewed for this segment of 60 Minutes:

Genealogy, researching family history, is one of the most popular hobbies in
the country, right up there with gardening. A nation of immigrants, we almost
all come from somewhere else we wish we knew more about. So searching for our
roots holds tremendous appeal. And today, there’s an exciting new addition to
the genealogist’s tool kit: genetic genealogy. It turns out that inside each one
of us, within every single cell of our bodies, is information about who our
ancestors were, where they lived and who we’re related to today. Our DNA
contains hidden stories about our past, and as we first reported last fall,
scientists, together with businessmen, are now offering ways to help us read
them.

…

STAHL: And that’s the rub. This business of genetic genealogy is
fraught with limitations. For one thing, it can only provide information about a
tiny fraction of our ancestry. Because we get half our DNA from our mothers and
half from our fathers, almost all of our DNA gets shuffled and remixed every
generation, making it impossible to trace what comes from whom. There are just
two bits of DNA that remain pure. The Y chromosome, which passes directly from
father to son, and something called mitochondrial DNA, which passes unchanged
from mother to child. Hank Greely, a law professor at Stanford University, has
studied this new field. He worries that people don’t realize just how many
ancestors they actually have.

HANK GREELY: Eight generations ago, both you and I had 256 great, great,
great, great, great, great-grandparents.

STAHL: Wait, you’re saying that if you go back eight generations…

GREELY: Uh-huh.

STAHL: …we have 256 great, great, great, great-grandparents?

GREELY: Yes. It doubles every generation. So, you’ve got two
parents, you have four grandparents. You have eight great-grandparents. Sixteen
great, great-grandparents. And it adds up fast. It adds up so fast, in fact,
that if you go back 20 generations, you’ve got over a million grandparents.

STAHL: One million, forty-eight thousand, five hundred
seventy-six, to be exact. And in each generation, DNA testing can provide
information about only two of them.

Mr. GREELY: So you could be Peruvian on your mother’s, mother’s,
mother’s side, Japanese on your father’s, father’s, father’s side. Swedish on
everything else.

STAHL: And you’ll never know?

GREELY: And you’ll never know the Swedish from the Y chromosome or the
mitochondrial DNA.