In science and math, the U.S. is ahead of only the really poor OECD countries -- Turkey, Mexico, etc. So yes, there is reason to worry.
Worry about what? If Dan has anything in common with Thomas Friedman, he's concerned about technology loss.
Theory is if Americans don't invent the "next big thing," we'll lag behind the rest of the world. In order for us to benefit from technology we have to create/own it. That's akine to thinking that if oranges aren't grown in the US, we won't get them.
The key is trade. It doesn't matter what nationality owns technology (though it does matter for government, but that's another story); it only matters if there's free trade. Suppose Korea invents the flying car and we don't. Does that mean we don't get the benefits of them? Not if there are few barriers to trade. And if we get the benefits, who cares who owns what? Do bananas stop being bananas if they are grown on foreign soil? Of course not.
Trade, of course, requires that we have something to give up in return, but that thing could be anything the Koreans marginally value more than we do. It could be art or McDonald's or Google ads. As long as we are free to trade, relax and stop scaring everyone!