The US won the math olympiad this year, and is pretty much always near the top. You might want to check out where certain highly praised European countries tend to come in every year by comparison.
The US has one of the highest GDP per capita levels, at $56,000 (#5 for 2015, behind only a few tiny nations), to go with one of the highest median incomes - you don't accomplish that without some amazing education output. The US leads in nobel prizes globally. The US leads in general innovation, R&D, and sheer scientific output. Its universities are productive in that regard in ways nobody else comes close to. Its economy is also one of the most productive.
The US leads in space, space tech, aerospace, medtech, biotech, pharma, software, Web, Internet, mobile, agriculture, entertainment, defense tech, is one of the leaders in computing hardware, and is also one of the leaders in pretty much every type of energy technology. It's also the world's #2 manufacturer.
So yeah, the US does a lot of things really really well. You don't accomplish all of that, and manage to produce such a massive economic engine for over a century, with extremely high output levels per capita, without at least a decent education system to go with it - which is why so few countries can match up to the US economically or scientifically.