This is interesting because paid education has been pretty bad for mathematics in the US as opposed to France which sees a continuous stream of brilliant and successful mathematicians.
It probably should be pointed out that most French-educated famous mathematicians actually came out of schools that pay you to be a student from the undergraduate level (actually third year out of high school).
There is also a continuous stream of brilliant and successful American mathematicians!
Where did they study ? (real question here, because USA is really good at attracting brilliant people from everywhere).
Well, as you might expect, many successful American mathematicians studied at top American universities such as Harvard, MIT, Princeton, Stanford, UC Berkeley, Chicago, Michigan, etc. (Not sure if your were expecting a significantly different answer.)
It's a pretty common pattern for brilliant people to do a PhD in the Ivy league while having done undergrad in some other country entirely. Not sure if that is less or more common than having done undergrad at an Ivy and/or some other US university.
To add to this, foreign students coming to do math in the US have a huge advance compared to other students (due to their educating system being more advanced), and are thus prone to continue over achieving.