With Math, there’s a bit of an exception. You’re not really supposed to know what you want to study. It obviously helps to have research experience going in, but most undergraduates know very little about math (grad school is where you learn it), and many do complete 180s, for example loving algebra throughout undergrad but finding analysis boring, then deciding to study functional analysis in grad school. There’s just no way as a senior in college you’re going to know whether you intend to study p-adic L-functions or the Arf-Kervaire invariant. (You’ll still need to write about some research interests in your SOP, but that’s a different issue.) That said, it seems unlikely a top 10 school in either Math or CS won’t have anyone working in areas you find interesting, should you get accepted at these schools.
Other fields seem to expect you to really know what specifically you want to study at the time of application.