Indeed. One of the schools I was looking at for undergrad was MIT (certainly a prestigious research institution). I asked the tour guide how easy it was to talk to a professor. “Oh, very easy. You just make an appointment with their secretary, and you’ll be able to see them within a couple of weeks!” I opted not to apply.
The most likely outcome is reversion to the mean: After her very bright start, she’ll settle down to become a perfectly competent but basically ordinary mathematician.
Possibly writing a critically-acclaimed novel while in high school, like S. E. Hinton? Discovering a lost work of Shakespeare isn’t really a personal accomplishment; it just means that you went to the right estate sale.