Although the end goal of a PhD is a specialized thesis, the first couple of years generally involves courses with a wide coverage of analysis and algebra at the graduate level.
Given her achievements, I'd be very surprised if Cairo hasn't already covered the material in an undergrad degree
The purpose of high school is to give you a wide foundation on everything.
The purpose of an undergraduate degree (in math) is to give you a wide foundation (in math).
In a (math) PhD, you are generally hyper-specialized in a very, very narrow area (of math).