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No, it's both.

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).

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

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