[JCEccles]

Do you suppose she'll use differential equations to cogitate a landmark decision on the constitutionality of hate crimes legislation?

[The Red Zone]

Boolean algebra would be better suited there.

[AmishDude]

At least she will understand that the Constitution is abstract enough to apply to the modern day. This is a concept that is beyond the grasp of, for example, Breyer.

Undoubtedly, you see mathematics as just another branch of engineering. Just another list of facts and techniques to be known. The mathematician (even an undergrad) does not simply learn a bunch of facts to be applied to a specific situation. She understands all things. That's right, all things. She is not tied down by terminology and past perceptions. All that we know that involves any high-level thought is nothing but mathematics. Her mind has been trained to think of things more deeply, more generally, and to relate seemingly unrelatable things.