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.
"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."
That doesn't make me any more confident she won't be a progressive activist judge on the Supreme Court.
People who think as you describe it are like those who thought Darwinism proved we can "evolve" society to a central leadership's goals. Perhaps she'd of been better suited for Stalin or Mao's regimes?