I would have taken a lot more psychology and a lot less circuit analysis and math. But I would certainly have taken an engineering degree. Yes, I would have persisted in my original intention of doing more engineering and math. As the field has matured, the involvement of students in official activities has changed. The CHI Doctoral Consortium.
Students are the lifeblood of a field.
An ability to get outside of themselves, to look at a problem as someone else might, to put oneself in another's shoes. This is the heart of understanding UI design. We design not for ourselves, but for our users. Good programming and math skills help a lot, although it's not the only possible way. Good students often develop interests that really get them into some topic or other that they start being an expert on.