It's funny because the math and physics majors I have met have in many cases been creative. I feel like they are special because I feel math and physics requires a level of abstract thinking that fuels creativity and on the other hand they have the hard science skills.

Yes engineering is all mathematics but I feel like since it is so application based, there is little room for creativity since many places in private industry do not pioneer products, but simply make widgets to supply to the next tier of company.

I think it's time I reconsider dropping this engineering Ph.D for a math Ph.D, I haven't had a conversation with this friend in quite some time now haha.