How much math has been involved in what you're mentor does on a daily bases?
Not too much, from what I gathered. My mentor mostly supervises, but he occasionally does math when needed, like for inventory or for a part size.
What part of what you do takes the longest time?
I'd have to say is fleshing out an idea. There are lot's of things to consider when pursuing an idea, all of which take time. I have spent probably more time figuring out solutions to in a design than I have on anything else.