Being involved without involving!

While solving mathematical problem I get so engrossed into it that I dont remember any other thing. I get so involved that I become a part of that problem solving, or can say I become the problem solving. This is good, but another philosophy which I am currently practicing, is I want to get involved with the act of problem solving without getting involved means, I can see myself doing the problem solving. I feel its possible, do you feel.
Means you become a second person seeing yourself doing a job!