There must be no other way than approaching a math problem without notes. Going into it with only the last few pages of work, which probably doesn't even give the answer.
What I envy is having one problem that a mathematician wishes to work on, and doesn't give up until she has exasperated every nook. For me, that problem would have to so boggle the mind that it would seem like I would have to invent something just to make it work. No, I'm not one to finish calculating a list of unknowns to come up with a super-law. No, I'm one to invent from nothing. Challenge authority. I say I can prove that a tangent plane can intersect a sphere in two points. It seems silly, but think what a new math could do! I must use all my psychic powers to do so, but don't tell anyone, just between me and you. Think of the possibilities!