For you, personally, the way you do maths, how much does the way forward seem like trial and error versus absolute?
I guess what I mean is that it seems to me that in maths there is kind of a goal that you are seeking, whether it be to solve a particular math problem or simply to direct the mind toward mathematical-type thinking. So the question is, to what extent does the path toward the goal feel kind of "preordained" versus... or maybe what I mean is if mathematics progresses in order (which i suppose is another question in itself but anyway), to what extent do some of the mathematical creatures that are observed turn out to be irrelevant to the goal / to what extent do particular constructions turn out to be unnecessary to the final construction? Do mathematicians allow walking down a certain path and then deciding the path is not important to the solution and turning around, walking back a ways before continuing down a new path, OR, does every path, all the ground that is tread on the way to the solution, contribute something to the solution?
Or as my dad says, it's a philosophical math question about dead-ends in math.