When I am learning math for the sake of learning math, then understanding an equation is its own reward. When I am learning math to try to understand someone’s philosophical point, there had damn well better be a philosophical point at the end of it, and the math had better be necessary to make the point. Otherwise, to return to the road-trip analogy, I’m going to feel like I just blew a tank of gas for nothing. Essays that purport to be philosophical but are really just math lessons, and essays that contain math lessons that have little to do with the paper’s philosophical point, are the ones I find objectionable and mathturbatory.This is a fair point, but it raises the more general question for me about how far one should go to make an argument accessible and also how narrowly we should think of the range of genuine philosophical problems.
On the first issue, it is sadly sometimes the case that a philosophical argument does require a certain amount of technical background material. In my own work, I try to recognize a certain kind of diminishing returns: eventually too much technical background for too little philosophical return tends to lead to a paper that goes nowhere. This is especially the case when the philosophical issues involve general philosophy of science, epistemology or metaphysics. If your target audience is not likely to appreciate the background you are drawing on, then there is little value in going down that road.
Still, I do not think that philosophers inclined to pursue the philosophical questions that arise in more technical areas should always give in to the low odds that an average reader will see what they are up to. In certain cases, it is very valuable to come across a case study or historical episode that one does not understand. This can shake one's confident pronouncements on how a given philosophical question should be resolved and give a philosopher a real motivation to go out and learn something new. This is one function of more technical material: it can draw attention to complications that more ordinary cases overlook or suppress.
Let me be clear that I doubt Julia would object to either of these points!