"We don't do science for the general public. We do it for each other. Good day." -- Renato Dalbecco, complete text of interview with H F Judson I assum

"We don't do science for the general public. We do it for each other. Good day." -- Renato Dalbecco, complete text of interview with H F Judson I assume the same applies to mathematics. I can sympathize with the frustration, but at the same time there's frustration from the other end. It takes a very skilled person who can at once describe something with enough detail to be understood by their peers and also be able to describe the same thing with enough preamble to cover and make clear where any obvious inference level gaps are for a layman. You simply cannot understand factorization (to use the example you've given before) without first understanding several things prior. For general literature, it is better to assume readers have the prerequisites and write for them. When there is confusion people can always do their own study and dive down the definition/link chain themselves. For literature aimed at a beginner of the subject matter, it makes sense to be more verbose and search for other analogies, but you still need to start at some base level and build inferences from there. Start too low, and it takes years, start too high, and it's inaccessible on its own. I remember some math concepts became a lot clearer to me when I realized how I could express them as computer programs, but it wasn't something any of my math teachers ever pointed out. It would have been helpful if they had. Still, having understood the concepts in the new way, I would rather use their mathematical formulation every time as there is no ambiguity and less room for error. Math is beautiful in that it doesn't really care what your internal representations are, in fact most people probably have widely different internal representations (Feynman's story about his friend who counts by visualizing instead of vocalizing comes to mind: https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y0EUlU-Y https://www.youtube.com/watch?list=PLE80C041156D48764&v=Cj4y...) so it's better to be precise independent of internal representation than to always burden yourself with some preferred internal representation that you use for metaphors.