You make a lot of points that I agree with. I just don't think your solution is the right one. Math, when it comes to writing proofs and peer review, should abs

You make a lot of points that I agree with. I just don't think your solution is the right one. Math, when it comes to writing proofs and peer review, should absolutely be optimized for other experts. Whatever makes communicating ideas precisely among themselves is what's important here. I don't see the benefit of changing this process so those of us as outsiders can take a peek. But as you said, there is a very large part of math that deals with applying these concepts and communicating them to non-mathematicians. The way we go about this is definitely in need of a do-over. Finding more intuitive ways to communicate these ideas is critical a critical part of this (possibly including more descriptive variable names). But, I think there will always be an inherent chasm between the math experts and those who are using the results they discover. An example is the difference between the calculus track of courses that every science major takes, and say, abstract algebra. The math that mathematicians do and the math that the rest of us learn will always be vastly different. It's just the nature of the beast.