How to decide the appropriate level of explanation for math in academic papers?
I find that the choice of how much explanation to give math is generally a three-way negotiation between three factors:


Your estimate of the audience: different communities will need radically different levels of explanation for the same mathematics.  
Adjustment based on the opinions of the reviewers about what needs more or less details
Any length constraints on the paper.


Of this #1 is really the important thing: you really need to understand your audience in order to decide how in-depth to go with your mathematics.

For example, I recently published a paper which spent several pages explaining a mathematical formulation in depth for its target cross-disciplinary audience.  The reviewers requested further expansion of the mathematical explanation (which I was happy to provide).  Were I writing for the community from which the mathematics came, however, I would instead spend several pages explaining the context of the problem, but then the math itself would be covered in just a few sentences.