When I took my process thermodynamics course as an undergraduate student, I was told to use what I had initially considered to be a completely redundant notation for partial derivatives for thermodynamic potentials. The notation involved wrapping the partial derivative in a set of parentheses and noting which variables were “held constant” as a subscript.
The derivation leading to this was woefully devoid of the mathematical basis for this apparently redundant notation. Furthermore, so was the general literature on the subject, most of which consisted of fleeting introductions to their respective application. As I played with the idea, it became clear why this notation was indeed very necessary. It was only as I was solving a separate problem on my own that such notation yielded valuable information about the nature of the potentials being described.