A mathematician doing math is more akin to a processor executing instruction than a developer doing programming. When you have to reference a variable X in your head 1000 times (an underestimate) in the process of working on a problem, it makes immense sense to name it X rather than DescriptiveVariableName.
In fact, in my own research for my Master's degree, I only made breakthroughs once I simplified the notation. And we're talking about a change like Q(x,y,z) -> Q, Q(x,0,y) -> Q_2^0, dQ(0,y,0)/dx -> Q_{1,3}^{1,0}. The power of concise notation can be quite a bit greater than that increase in opaqueness it creates.
The way math is communicated suffers from this, for sure. However, you gotta think about what will happen once you read a paper that has more descriptive variable names. You sit down to prove a few results. You start manipulating concepts and symbols. You end up shortening the names until you basically come up with your own concise notation. The thing is that how math is read is very much linked to how math is done.
In fact, in my own research for my Master's degree, I only made breakthroughs once I simplified the notation. And we're talking about a change like Q(x,y,z) -> Q, Q(x,0,y) -> Q_2^0, dQ(0,y,0)/dx -> Q_{1,3}^{1,0}. The power of concise notation can be quite a bit greater than that increase in opaqueness it creates.
The way math is communicated suffers from this, for sure. However, you gotta think about what will happen once you read a paper that has more descriptive variable names. You sit down to prove a few results. You start manipulating concepts and symbols. You end up shortening the names until you basically come up with your own concise notation. The thing is that how math is read is very much linked to how math is done.