It really depends. Within a given field certain concepts are so common that you really do want a way to express them in the most terse possible way, just as pro

It really depends. Within a given field certain concepts are so common that you really do want a way to express them in the most terse possible way, just as programmers use i for index, err for error and n for counts. This allows you to put more stuff in a smaller space which means you don't have to jump back and forth to understand something -- sort of like how it's nice to put different parts of an app into different files and even to split them up into separate libraries, but go too far and the flow of the application becomes opaque. Have you ever had a chance to read some of those really old mathematical proofs that didn't use any mathematical symbols at all? They're a nightmare to try and understand. There's a tradeoff. No disagreement, though, that mathematicians tend not to be very great at finding the sweet spot where the trade-off balances :-) (Also, the sample mean of y would be `\bar y`, hats are for estimators in general.)