Somewhat off topic rant, but am I the only one who find mathematical notation unnecessarily obtuse?

The bit that gets me is defining degree as n-1. For someone without a mathematical background, it takes a bit of pondering to figure out that you have to define n as one more than the actual degree, the opposite of what seems natrual. My mind at least just wants to think about n as the degree, and use n+1 as the last index. To me it seems aggressively unintuitive.

I guess you want to align the coefficient numbers but would it be a sin to define another index c = n-1 for that purpose?

But I'm a mathematical lightweight and maybe mathematical thinking is all about this. Perhaps some greater talent can correct my thinking.