In databases class, they used Pi for projection, bowtie for natural join, and sigma for row filtration. They added conditions on the operators with subscripts. SQL is just the standardized version of that.
"Standardized"...and without the legibility of symbolic notation and the option to use intermediate named relvars?
It's designed to be "natural", meaning that technical symbols were largely avoided. Someone who knows little about formal notation but a decent amount about databases can usually figure out what's going on. It's also easier to type, seeing how most of the relevant symbols aren't on your average keyboard.