I got exactly the same impression from my compilers class, especially for parsing - it's a bunch of techniques, which vary in their applicability. I still have that opinion, after years of research and commercial work using parsing.
Although there's some mathematical theory in the background (regular expressions, context free grammars), the techniques don't fully correspond to them, and aren't really implementations of the theory, but a convenient, useful, doable subset. The adoption of the techniques seems to be dictated by what works to solve specific practical problems. The techniques themselves are pretty ad hoc; but they have been studied, and there is a body of knowledge about where each technique is applicable. Although certain correspondences have been proven, it's not neat and beautiful like physics; but truth and beauty aren't what ye need to know here.
Although there's some mathematical theory in the background (regular expressions, context free grammars), the techniques don't fully correspond to them, and aren't really implementations of the theory, but a convenient, useful, doable subset. The adoption of the techniques seems to be dictated by what works to solve specific practical problems. The techniques themselves are pretty ad hoc; but they have been studied, and there is a body of knowledge about where each technique is applicable. Although certain correspondences have been proven, it's not neat and beautiful like physics; but truth and beauty aren't what ye need to know here.
It's really "Compiler Engineering".