I personally have a great respect and love of the intuitive and consider formalism or abstract mathematics only interesting in the service of elaboration or exploration of the intuitive.

Basically all optimizing compilers have a simplifier or rewriter in them. I don't see it as a requirement or even necessarily a priori desirable to frame their discussion or formulation in terms of high barrier mathematical language. Do so if it is fun or useful. Sometimes it is. It is to my subjective taste to do so. Compiler writers are a pretty clever group by and large and are aware of a decent amount of useful math.

There is also a tendency to underestimate where 10 years of study and effort applied to a subject can bring you and attribute it totally to some intrinsic intelligence.

Term rewriting _is_ really neat. Realizing and remembering what you find neat and exciting is important. I like equations.