All programs can be mapped to a more traditionally mathematical representation, no matter the level of abstraction. You gain reasoning ability, nothing is lost.

Programming language research has also shown that there are many mathematical structures, e.g. in lambda calculus, category theory, graph theory etc. that map directly to useful computational structures. These tend to be more rigorously defined and more generic than the programming equivalents, which are often limited, ad-hoc, special case instantiations of more general structures.

This argues for the opposite of your claim: if you want to reason about programming, you are seriously limiting yourself and your ability to reason about programming by ignoring the mathematical models that underlie the code you're working with.