Often times the symbols may not even be concrete numbers. Often the “real” number may not even be representable on a computer. Often a symbol does represent a concrete number but indirectly defined by some set of rules (e.g., x is the smallest eigenvalue of M; or y is the greatest value less than the supremum of f) that may require a whole library of code to calculate.
The mathematical notation is “meant” to be flexible and manipulated, not to be interpreted (necessarily) as a rigid computational process. It should also be noted that while some notation comes from convention, a lot of it is improvised and contextual!