"There is a well-known gap between metamathematical theorems and their philosophical interpretations. Take Tarski's Theorem. According to its prevalent interpretation, the collection of all arithmetical truths is not arithmetically definable. However, the underlying metamathematical theorem merely establishes the arithmetical undefinability of a set of specific Gödel codes of certain artefactual entities, such as infix strings, which are true in the standard model. That is, as opposed to its philosophical reading, the metamathematical theorem is formulated (and proved) relative to a specific choice of the Gödel numbering and the notation system. Similar observations apply to Gödel and Church's theorems, which are commonly taken to impose severe limitations on what can be proved and computed using the resources of certain formalisms. The philosophical force of these limitative results heavily relies on the belief that these theorems do not depend on contingencies regarding the underlying representation choices. The main aim of this talk is to put this belief under scrutiny by exploring the extent to which we can abstract away from specific representations in the formulations and proofs of several metamathematical results. The talk is based on technical results which are contained in the following three papers: (2024) A Step Towards Absolute Versions of Metamathematical Results Journal of Philosophical Logic, 53: 247–291 [Official Publication (open access)] (2023) Self-Reference Upfront: A Study of Self-Referential Gödel Numberings (with Albert Visser) Review of Symbolic Logic, 16 (2): 385–424 [Official Publication (open access)] (2021) On the Invariance of Gödel’s Second Theorem with regard to Numberings Review of Symbolic Logic, 14 (1): 51-84 [Official Publication (open access)]"