The mathematical formulation of theories is a key driver of modern physics' successes, and reflects a foundational principle. Physicists are guided by this principle, and in doing so are granted all the benefits afforded by a hard science. Herein, I argue that this principle has even more to offer. For physicists to make sense of each other's mathematically formulated theories (MFTs) they must share a universal understanding on how to interpret them. In terms of model theory, there must be a (...) set of (basic but) universally accepted interpretations that relate the language of MFTs to meaningful elements. Because these interpretations apply to all MFTs, a model of (just) these interpretations would be a submodel of all models of MFTs. These universally accepted interpretations were, effectively, the bases for Max Tegmark’s mathematical universe hypothesis (MUH). This allowed Tegmark to relate many aspects of quantum and relativistic physics back to his hypothesis. However, Tegmark's goal of accounting for spacetime and quantum phenomena requires a model beyond universally accepted interpretations. I show that as a result, the model described by Tegmark's MUH is not a submodel of all existing models of MFTs. In contrast, I derive a novel model of just these universally accepted interpretations such that all models of all potential MFTs are, effectively, extensions to this novel model. Therefore, this novel model can enhance our understanding of every MFT, and facilitate collaboration and the unification of models across the branches of modern physics. (shrink)