Two separate but related fields, mathematical morphology (MM), a particular theory for image and signal analysis, and the larger, more general field of morphological mathematics—which covers the mathematical study of shape and form across many disciplines—are investigated in this paper for their conceptual and practical linkages. Although morphological mathematics offers a rich tapestry of ideas from geometry, topology, and other fields to characterize form, mathematical morphology provides a precise, operator-based approach for evaluating geometric structures. A significant gap exists between MM's specific applications and the broader theoretical potential of a mathematically-grounded study of form. This paper argues for a conscious "entwining" of these two domains. We propose that by generalizing the foundational principles of mathematical morphology using tools from abstract algebra and topology, and conversely, by applying the structured, operational approach of MM to problems in broader morphological mathematics, a new, more powerful synergistic discipline can emerge. This unified framework promises to enhance our ability to analyze complex structures in fields ranging from materials science and biology to data analysis and artificial intelligence. The fundamentals of both disciplines are examined in this study together with an investigation of the present gap and suggestions for theoretical and practical means of their fusion, stressing the possibility for fresh ideas and uses.