Inventio et Mathematica: Is Mathematics Discovered or Invented?

The perennial question---"Is mathematics discovered or invented?''---has long polarized mathematicians, philosophers and scientists into camps of Realism and Anti-Realism, yet both reduce a relation---mathematics---into objects, into a subject or a formal process. This paper proposes a synoptic integration, drawing from philosophy, cognitive science, phenomenology, and mathematical history, to re-frame mathematics as co-constituted by human minds and reality, making plausible that mathematics is both discovered and invented as an emergent phenomenon. Through a critical review of Realism and Anti-Realism, their limitations are exposed and revealed to point towards the thesis, then bridged with Vervaeke's transjectivity and Gibson's affordance. Mathematics emerges not as a fixed entity but as a self-organizing system, driven by a virtual engine of feedback cycles and constraints---enabling invention and selective pruning---historical shifts evidence this evolution. These independent yet convergent arguments, embedded in a broader plausibility argument, form the primary structure of this paper's case for mathematics as a relational phenomenon. This relational ontology resolves the dichotomy, recasting mathematics as a shared, adaptive affordance. Implications suggest a dynamic, collective view of mathematics, with future inquiry into its role in emerging fields like artificial intelligence.