Two fundamental problems have long remained unresolved in mainstream philosophy of mathematics: the ontological definition of mathematics itself, and the origin of its extraordinary effectiveness in the natural sciences. From these problems arise a series of undecidable debates: Is mathematics invented or discovered? Is it a tool for describing the cosmos, or the underlying code of the cosmos itself? This paper argues that the root cause of these disputes is the persistent failure to clearly define the two basic concepts of “mathematics” and “the cosmos. ” Based on the PFUSRC biconic ontology, this paper first distinguishes the Universal Universe (a pre-physical, chaotic, structureless state) from the 4D Mother Universe (the primary steady-state topological structure with 45^ triple coaxial biconic geometry, serving as the source of all projection). It further distinguishes projective mathematics (the mainstream axiomatic symbolic and computational systems, which are statistical approximations of ontological structures at the projection layer) from ontological mathematics (the innate relational patterns of the cosmic ontology itself, including the 45^ equilibrium relation, the 12/11 topological ratio, the 55 reference points, the - anchoring mechanism, the unary ontological marking system, and the point-field mode of operation). The central thesis of this paper is that ontological mathematics is neither an external tool for describing the cosmos nor a simulation code for it; it is itself the intrinsic constraint structure of the 4D Mother Universe. All mathematical activities carried out by humans at the projection layer are essentially projective interpretations of these ontological topological relations. This paper completes a dual conceptual clarification and re-anchoring — of the hierarchy of the cosmos and the nature of mathematics — and demonstrates that the many contradictions in both the philosophy of mathematics and fundamental physics arise from conflating the two levels of the cosmos and the two kinds of mathematics. This paper also builds upon the topological conclusions of PFUSRC-044 and PFUSRC-045 concerning the speed of light, the mass-energy relation, spacetime geometry, and cosmic evolution, thereby establishing a unified foundational mathematical-physical philosophy for the entire biconic ontology.
Zhenmin Wang (Tue,) studied this question.
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