The Epistemology of Mathematics: The Identity M ≡ P + N as an Equation of Cognitive Emergence

This essay formulates and grounds the fundamental identity M ≡ P + N, where Mathematics is understood not as a Platonic realm of ideal entities but as an emergent language arising at the interface of Physics (above all, gravity as the universal structuring interaction) and Neurophysiology (the embodied biological processor that evolved to navigate this physical reality). Key concepts are introduced and linked into a unified diagnostic framework: the cognitive emergence function f: N × P → M; the infinity generator G_∞ as the algorithmic potential for unlimited iteration; the processual operator Proc, which restores an object to its genesis; the cognitive extrapolation operator Ext, which explains the emergence of higher mathematics from the recombination of basic patterns; the systemic resonance coefficient Kᵣes as a measure of the coherence between cognitive patterns and physical laws; the gravitational calibration coefficient γ; the reification entropy Sᵣeif as a measure of a concept’s detachment from its processual genesis; and mathematical truth as Resonance (N, P). The theorem of processual incompleteness is formulated, linking Gödel’s theorems to the fundamental processuality of thought. It is shown that fundamental mathematical concepts are not static objects but “frozen” processes. The paradoxes of foundations are interpreted as predictable points of reflection, diagnosable through the ladder of abstraction. A closed loop of cognition P ⇄ N → M is formulated with concrete historical examples. Prognostic implications are outlined for AI, quantum gravity, and the possibility of multiple mathematics.