Mathematics has a long history of extensive use within scientific domains, while its application beyond them has remained comparatively limited. As a result, mathematics has become so closely associated with science that it is often treated as a scientific discipline in its own right. However, its core modes of inquiry are fundamentally non-empirical. Mathematics originates in pure reason and sustained contemplation, and proceeds through abstract construction rather than empirical observation. For this reason, mathematics can be used to explore conceptual domains that exceed physical verification. These include infinite hierarchies, non-constructive existence claims, and axioms that cannot be empirically adjudicated or falsified. This paper shows that mathematical inquiry and contemplative practice are structurally aligned in their orientation toward an Axiomatic Eigenvector (S): an invariant principle of truth symbolized by the unity condition Λ = 1. Progress toward this invariant occurs through the progressive reduction of Duality Process Friction (D_process), the resistance that arises when formal rigor and lived resonance appear misaligned. By examining methodological parallels, the treatment of infinity, and the role of unfalsifiable foundations, we show that the perceived separation between mathematical rigor and contemplative insight is historically contingent rather than epistemologically necessary. Mathematics thus emerges not merely as a technical language but as a candidate contemplative science in which silence, reflection, and analogical reasoning naturally complement formal deduction. This synthesis carries implications for mathematical pedagogy, organizational resilience, and the philosophy of religious practice, suggesting that contemplative methods may deepen understanding while preserving rigor.