MATHEMATICAL CERTAINTY IN CONTEMPORARY FORMAL SYSTEMS: A SYSTEMATIC LITERATURE REVIEW OF AXIOMATIC STRUCTURES, PROOF THEORY, LOGICAL ARCHITECTURES, AND COMPUTATIONAL VERIFICATION: Bengkulu, Indonesia and Johor Baru, Malaysia - Veggi Yokri; Wahyu Widada; Nurul Astuty Yensy; Norma Alias; Poni Saltifa (Jurnal Math-UMB.EDU, 2026)
Mathematical certainty in formal mathematics is commonly associated with the validity, consistency, and correctness of reasoning within explicitly defined formal systems. However, recent developments in axiomatic foundations, proof theory, non-classical logic, and computational verification suggest that certainty is increasingly discussed as a structured and system-relative phenomenon. This study aims to synthesize how mathematical certainty is conceptualized in contemporary literature through axiomatic structures, proof-theoretic mechanisms, logical architectures, and computational verification. A systematic literature review was conducted using the PRISMA framework. Twenty peer-reviewed studies published between 2020 and 2026 and retrieved from the Scopus database were selected based on predefined inclusion and exclusion criteria. Thematic synthesis identified four interrelated dimensions: axiomatic foundations as formal constraints, proof-theoretic mechanisms as procedures for validating derivations, logical architectures as system-relative frameworks of inference, and computational verification as a mechanism for strengthening reproducibility in formal proof validation. The findings suggest that mathematical certainty in the reviewed literature is not treated solely as a fixed metaphysical guarantee, but may be interpreted as a structurally mediated condition supported by coherence, rule-governed derivation, logical validity, and verifiable formalization. This review contributes a conceptual framework for understanding mathematical certainty within contemporary formal mathematical systems while acknowledging the limitations of a Scopus-based corpus. Keywords: Axiomatic Systems, Computational Verification, Formal Logic, Mathematical Certainty, Proof Theory