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 (Universitas Muhammadiyah Bengkulu, 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