Localization methods：simplifying complexity

Perturbative methods in quantum field theory often encounter limitations in explaining many crucial physical phenomena. Moreover, there remains a lack of general theoretical frameworks for analyzing non-perturbative effects. The introduction of supersymmetry provides a critical pathway to overcome this bottleneck. Leveraging the unique properties of supersymmetry, localization methods reduce infinite-dimensional functional integrals to manageable finite-dimensional integrals, discrete summations, or matrix integrals. This development has established localization methods as a cornerstone tool for non-perturbative computations. This article provides a concise overview of the fundamental principles of localization methods, traces their historical evolution, and highlights their profound implications at the intersection of physics and mathematics.