When Mathematical Methods Meet Artificial Intelligence and Mobile Edge Computing

The integration of mathematical methods with artificial intelligence (AI) and mobile edge computing (MEC) has emerged as a promising research direction to address the growing complexity of intelligent distributed systems. To chart the landscape of this interdisciplinary field, we first examine recent surveys that primarily focus on architectural designs, learning paradigms, and system-level deployments in edge AI. However, these studies largely overlook the theoretical foundations essential for ensuring reliability, interpretability, and efficiency. This paper fills this gap by conducting a comprehensive survey of mathematical methods and analyzing their applications in AI-enabled MEC systems. We focus on addressing three key challenges: heterogeneous data integration, real-time optimization, and computational scalability. We summarize state-of-the-art schemes to address these challenges and identify several open issues and promising future research directions.