This paper examines the mathematical foundations underlying modern artificial intelligence systems, analyzes current limitations, and explores emerging paradigms that will shape the future of AI. Through a comprehensive review of the recent literature and mathematical analysis, we investigate key areas, including neural network architectures, optimization algorithms, and theoretical frameworks. Our analysis reveals that while current AI systems demonstrate remarkable capabilities in specific domains, fundamental mathematical and computational constraints limit their generalization and reasoning abilities. We propose a framework for understanding these limitations and discuss promising research directions that include quantum-enhanced machine learning, neuromorphic computing, and hybrid symbolic connectionist approaches. The paper concludes with recommendations for future research priorities and policy considerations for the development of artificial intelligence.