Journal of Modern Technology and Engineering

he evolution of AI can be interpreted as a succession of mathematical frameworks that have progressively redefined the modes of representation, learning, and information processing. After symbolic approaches based on formal logic, then statistical approaches centered on inference and optimization, the rise of deep learning has fostered a geometric interpretation of representations through latent spaces and high-dimensional data structures. Despite their remarkable performance, contemporary architectures still face several limitations, particularly regarding out-of-distribution generalization, context integration, explainability, causality, and the robustness of representations. Based on a conceptual and epistemological analysis, this article examines to what extent certain recent developments in mathematics could contribute to broadening the theoretical foundations of AI. Three mathematical families are studied in particular: manifold theory, category theory, and topos theory. The first provides tools for analyzing the geometry of learned representations and latent spaces; The second approach offers an abstract language for formalizing relationships, transformations, and composition mechanisms; the third introduces a framework for modeling contextuality, the plurality of interpretive frameworks, and forms of local truth. The analysis shows that these approaches should not be considered as competing paradigms, but rather as complementary levels of description corresponding to the geometric, relational, and contextual dimensions of intelligent systems. Their value lies less in the prospect of an already established unified theory than in their ability to illuminate, from convergent perspectives, certain fundamental challenges of contemporary AI. The article concludes that geometry, composition, and contextuality constitute promising research directions for enriching the conceptual frameworks of AI. It also emphasizes the need to strengthen the links between fundamental mathematics, cognitive science, and AI in order to assess the potential of these approaches for future generations of intelligent systems.