Abstract

This presentation explores the organic and inseparable relationship between Applied Mathematics and Artificial Intelligence (AI). Rather than viewing AI as an isolated technological entity, the author elucidates its true nature as a sophisticated mathematical system operating on three core pillars: Linear Algebra (the language of data representation), Multivariable Calculus (the mechanism for optimization and learning), and Probability and Statistics (the foundation for inference and prediction). Beyond its role as a theoretical "backbone," the discussion highlights the generative power of Mathematics in shaping groundbreaking architectures, such as Graph Neural Networks (GNNS), Manifold Learning, and Transformer models. This paper addresses the critical issue of algorithmic transparency, asserting that Mathematics is the key to demystifying the "Black Box" problem, paving the way for a more explainable and trustworthy era of AI.

Keywords: Algorithmic architecture, applied mathematics, artificial intelligence, deep learning, explainable AI, multidimensional data structures, optimization.