Mathematical Methods in the Context of Artificial Intelligence: Foundations, Approaches, and Applications

Author(s)	Dr. Jayprakash Satyanarayan Yadav
Country	India
Abstract	Artificial Intelligence (AI) has emerged as a transformative field that depends fundamentally on mathematical principles. Mathematical methods provide the structure, logic, and computational framework required for intelligent systems to learn, reason, and make decisions. This research paper examines the essential mathematical foundations of AI, including linear algebra, calculus, probability theory, optimization, discrete mathematics, numerical methods, and information theory. The paper highlights how these mathematical tools contribute to machine learning, neural networks, computer vision, natural language processing, and other AI subfields. It also discusses current challenges, future directions, and the evolving role of mathematical modeling in next-generation AI systems.
Keywords	Keywords: Mathematical Models, Artificial Intelligence, Linear Algebra, Calculus
Field	Mathematics
Published In	Volume 7, Issue 6, November-December 2025
Published On	2025-11-24
DOI	https://doi.org/10.36948/ijfmr.2025.v07i06.61601
Short DOI	https://doi.org/hbb99x

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International Journal For Multidisciplinary Research