Abstract Artificial Neural Networks (ANNs) are at the core of modern artificial intelligence (AI), enabling machines to learn from data, recognize complex patterns, and make accurate predictions. We explore the essential mathematical principles that form the backbone of ANNs. We use linear algebra for data representation and matrix transformations. Calculus is applied for optimization through backpropagation, and probability and statistics are used for uncertainty modeling and predictive reasoning. Advanced optimization algorithms are focused for performance tuning. By uncovering the mathematical mechanisms that drive neural computations, this study provides a comprehensive understanding of how ANNs function and evolve. These foundational concepts not only enhance our grasp of machine learning models but also empower researchers, developers, and educators to build more intelligent, efficient and adaptive AI systems. Article – Mathematics of Artificial Neural Networks: Science Behind AI...