Mathematical methods for artificial intelligence

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In an era in which artificial intelligence is reshaping every domain of knowledge and human action, understanding its mathematical foundations is no longer an option—it is a necessity. This volume guides the reader through a rigorous and compelling journey across the mathematical structures that make modern AI possible: from linear algebra to probability, from optimization to deep learning, up to the most advanced models of learning, reasoning, and decision-making. It is not merely a collection of techniques, but a unified vision: mathematics as the deep language of artificial intelligence. With a rare balance between theory and application, the text sheds light on what often remains hidden behind the empirical success of algorithms: the principles, the limits, and the implications of increasingly powerful systems. From the data pipeline to generative models, from transformers to AGI, each chapter builds a piece of a broader and more conscious understanding. Designed for students, researchers, and professionals, this book is also an invitation to look beyond the technological surface, to grasp the structure, the logic, and the responsibility underlying artificial intelligence. Because truly understanding AI means, first and foremost, understanding its mathematics—and, like in a hermeneutic mirror, coming to understand the human being ever more deeply.