The book "Philosophical-methodological analysis of the problem of substantiation of modern mathematics" by N. In. Mikhailova is a deep and comprehensive study that touches on one of the most pressing topics in the philosophy of science and mathematics. In it, the author not only analyzes the philosophical foundations of mathematical theory, but also offers methodological approaches to understanding and substantiating mathematical concepts, which makes it a valuable resource for both specialists and for a wide audience interested in science and philosophy. The book focuses on the question of how we can substantiate mathematical truths in the context of modern scientific discourse. Mikhailov examines various philosophical schools and their approaches to mathematics, ranging from Platonism to Constructivism, which allows the reader to see how different views affect the understanding of mathematical objects and theories. The author seeks to answer difficult questions: what is mathematical truth? What are the sources of mathematical knowledge? And how can we be sure of that, that our mathematical constructs really reflect reality? This book will be of interest not only to professional mathematicians and philosophers, but also students, Post-graduate students and all , who is interested in the methodology of scientific knowledge . It will be a real discovery for those who want to deepen their knowledge of mathematics and its philosophical foundations, as well as for those who are looking for answers to questions about the nature of mathematical knowledge. Readers interested in topics such as logic, set theory, and the philosophy of science will find in this work many valuable ideas and concepts. The topics raised in the book go beyond mathematics itself and address broader questions about the nature of knowledge and its rationale. Mikhailov explores how social and cultural factors influence the development of mathematical theories and how they can be used to substantiate or refute various mathematical approaches. This makes the book particularly relevant in light of contemporary discussions about the role of science in society and how we perceive and interpret scientific knowledge. Style N. In. Mikhailov is distinguished by clarity and logic, which allows the reader to easily follow his argument. He skillfully combines complex philosophical concepts with accessible language, which makes his work understandable even for those who are not specialists in philosophy or mathematics. In this context, the book is excellent.