All formulas of peace (Category PopularScience)

I read this book with great pleasure by Sergei Popov, a modern Russian astrophysicist, popularizer of science, who is known for his ability to explain the most complex concepts of physics and mathematics in an accessible, living language. In fact, this book is written in a living language and is an invitation to look at mathematics not as a boring set of equations, but as a universal language of nature and a tool for penetrating the very essence of physical phenomena. Sergey shows that mathematical methods not only allow building bridges and launching satellites, but also underlie the most daring theories about the birth of the universe, black holes and quantum effects.

The book is divided into 4 parts 1) New language Popov explains why mathematics is not just a tool, but a new language for describing nature. He shows how ideas go from vague, gas-like fantasies and philosophical concepts to liquid hypotheses and finally to the crystals of scientific theories expressed in formulas. This process is similar to phase transitions: only at the stage of "crystallization" the idea becomes suitable for rigorous testing and application. Mathematics is not only a means of expression, but also a filter that separates the real from the impossible. For example, the attempt to transfer the laws of gravitation into four-dimensional space makes it impossible to have stable orbits – a limitation imposed by mathematics, not physical experiment. 2) Evolution The second part deals with the evolution of ideas and scientific theories. Popov compares the development of scientific concepts with biological evolution: random mutations (hypotheses) They are selected, and only the most resilient and fit survive. In science, as in nature, “selection” is not a random process, but a powerful organizing force that forms a logical result out of chaos. At the same time, the “landscape of fitness” of scientific ideas is constantly changing: a new discovery in one field can change the requirements for theories in another, and even a small change in the “environment” leads to a restructuring of the entire knowledge system. 3) Metamorphosis and options This part examines how the same idea can be transformed, give rise to different variants and modifications depending on the conditions and new data. Scientific concepts, like living organisms, are prone to metamorphosis: details change, formulations are refined, alternative approaches appear. Science is not a static system, but a dynamic process in which even established formulas can be revised or replaced as new facts accumulate and methods develop. 4) Foresight The fourth part is devoted to the predictive power of science. Povov shows that one of the main tasks of scientific theory is to make quantitative predictions that can be tested experimentally. Formulas allow you to look beyond the horizon of known facts, predict new phenomena and even discover previously unknown objects. In science, foresight always involves risk: sometimes a theory predicts the impossible or faces the limits of the applicability of mathematics. In such cases, one must either revise the premises or look for new mathematical tools. 5) Annexes In the final part, Sergei Popov gives examples from different fields of science and technology, where mathematics becomes the key to solving practical problems. Here real cases from astronomy, physics, engineering are discussed.

To sum up, this small non-fiction book is great for anyone who wants to understand how the universe works and mathematics.

#PopularScience #Cosmos #Physics #Math