Symmetric

Author: (German) Weyl
Translator: Feng Chengtian / Lu Jizong
Publisher:
Publishing Date: 2002-06-01
Features: As one of the greatest mathematicians of the 20th century, the Princeton mathematics professor Weyl may be the most qualified person to discuss symmetry in the physical sciences. To expand the readership of Symmetry, Weyl also included numerous exquisite art and biological images, using these examples to provide vivid yet rigorous descriptions of various concepts such as bilateral symmetry, translational symmetry, and rotational symmetry. From the perspective of symmetry, the entire book offers a comprehensive mathematical interpretation of both the inorganic and biological worlds, as well as human culture. It has long been observed that symmetry is an important order reflected in the objective world, connecting disciplines such as mathematics, physics, chemistry, and biology. However, it was only in the past century that it became a significant way for scientists to view the world. Among them, the Princeton mathematics professor Weyl played an indispensable role. He creatively applied the theory of symmetry in mathematics—group theory—to quantum mechanics and gauge field theory. Groups are a fundamental basis of modern science, possessing both profound practical significance and endless depth. However, current teaching methods, due to their detachment from reality, are highly ineffective. Symmetry, on the other hand, not only allows readers to fully appreciate the beauty of science but also effectively guides them into the realm of groups. For example, after introducing crystal structures, Weyl finally points out, "Whenever one deals with a structured entity S, one should strive to determine its automorphism group. By using this method, you can gain an in-depth understanding of the structure of S." Such enlightening and powerful statements are commonplace, giving the impression that they were grasped effortlessly rather than meticulously arranged. This is precisely because Weyl's understanding has reached a profound level. This small book vividly reflects the masterful style of deep yet accessible explanations.