From the Preface: "The name of Hermann Weyl is enshrined in the history of mathematics. A thinker of exceptional depth, and a creator of ideas, Weyl possessed an intellect which ranged far and wide over the realm of mathematics and beyond. His mind was sharp and quick, his vision clear and penetrating. Whatever he touched he adorned. His personality was suffused with humanity and compassion and a keen aesthetic sensibility. Its fullness radiated charm. He was young at heart to the end. By precept and example, he inspired many mathematicians and influenced their lives. The force of his ideas has affected the course of science. He ranks among the few universalists of our time. This collection of papers is a tribute to his genius. It is intended as a service to the mathematical community....These papers will no doubt be a source of inspirations to scholars through the ages." Volume IV comprises 46 articles written between 1941 and 1953.

Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as "conflicts of conscience"--the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy. Yet the two disciplines were already intertwined. In "Philosophy of Mathematics and Natural Science," Weyl examines how advances in philosophy were led by scientific discoveries--the more humankind understood about the physical world, the more curious we became. The book is divided into two parts, one on mathematics and the other on the physical sciences. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, Weyl provides readers with a guide to understanding science through the lens of philosophy. This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to "p"-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields.

Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.

This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.
The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.

This original anthology assembles eleven accessible essays by a giant of modern mathematics. Hermann Weyl (1885-1955) made lasting contributions to number theory as well as theoretical physics, and he was associated with Princeton's Institute for Advanced Study, the University of Gottingen, and ETH Zurich. Spanning the 1930s-50s, these articles offer insights into logic and relativity theory in addition to reflections on the work of Weyl's mentor, David Hilbert, and his friend Emmy Noether.
Subjects include "Topology and Abstract Algebra as Two Roads of Mathematical Comprehension," "The Mathematical Way of Thinking," "Relativity Theory as a Stimulus in Mathematical Research," and "Why is the World Four-Dimensional?" Historians of mathematics, advanced undergraduates, and graduate students will appreciate these writings, many of which have been long unavailable to English-language readers.

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.

Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In "The Classical Groups," his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which "The Classical Groups" has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, "Algebraic Theory of Numbers" inaugurated the "Annals of Mathematics Studies" book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.

From the Preface: "The name of Hermann Weyl is enshrined in the history of mathematics. A thinker of exceptional depth, and a creator of ideas, Weyl possessed an intellect which ranged far and wide over the realm of mathematics, and beyond. His mind was sharp and quick, his vision clear and penetrating. Whatever he touched he adorned. His personality was suffused with humanity and compassion, and a keen aesthetic sensibility. Its fullness radiated charm. He was young at heart to the end. By precept and example, he inspired many mathematicians, and influenced their lives. The force of his ideas has affected the course of science. He ranks among the few universalists of our time. This collection of papers is a tribute to his genius. It is intended as a service to the mathematical community....These papers will no doubt be a source of inspirations to scholars through the ages." Volume III comprises 52 articles written between 1926 and 1940.

From the Preface: "The name of Hermann Weyl is enshrined in the history of mathematics. A thinker of exceptional depth, and a creator of ideas, Weyl possessed an intellect which ranged far and wide over the realm of mathematics, and beyond. His mind was sharp and quick, his vision clear and penetrating. Whatever he touched he adorned. His personality was suffused with humanity and compassion, and a keen aesthetic sensibility. Its fullness radiated charm. He was young at heart to the end. By precept and example, he inspired many mathematicians, and influenced their lives. The force of his ideas has affected the course of science. He ranks among the few universalists of our time. This collection of papers is a tribute to his genius. It is intended as a service to the mathematical community....These papers will no doubt be a source of inspirations to scholars through the ages." Volume II comprises 38 articles written between 1918 and 1926.

From the Preface: "The name of Hermann Weyl is enshrined in the history of mathematics. A thinker of exceptional depth, and a creator of ideas, Weyl possessed an intellect which ranged far and wide over the realm of mathematics, and beyond. His mind was sharp and quick, his vision clear and penetrating. Whatever he touched he adorned. His personality was suffused with humanity and compassion, and a keen aesthetic sensibility. Its fullness radiated charm. He was young at heart to the end. By precept and example, he inspired many mathematicians, and influenced their lives. The force of his ideas has affected the course of science. He ranks among the few universalists of our time. This collection of papers is a tribute to his genius. It is intended as a service to the mathematical community....These papers will no doubt be a source of inspirations to scholars through the ages." Volume I comprises 29 articles written between 1908 and 1917.

Dieser Text ist die Transkription einer Vorlesung zur Funktionentheorie, die Hermann Weyl im Wintersemester 1910-11 an der UniversitAt GAttingen gehalten hat, kurz vor der Entstehung seines einflussreichen Buches A1/4ber Riemannsche FlAchen, das auf der Fortsetzung dieser Vorlesung im Sommersemester 1911 beruht. Weyl betont in dieser Vorlesung die kinematische Deutung gebrochen-linearer Transformationen und die Beziehungen zwischen konformen Abbildungen und StrAmungstheorie. HAhepunkt der Vorlesung ist der Vergleich der Riemannschen und WeierstraAschen Behandlung mehrdeutiger analytischer Funktionen durch Riemannsche FlAchen beziehungsweise analytische Fortsetzung.

Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt dieser Beitrag einen Bericht uber die Entstehung der grundlegenden Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift spiegelt in einzigartiger Weise Weyls mathematische Personlichkeit wider. Sie richtet sich an alle, die sich mit Fragen der Topologiegruppentheorie, Differentialgeometrie und mathematischer Physik beschaftigen. From the foreword of the editor K. Chandrasekharan: "Written in Weyl's finest style, while he was rising forty, the article is an authentic report on the genesis and evolution of those fundamental ideas that underlie the modern conception of geometry. Part I is on the continuum, and deals with analysis situs, imbeddings, and coverings. Part II is on structure, and deals with infinitesimal geometry in its many aspects, metric, conformal, affine, and projective; with the question of homogeneity, homogeneous spaces from the group-theoretical standpoint, the role of the metric field theories in physics, and the related problems of group theory. It is hoped that this article will be of interest to all those concerned with the growth and development of topology, group theory, differential geometry, geometric function theory, and mathematical physics. It bears the unmistakable imprint of Weyl's mathematical personality, and of his remarkable capacity to capture and delineate the transmutation of some of the nascent into the dominant ideas of the mathematics of our time".

Aus dem Vorwort von Jurgen Ehlers zur 7. Auflage: "Die ... Entwicklung der Physik macht verstandlich, warum ein so "altes" Werk wie Raum, Zeit, Materie noch aktuell ist: Die Riemann-Einsteinsche Raumzeitstruktur, die von Weyl so meisterhaft beschrieben und aus ihren mathematischen und physikalischen Wurzeln hervorwachsend dargestellt wird, ist immer noch die physikalisch umfassendste und erfolgreichste Raumzeittheorie, die bisher entwickelt und mit der Erfahrung konfrontiert wurde. (...) Als erstes Lehrbuch der noch neuen Theorie setzt es sich grundlicher als spatere Bucher mit den historischen Wurzeln und den sachlichen Motiven auseinander, die zur Einfuhrung der damals neuen Begriffe wie Zusammenhang und Krummung in die Physik gefuhrt haben. Zweitens ist es von dem vielleicht letzten Universalisten geschrieben worden, der alle wesentlichen Entwicklungen der Mathematik und Physik seiner Zeit nicht nur uberblickte, sondern in wesentlichen Teilen mitgestaltete. Das Studium dieses Werkes vermittelt nicht nur die Grundzuge der beiden Relativitatstheorien, sondern zeigt Zusammenhange mit anderen Ideen, nicht zuletzt auch der Naturphilosophie auf.""

Das Studium von Hermann Weyls "Raum . Zeit . Materie" ist auch heute noch lohnenswert. Als erste systematische Gesamtdarstellung der speziellen und allgemeinen Relativitatstheorie einschliesslich der zugehorigen Mathematik setzt es sich grundlich mit den historischen Wurzeln auseinander. Die Betonung des Begriffs des linearen Zusammenhangs unabhangig von der Metrik kommt der heutigen Auffassung und den Verallgemeinerungen in den Eichtheorien entgegen. Fur ein grundliches Verstandnis der modernen Eichtheorie ist Weyls Buch immer noch eine wichtige Grundlage."

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. "Mind and Nature" is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished.

Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, "The Open World" (1932) and "Mind and Nature" (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.