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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.
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Symmetry (Paperback)
Hermann Weyl
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R429
R394
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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.
In this classic text first published in German in 1918-this is a
translation by HENRY L. BROSE (1890-1965) of the 1921 fourth
edition-Weyl considers the role of Euclidean space in physics and
the mathematics of Einstein's general theory of relativity,
exploring: foundations of affine and metrical geometry conception
of n-dimensional geometry tensor algebra the stationary
electromagnetic field Riemann's geometry affinely connected
manifolds space metrics from the point of view of the Theory of
Groups relativistic geometry, kinematics, and optics
electrodynamics of moving bodies mechanics of the principle of
relativity mass and energy gravitational waves concerning the
interconnection of the world as a whole and more.HERMANN KLAUS HUGO
WEYL (1885-1955)was a German mathematician who spent most of his
life working in Zurich, Switzerland. When the Nazi party began to
gain power he fled to a job at the Institute of Advanced Study in
Princeton, New Jersey where he continued to develop his
representation theory. He was one of the most influential
mathematicians of the 20th century. He greatly impacted theoretical
physics and number theory and was the first to combine general
relativity and electromagnetism
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.
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.
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.""
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