Rowe

Felix Klein

The Erlangen Program

Birkhäuser Verlag GmbH

ISBN 978-3-031-85473-6

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85,59 €

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Bibliografische Daten

Fachbuch

Buch. Hardcover

2025

In englischer Sprache

Umfang: xvi, 456 S.

Format (B x L): 16,8 x 24 cm

Verlag: Birkhäuser Verlag GmbH

ISBN: 978-3-031-85473-6

Weiterführende bibliografische Daten

Das Werk ist Teil der Reihe: Classic Texts in the Sciences

auch verfügbar als eBook (PDF) für 85,59 €

Produktbeschreibung

This book presents a historical account of Felix Klein's "Comparative Reflections on Recent Research in Geometry" (1872), better known as his "Erlangen Program.” Originally conceived and written when Klein was collaborating with Sophus Lie, this bold essay initially made little impression on contemporary researchers. Decades later, however, it eventually became a famous classic. Eminent mathematicians hailed Klein’s main message – the role of invariants of transformation groups in geometry – as presaging major developments in mathematics and physics.

The first part of this book focuses on the prehistory surrounding Klein’s “Erlangen Program,” stressing the motivations that led Klein to write it. The core of the book (Part II) then presents a new translation of Klein's original text, followed by detailed textual analysis aimed at guiding the reader through its rather terse and opaque prose. Part III deals with its complicated reception history, treated in four periods spanning the years from 1872 to 1930. This culminated during Klein’s lifetime with his efforts to promote the "Erlangen Program” as a framework for interpreting Einstein’s theory of relativity. After his death in 1925, the viability of this framework became a contentious issue among leading differential geometers. Part IV looks back on the transformations in mathematics that led to a modernized interpretation of Klein’s message. The book also explores in depth how the growing fame of the “Erlangen Program” undermined Klein’s friendship with Sophus Lie, leading to a dramatic public break between them in 1893.

Beyond the "Erlangen Program” itself, this book deals with many of Felix Klein’s other works. As an introduction to a largely forgotten world of ideas, this study will appeal not only to experts but also to graduate students and all those with a serious interest in the history of modern mathematics.

Autorinnen und Autoren

Kundeninformationen

Provides a new English translation and discusses other earlier studies of Klein's "Erlangen Program" Contextualizes this work as part of Klein’s collaboration with Sophus Lie Carefully examines four phases in the reception history of the "Erlangen Program" covering more than fifty years

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De Gruyter GmbH

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10785 Berlin, DE

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