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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
30.05.2025
Sprache
Englisch
EAN
9783031854736
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Classic Texts in the Sciences
Sonderedition
Nein
Autor
David E. Rowe
Seitenanzahl
456
Einbandart
Gebundene Ausgabe
Buch Untertitel
The Erlangen Program
Schlagwörter
Erlangen Program, Felix Klein, Sophus Lie, Classical Geometry, Julius Plücker, Classical Invariant Theory, Geometry in 19th-Century Germany, Line and Sphere Geometry, Transformation Groups in Geometry
Thema-Inhalt
PBX - Geschichte der Mathematik
PBM - Geometrie
PBG - Gruppen und Gruppentheorie
Höhe
240 mm
Breite
16.8 cm
Hersteller: Springer Nature Customer Service Center GmbH, ProductSafety@springernature.com
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