A History of Algebraic and Differential Topology, 1900 – 1960 (Modern Birkhäuser Classics) by Jean Dieudonné (PDF)

Description

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results…. Within its chosen boundaries the coverage of this book is superb. Read it!―MathSciNet

User’s Reviews

Editorial Reviews: Review From the reviews: “This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results…. Within its chosen boundaries the coverage of this book is superb. Read it!” (MathSciNet)”[The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders.” (Zentralblatt MATH) From the Back Cover Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.*****************************This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results…. Within its chosen boundaries the coverage of this book is superb. Read it!―MathSciNet[The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders.―Zentralblatt MATH

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐On the same standard as the Bourbaki works and Dieudonne’s 9 volume ‘Treatise on Analysis’. Wonderful and immensely satisfying!

⭐I thought I’d write a quick review of this book because I’ve never seen anything quite like it. My background: I am currently a graduate student of mathematics hoping to earn my PhD, and topology is my favorite branch of math; my algebraic topology professor recommended this book to the class as a supplement to our studies. The great thing about this book is that it’s packed with rigorous math that motivates the entire subject in a mostly-chronological order. The tough thing about this book is that, well, it’s packed with rigorous math, and it unabashedly assumes total familiarity with this extremely difficult subject. Page 1 busts out the modern definition of an abstract chain complex, and then things back up and show how people got there, but not in a way that could be accessible to anybody who hasn’t already studied this stuff intensely. It’s somewhat of a shame because I think the historical development, separate from the lofty concepts, is interesting in itself and could attract a lay-audience if handled in the right way, but this would necessarily have to suppress 99% of the technical details. A ‘best of both worlds’ book would have to run on for thousands of pages and probably will never exist. But this is quite a treat for people who have already taken the plunge deep into this stuff.Dieudonne, by the way, is a mathematical legend, which explains the super high level of the text. He was one of the authors of the Bourbaki circle which modernized all of mathematics. It’s a delight to read about the historical stuff from somebody of that caliber of involvement with the history.

⭐This book painstakingly describes and explains algebraic topology in the chronological order of its development. I quite agree with Glen Bredon’s remark in his “Geometry and Topology” that goes like “this is more than a history and should be in the bookshelf of every student of topology” (not word-for-word, as the citation is done offhand).

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