Overview
- Includes in-depth discussions on the developement of algebraic geometry in the 20th century
- Provides a comprehensive study of the changes of a unique mathematical object: the branch curve
- Delivers an extensive overview of the evolving research on algebraic surfaces
Part of the book series: Frontiers in the History of Science (FRHIS)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization.
By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods.
Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.
Reviews
of mathematics.” (Judith R. Goodstein, Mathematical Reviews, September, 2023)
Authors and Affiliations
About the author
Michael Friedman is a historian of mathematics and a senior lecturer at the Tel Aviv University. The focus of his research is how material, visual and symbolical knowledge and practices in mathematics interact with each other. More specifically, his research examines how material practices (folding, weaving, braiding, knotting, as well as three-dimensional models) prompt symbolical mathematical knowledge. Recent publications: A History of Folding in Mathematics. Mathematizing the Margins (Birkhäuser, 2018).
Bibliographic Information
Book Title: Ramified Surfaces
Book Subtitle: On Branch Curves and Algebraic Geometry in the 20th Century
Authors: Michael Friedman
Series Title: Frontiers in the History of Science
DOI: https://doi.org/10.1007/978-3-031-05720-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-05719-9Published: 28 September 2022
eBook ISBN: 978-3-031-05720-5Published: 26 September 2022
Series ISSN: 2662-2564
Series E-ISSN: 2662-2572
Edition Number: 1
Number of Pages: IX, 252
Number of Illustrations: 35 b/w illustrations, 6 illustrations in colour
Topics: History of Mathematical Sciences, History of Science, Algebraic Geometry