Alfred Clebsch's ``geometrical clothing'' of the theory of the quintic equation
type: Item
instance of: scholarly article
title: Alfred Clebsch's ``geometrical clothing'' of the theory of the quintic equation
zbMATH Open document ID: 1360.01025
author: François Lê
published in: Archive for History of Exact Sciences
publication date: 2017-01-25T00:00:00Z
review text: Let us start with the author's summary: ``This paper describes \textit{A. Clebsch}'s article [Math. Ann. 4, 284--345 (1871; JFM 03.0031.01)] that gave a geometrical interpretation of elements of the theory of the general algebraic equation of degree 5. Clebsch's approach is used here to illuminate the relations between geometry, intuition, figures, and visualization at the time. In this paper, we try to delineate clearly what he perceived as geometric in his approach, and to show that Clebsch's use of geometrical objects and techniques is not intended to aid visualization matters, but rather is a way of directing algebraic calculations. We also discuss the possible reasons why the article of Clebsch has been eventually completely forgotten by the historiography.'' As a reviewer, I am able to admit that the author did do a perfect job in fulfilling his aims. The paper brings to light many not so commonly things regarding the history of the quintic equation. Also, much has been revealed of Alfred Clebsch as a scientist in his time, and about all the work he did and also his contemporaries in treating the quintic equation. In short, highly recommended, a very good historical account from which one can learn and read a lot.
reviewed by: Robert W. van der Waall
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A70
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11E99
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 01A85
zbMATH DE Number: 6677757
zbMATH Keywords: quintic equation
zbMATH Keywords: Alfred Clebsch (1833--1872) resolvents
zbMATH Keywords: Jerrard form of the modular equation
zbMATH Keywords: geometrical models
zbMATH Keywords: icosahedron
zbMATH Keywords: cubic surfaces
MaRDI profile type: Publication
full work available at URL: s00407-016-0180-5
OpenAlex ID: W2461147098
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DOI: 10.1007/S00407-016-0180-5
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description: scientific article; zbMATH DE number 6677757