Évariste Galois: Principles and applications
type: Item
instance of: scholarly article
title: Évariste Galois: Principles and applications
zbMATH Open document ID: 1035.01008
author: Ivo Radloff
published in: Historia Mathematica
publication date: 2002-07-08T00:00:00Z
review text: After Abel had given a generally accepted proof of the fact that, in general, quintic polynomials cannot be solved using radicals, Galois found necessary and sufficient conditions for solvability; over the years, his theory evolved into what is now known as Galois theory. There are, however, some basic differences between the modern version and that of Galois: modern Galois theory deals with certain ring homomorphisms between field extensions, whereas the main objects in Galois's work are polynomials and certain permutations (or substitutions, as Galois called them) of their roots. Of course Galois's main results can all be formulated within the modern language, and although today we are in a better position to understand Galois's papers than his contemporaries were, working through them still requires a lot of effort, maybe more than the average working mathematician interested in the history of mathematics is willing to invest. For these mathematicians, articles such as the one reviewed here are most welcome. The article gives what may be called a `faithful representation' of Galois's article from 1831 in modern language. The original notions are explained, and then the main steps in Galois's work are discussed one by one. The last section gives applications of Galois's theory to Jacobi's modular equation, applications that Galois hinted at in his farewell letter to Chevalier.
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 12-03
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12E10
zbMATH DE Number: 1764728
zbMATH Keywords: Galois group
zbMATH Keywords: Galois theory
zbMATH Keywords: Chevalier
zbMATH Keywords: solvability
zbMATH Keywords: modular equation
MaRDI profile type: Publication
full work available at URL: hmat.2001.2337
OpenAlex ID: W2039242504
cites work: Q3313943
cites work: Q5586187
cites work: Q3934684
cites work: The development of Galois theory from Lagrange to Artin
cites work: Q3996488
cites work: Q4354374
cites work: Abel's impossibility proof as reflected in modern Galois theory
DOI: 10.1006/HMAT.2001.2337
description: scientific article; zbMATH DE number 1764728