Algebra from al Khwarizmi to Galois, 830--1830
type: Item
instance of: scholarly article
title: Algebra from al Khwarizmi to Galois, 830--1830
zbMATH Open document ID: 1465.01003
author: J.-H. Eschenburg
published in: Bulletin of the Iranian Mathematical Society
publication date: 2020-07-14T00:00:00Z
review text: Let me start by providing the reader with a list of books (not mentioned by the author in the paper under review) whose contents contain serious studies in the history of algebra, namely \begin{itemize} \item \textit{Peter M. Neumann}, The mathematical writings of Évariste Galois [Zbl 1237.01011]; \item \textit{Dirk J. Struik}, A concise history of mathematics [Zbl 0032.09701]; \item \textit{Dirk J. Struik} (ed.), A source book in mathematics (1200--1800) [Zbl 0205.29202]; \item \textit{Bartel van der Waerden}, A history of algebra. From al-Khwārizmī to Emmy Noether [Zbl 0569.01001]; \item \textit{Bartel van der Waerden}, Geometry and algebra in ancient civilizations [Zbl 0534.01001]; \item \textit{Emil Artin}, Galoissche Theorie [Zbl 0086.25703]; \item \textit{Ian Stewart}, Galois theory [Zbl 0269.12104]. \end{itemize} Very important for the history of mathematics, historians practicing in mathematics, and personalities in the mathematical community is the \begin{itemize} \item MacTutor History of Mathematics Archive (\url{https://mathshistory.st-andrews.ac.uk/}). \end{itemize} Now, let us deal with the paper under review. The aim of the author is to sketch a condensed development of solving polynomial equations by means of radicals (in our terminology). On Page~614 he speaks about al-Khwarizmi and his efforts in dealing with cubic equations. On Page~615 the author connects cubic equations with geometrical problems such as the problem of trisecting an angle by particular ``apparatus'' or ``means'', due to the Greeks and the Islamic authors Omar Khayyam and al-Khwarizmi. And then, beginning with Page~617, he starts considering the works and attempts by the 16th and 17th-century mathematicians from Italy, see below. The paper ends with the story around Galois, Abel, Ruffini and the author gives some worked-out examples of what Galois theory should be, as well as there should exist a notion of the so-called Galois groups. Despite the author's enthusiasm about the subj…
Mathematics Subject Classification ID: 01A30
Mathematics Subject Classification ID: 01A40
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 12-03
zbMATH DE Number: 7220159
zbMATH Keywords: history of algebra
zbMATH Keywords: equations
zbMATH Keywords: solvability
zbMATH Keywords: Galois group
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: s41980-019-00279-3
OpenAlex ID: W2970151999
Wikidata QID: Q114687080
cites work: 4000 years of algebra. History, cultures, people
cites work: The algebra of Omar Chayyam
cites work: Galois theory.
DOI: 10.1007/S41980-019-00279-3
description: scientific article; zbMATH DE number 7220159