`Nobody could possibly misunderstand what a group is': a study in early twentieth-century group axiomatics
type: Item
instance of: scholarly article
title: `Nobody could possibly misunderstand what a group is': a study in early twentieth-century group axiomatics
zbMATH Open document ID: 1379.01014
author: Christopher Hollings
published in: Archive for History of Exact Sciences
publication date: 2017-10-26T00:00:00Z
review text: The comprehensive and bibliographically well documented paper focuses on early twentieth-century American postulational analysis, in particular in group axiomatics. As the main contributor E. V. Huntington (1874--1952) is presented, and his effort from about 1901 to prove the independence of group postulates and to remove redundancies. The author follows up the reception of this work within group theory by mathematicians such as E. T. Bell, E. H. Moore, but also by mathematicians outside the U.S., including Eastern Europe. The historical analysis includes broader group theoretic work as well, such as semigroups. The main result seems that postulational analysis in group theory remained limited in its effects on both research and pedagogy, having ``been little more than a passing fad'' (p. 463), although the author finds also some ``subtle influence'' on group theory texts. He points briefly to parallels in mathematical logic and in general pedagogic and mathematical trends such as New Math and Bourbaki but reserves more analysis for future work. A broad introduction about the establishment of the group concept in the 19th century is also given, drawing much on work by the German historian \textit{H. Wussing} [Die Genesis des abstrakten Gruppenbegriffes. Ein Beitrag zur Entstehungsgeschichte der abstrakten Gruppentheorie. Berlin: VEB Deutscher Verlag der Wissenschaften (1969; Zbl 0199.29101)].
reviewed by: Reinhard Siegmund-Schultze
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 20-03
Mathematics Subject Classification ID: 20A05
zbMATH DE Number: 6798746
zbMATH Keywords: group axiomatics
zbMATH Keywords: postulational analysis
zbMATH Keywords: American mathematics
MaRDI profile type: Publication
full work available at URL: s00407-017-0193-8
OpenAlex ID: W2738434166
Wikidata QID: Q41537957
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`Nobody could possibly misunderstand what a group is': a study in early twentieth-century group axiomatics (DOI)
DOI: 10.1007/S00407-017-0193-8

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