Eliakim Hastings Moore's ``General Analysis''
type: Item
instance of: scholarly article
title: Eliakim Hastings Moore's ``General Analysis''
zbMATH Open document ID: 0890.01013
author: Reinhard Siegmund-Schultze
published in: Archive for History of Exact Sciences
publication date: 1998-03-30T00:00:00Z
review text: Like main stream functional analysis (or topological vector spaces) the two approaches (before and after 1915) of E. H. Moore (1862-1932) toward his General Analysis (GA) originated from linear integral equations. GA was to be a theory of classes of (numerically valued) functions, and of functional operations, involving at least one ``general'' variable on a ``general'' range. With the exception of the notion of Moore-Smith convergence (1922) Moore's work did not exert any temporary or lasting influence. Few of his many students at Chicago kept to his ideas, and did so only temporarily. The author presents a thorough research, based also on archival sources, of Moore's work in GA, as compared to that of Fréchet and others. He offers explanations, some of them of a sociological nature, for the failure of GA. Obvious reasons are the peculiar symbolic presentation (following Peano's), the lack of the concepts of vector spaces and of linearity, and the lack of applications (GA failed to consider eigenvalue problems). Though not so general as Moore pretended, GA was too general to produce significant results. The paper deserves attention as a case study on alternative approaches toward a significant field of modern mathematics. It shows that the historical development was not as straightforward and inevitable as other papers try to make believe.
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 46-03
zbMATH DE Number: 1123668
zbMATH Keywords: E. H. Moore
zbMATH Keywords: general analysis
zbMATH Keywords: functional analysis
reviewed by: Detlef Laugwitz
MaRDI profile type: Publication
full work available at URL: s004070050010
OpenAlex ID: W1998529789
DOI: 10.1007/S004070050010
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description: scientific article; zbMATH DE number 1123668