Mathematical analysis during the 20th century
type: Item
instance of: scholarly article
zbMATH Open document ID: 0983.01011
author: Jean-Paul Pier
publication date: 2001-07-26T00:00:00Z
Mathematics Subject Classification ID: 01A65
Mathematics Subject Classification ID: 01-02
Mathematics Subject Classification ID: 26-03
Mathematics Subject Classification ID: 28-03
Mathematics Subject Classification ID: 43-03
Mathematics Subject Classification ID: 22-03
Mathematics Subject Classification ID: 30-03
Mathematics Subject Classification ID: 34-03
Mathematics Subject Classification ID: 35-03
Mathematics Subject Classification ID: 55-03
Mathematics Subject Classification ID: 57-03
Mathematics Subject Classification ID: 60-03
Mathematics Subject Classification ID: 14-03
Mathematics Subject Classification ID: 19-03
Mathematics Subject Classification ID: 11-03
zbMATH DE Number: 1624444
zbMATH Keywords: analysis
zbMATH Keywords: history
zbMATH Keywords: 20th Century
zbMATH Keywords: general topology
zbMATH Keywords: integration and measure
zbMATH Keywords: functional analysis
zbMATH Keywords: distributions
zbMATH Keywords: harmonic analysis
zbMATH Keywords: Lie groups
zbMATH Keywords: theory of functions
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: partial differential equations
zbMATH Keywords: differential topology
zbMATH Keywords: probability
zbMATH Keywords: algebraic geometry
zbMATH Keywords: Riemann hypothesis
MaRDI profile type: Publication
title: Mathematical analysis during the 20th century
review text: This is a superb history of 20th century mathematical analysis. One is taken on a tour of all the major areas with a lot of clear detail and many quotes from those who took part in the developments. NEWLINENEWLINENEWLINEIn the introduction the scope and the definition of analysis is discussed with many quotes, including one by Temple (1981) who says that the only fault of the French analysts is that they did not provide an effective definition of their subject, and one by Penrose (1978) who claims that the picture of physical space led to the basic ideas of continuity and smoothness in analysis.NEWLINENEWLINENEWLINEIn each topic considered the chapters are divided into ``Evolution 1900-1950'' and ``Flashes 1950-2000''. NEWLINENEWLINENEWLINEThe first chapter is General Topology which is fairly thorough but unfortunately, only contains a very small section at the end on Robinson's non-standard analysis that seeks to justify the infinitesimal. We proceed through chapters on Integration and Measure to Functional Analysis. In the latter I was particular interested in the historical development of distributions, although I would have expected some reference to Lighthill's work. The work of Dirac and Schwartz are well covered and there is an interesting comment from the latter to the effect that if he had not found the theory of distributions it would soon have been discovered during this time because of the recent work of other mathematicians. ( This was from a book in 1997). NEWLINENEWLINENEWLINEThe next chapter is on Harmonic Analysis linking to physics through von Neumann's work but also mentioning the classical work of Hardy and Littlewood. Throughout these chapters there are so many topics that one is forced to concentrate on those for which one has a firm interest and I was particularly interested in the next chapter on Lie Groups. Many aspects are covered and inevitably minor errors will occur. I note that on page 181 the last equation should be an expression for \…
reviewed by: Brian L. Burrows
description: scientific article; zbMATH DE number 1624444