An appreciation of Kronecker
type: Item
instance of: scholarly article
title: An appreciation of Kronecker
zbMATH Open document ID: 0609.01022
DOI: 10.1007/BF03023570
author: H. M. Edwards
published in: The Mathematical Intelligencer
publication date: 1987-01-01T00:00:00Z
review text: This appreciation of Leopold Kronecker is a masterly and graceful exposition for a non-expert audience of the nature of that great mathematician's work. Inter alia, the author makes a good case for his belief that there are important passages in Kronecker's work ''that no one ever has fully understood,'' and that his works while admittedly difficult to read are undeservedly unread (a point which, as the author remarks, was also made by André Weil in a 1950 address). As well as a sketch of Kronecker's life, this article contains a discussion of Kronecker's Jugendtraum theorem, incidentally pointing out that the generally received opinion that Kronecker's statement of the theorem (proved by Takagi) was false is simply untrue (Hasse, at first misread Kronecker !), a lucid discussion of the nature of Kronecker's ideological conflict with Weierstrass and the hurt feelings it left in both men, and examination of Kronecker's quarrel with Mittag-Leffler. Kronecker had the misfortune that ''the other side'' as represented by Weierstrass and above all Dedekind (not to mention Hilbert in the Zahlbericht) were much more lucid expositors than he. Among the myths debunked in this article is that Kronecker felt a particular animus against Cantor, whereas he probably simply thought of him as another misled ''Weierstrassian''. Today the influence of computers has renewed an interest in Kronecker's algorithmic and ''constructive'' approach (though it is unlikely that his work will influence the technology of computation). The sympathetic twentieth- century readers of Kronecker, prior to the advent of computers while small in number, have included such figures as Erich Hecke, Hermann Weyl, André Weil, and Carl Ludwig Siegel. This article should be read not only by algebraists but by all concerned with mathematics or its history - it gives an intriguing and valuable picture of both mathematics and its creators.
Mathematics Subject Classification ID: 01A70
Mathematics Subject Classification ID: 01A55
zbMATH DE Number: 3985155
zbMATH Keywords: algorithmic approach
zbMATH Keywords: Weierstrass
zbMATH Keywords: Mittag-Leffler
zbMATH Keywords: Dedekind
zbMATH Keywords: Hilbert
zbMATH Keywords: Cantor
reviewed by: Jack Segal
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf03023570
OpenAlex ID: W1979695012
description: scientific article; zbMATH DE number 3985155