Partial triumph or total failure?
type: Item
instance of: scholarly article
title: Partial triumph or total failure?
zbMATH Open document ID: 0558.01014
DOI: 10.1007/BF03024176
author: Raymond G. Ayoub
published in: The Mathematical Intelligencer
publication date: 1985-01-01T00:00:00Z
review text: Three examples of incorrect or incomplete proofs by outstanding mathematicians are discussed. They are: Euler's proof (1749) of the fundamental theorem of algebra, Stieltjes' proof (1885) of the Riemann hypothesis and Appell's proof (1926) that Euler's constant is irrational. The author gives short modern versions of the arguments; in the first two cases he indicates where the proofs are wrong or incomplete, in the last case he leaves it to the reader to find out. (Appell also found out himself and retracted his proof within weeks.) He also speculates about the influence these ''proofs'' might have had, for example because they suggested ideas to other mathematicians. He draws no conclusions and ends the article thus: ''Perhaps in the final analysis, the significance of an idea depends on the imagination and creativity of those dealing with it.''
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 3889468
zbMATH Keywords: proofs
zbMATH Keywords: Stieltjes
zbMATH Keywords: Riemann hypothesis
zbMATH Keywords: Appell
zbMATH Keywords: Euler's constant
reviewed by: Henk Bos
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf03024176
OpenAlex ID: W2088895818
description: scientific article; zbMATH DE number 3889468