Euler and the structure of mathematics
type: Item
instance of: scholarly article
title: Euler and the structure of mathematics
zbMATH Open document ID: 1440.01004
author: Giovanni Ferraro
published in: Historia Mathematica
publication date: 2020-04-09T00:00:00Z
review text: The aim of this paper is to investigate Euler's reorganization of mathematics centered around analysis. The author emphasizes three features of Euler's conception: First, the notion of analysis changed the concept of mathematical theory and made its later development possible. Secondly, the crucial aspect was the rebuilding of the edifice of the mathematical science. Thirdly, his conception concerned the foundations of analysis. His foundations proved to be inadequate to include the new apparatus in a coherent theory and were rejected by mathematicians of the nineteenth century. Thus, the author demonstrates that the use of the term `analysis' in Pappus's sense disappeared from Euler's papers in the middle of the 1730s. Analysis became the science of abstract quantities. The principle of the generality of analysis was the cornerstone of Euler's understanding of analysis. Geometry and mechanics were transformed into a branch of applied analysis.
reviewed by: Eberhard Knobloch
Mathematics Subject Classification ID: 01A50
zbMATH DE Number: 7188915
zbMATH Keywords: analysis
zbMATH Keywords: synthesis
zbMATH Keywords: architecture of mathematics
zbMATH Keywords: foundations of analysis
zbMATH Keywords: analytical mechanics
MaRDI profile type: Publication
full work available at URL: j.hm.2019.06.002
OpenAlex ID: W2955423498
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DOI: 10.1016/J.HM.2019.06.002
description: scientific article; zbMATH DE number 7188915