Leibniz and the infinite
type: Item
instance of: scholarly article
title: Leibniz and the infinite
zbMATH Open document ID: 1267.01019
author: Eberhard Knobloch
published in: Documenta Mathematica
publication date: 2013-04-17T00:00:00Z
full work available at URL: 12 knobloch-eberhard-4.html
review text: In this beautiful survey paper it is mentioned that people were wrong over the ages in thinking that Leibniz's work on introducing the theory of integration was not done rigorously. According to this article's author, this was due to the fact that only about half of the known 200,000 sheets of paper that Leibniz did produce are published up to now. Indeed, the author refers to \textit{G. W. Leibniz}'s work [De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis. Göttingen: Vandenhoeck \& Ruprecht (1993; Zbl 0919.01016)] that was published as late as 1993 for the first time. One can find there, in Theorem 6, a completely rigorous foundation of infinitesimal geometry by means of Riemannian sums; in the paper under review it is stated what this is all about. The author refers in this respect also to his paper in [Synthese 133, No. 1--2, 59--73 (2002; Zbl 1032.01011)]. Perhaps he should have taken also a small side glance at the theory of nonstandard analysis as given by A. Robinson.
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 28-03
zbMATH DE Number: 6155074
zbMATH Keywords: Leibniz
zbMATH Keywords: infinite
zbMATH Keywords: infinitely small
zbMATH Keywords: mathematical rigour
zbMATH Keywords: Riemann sums
zbMATH Keywords: integration theory
zbMATH Keywords: \(\varepsilon\)-\(\delta\) techniques
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: survey paper
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6155074