How to take advantage of the blur between the finite and the infinite
type: Item
instance of: scholarly article
title: How to take advantage of the blur between the finite and the infinite
zbMATH Open document ID: 1262.00004
author: Pierre Cartier
published in: Logica Universalis
publication date: 2013-03-08T00:00:00Z
review text: This is a historically oriented essay on some factors of development in mathematics. The author focuses on the difference between true finite as opposed to theoretical finite. He starts with the discussion of mathematical induction and the principle of Fermat being the sophisticated version of the principle of complete induction. He stresses the fact that mathematical activity is always connected with pushing the borders between what seems to be founded on firm grounds and the ``grey zone'' of phenomena not yet penetrated or not easily graspable. According to author this activity is constantly rooted in social needs and strongly connected with the developments on other fields. In particular, some examples from physics are discussed, as well as the problem of ``invisible numbers'' for which we do not have any intuition or form of convenient representation. The text is written in informal, easily accessible (even for nonmathematician) form and contains a lot of historical examples.
reviewed by: Andrzej Indrzejczak
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A05
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B53
zbMATH DE Number: 6143018
zbMATH Keywords: finite
zbMATH Keywords: infinite
zbMATH Keywords: mathematical induction
zbMATH Keywords: Fermat's principle
MaRDI profile type: Publication
full work available at URL: s11787-012-0043-z
OpenAlex ID: W2062595138
DOI: 10.1007/S11787-012-0043-Z
description: scientific article; zbMATH DE number 6143018