Continuity in nature and in mathematics: Boltzmann and Poincaré
type: Item
instance of: scholarly article
title: Continuity in nature and in mathematics: Boltzmann and Poincaré
zbMATH Open document ID: 1362.01006
author: Marij van Strien
published in: Synthese
publication date: 2017-03-08T00:00:00Z
review text: Boltzmann and Poincaré both saw a need to justify the applicability of mathematics to physics in the nature of our understanding of physical processes. They both relied heavily on the theory of differential equations, and this raised the issue of whether the implied continuity considerations in the mathematics matched what was happening in nature. Poincaré concluded that this was allowable, whether nature was fundamentally discrete or continuous. Boltzmann argued that there could be no choice: nature was ultimately discrete. The author has considered a wide range of sources, and notes that only Poincaré lived long enough to respond to Planck's ideas about black body radiation (which he accepted was discrete).
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 26-03
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 6692980
zbMATH Keywords: continuity
zbMATH Keywords: differential calculus
reviewed by: Jeremy Gray
MaRDI profile type: Publication
full work available at URL: s11229-015-0701-9
OpenAlex ID: W1990649677
cites work: Ludwig Boltzmann (1844–1906)
cites work: Q4875403
cites work: Reconsidering logical positivism
cites work: Q4401917
cites work: Conflicts between generalization, rigor and intuition. Number concepts underlying the development of analysis in 17th--19th century France and Germany
cites work: The nineteenth century conflict between mechanism and irreversibility
cites work: When realism made a difference: the constitution of matter and its conceptual enigmas in late 19th century physics
DOI: 10.1007/S11229-015-0701-9
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description: scientific article; zbMATH DE number 6692980