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Discrete and continuous: A fundamental dichotomy in mathematics

Franklin, James (2017) Discrete and continuous: A fundamental dichotomy in mathematics. Journal of Humanistic Mathematics, 7 (2). pp. 355-378. ISSN 2159-8118

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Abstract

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Franklin, Jamesj.franklin@unsw.edu.au0000-0002-4603-1406
Keywords: Discrete; continuous; atomic
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Methodology
Depositing User: James Franklin
Date Deposited: 20 Oct 2019 01:03
Last Modified: 20 Oct 2019 01:03
Item ID: 16561
Journal or Publication Title: Journal of Humanistic Mathematics
Publisher: Claremont Colleges Library
Official URL: https://scholarship.claremont.edu/jhm/vol7/iss2/18...
DOI or Unique Handle: https://doi.org/10.5642/jhummath.201702.18
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Methodology
Date: 2017
Page Range: pp. 355-378
Volume: 7
Number: 2
ISSN: 2159-8118
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16561

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