Discrete and continuous: a fundamental dichotomy in mathematics

Journal of Humanistic Mathematics 7 (2):355-378 (2017)
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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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James Franklin
University of New South Wales

Citations of this work

Finitism in Geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.
The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - “Metafizika” Journal 2 (8):p. 87-100.

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