Journal of Humanistic Mathematics 7 (2):355-378 (2017)
AbstractThe 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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An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
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Discrete or Continuous? The Quest for Fundamental Length in Modern Physics.Amit Hagar - 2014 - Cambridge University Press.