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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离散和连续：数学的基本二分法

离散和连续之间的区别是数学的核心。离散数学（算术，代数，组合数学，图论，密码学，逻辑）具有一组与连续数学（传统几何，微积分，大部分功能分析，微分方程，拓扑结构）截然不同的概念，技术和应用领域。两者之间的相互作用（例如在连续系统的计算机模型（例如流体流动）中）是最近一百年来适用数学中的中心问题。本文解释了这种区别，以及为什么它被证明是数学的重要组织主题之一。