I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) ‘algorithms’.

中文翻译：

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关于算法、有效程序及其定义

我将“算法”的经典概念视为一个连续的、逐步的、确定性的过程（即 20 世纪 30 年代已经使用的“算法”概念），涉及三个主题，即它与“有效程序”的概念，它在逻辑、计算机科学和数学（侧重于数值分析）中的不同作用和用途，以及这些领域的从业者提出的不同形式定义。我认为“算法”在上述领域已经被概念化并以对比的方式使用，并讨论了采用（经典）“算法”的最终基础理论的挑战和前景。