In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity.” This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The starting point is to recognize that to each mathematical proof corresponds a proof activity which consists of a sequence of deductive inferences—i.e., a sequence of epistemic actions—and that any written mathematical proof is only a report of its corresponding proof activity. The main idea to be developed is that the plan of a mathematical proof is to be conceived and analyzed as the plan of the agent(s) who carried out the corresponding proof activity. The core of the paper is thus devoted to the development of an account of plans and planning in the context of proof activities. The account is based on the theory of planning agency developed by Michael Bratman in the philosophy of action. It is fleshed out by providing an analysis of the notions of intention—the elementary components of plans—and practical reasoning—the process by which plans are constructed—in the context of proof activities. These two notions are then used to offer a precise characterization of the desired notion of plan for proof activities. A fruitful connection can then be established between the resulting framework and the recent theme of modularity in mathematics introduced by Jeremy Avigad. This connection is exploited to yield the concept of modular presentations of mathematical proofs which has direct implications for how to write and present mathematical proofs so as to deliver various epistemic benefits. The account is finally compared to the technique of proof planning developed by Alan Bundy and colleagues in the field of automated theorem proving. The paper concludes with some remarks on how the framework can be used to provide an analysis of understanding and explanation in the context of mathematical proofs.

中文翻译：

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数学证明中的计划和计划

在实践中，数学证明通常是产生它们的代理人仔细计划的结果。结果，每个数学证明都根据其产生方式继承了一个计划，该计划是其“架构”或“统一性”的基础。本文提供了一个帐户计划和规划在数学证明的背景下。这里采用的方法在于不是在数学证明本身中寻找这些概念，而是在代理谁生产了它们。出发点是要认识到每个数学证明都对应一个证明活动它由一系列演绎推理——即，一系列认知行为——并且任何书面的数学证明只是其相应证明活动的报告。要开发的主要思想是将数学证明的计划设想和分析为执行相应证明活动的代理的计划。因此，本文的核心致力于在证明活动的背景下制定计划和规划的说明。该帐户基于迈克尔布拉特曼在行动哲学中开发的计划代理理论。它通过提供对以下概念的分析来充实意图——计划的基本组成部分——和实践推理——构建计划的过程——在证明活动的背景下。然后使用这两个概念来提供对证明活动计划所需概念的精确表征。然后可以在最终的框架和最近的主题之间建立富有成效的联系模块化杰里米·阿维加德（Jeremy Avigad）介绍的数学。这种联系被利用来产生模块化演示数学证明对如何编写和呈现数学证明以提供各种认知收益具有直接影响。最后将该帐户与 Alan Bundy 及其同事在自动定理证明领域开发的证明计划技术进行了比较。本文最后对如何使用该框架在数学证明的背景下提供对理解和解释的分析进行了一些评论。