Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency.

中文翻译：

---

数学理解：数学证明的案例

尽管理解是认识论和科学哲学领域越来越多文献的研究对象，但只有很少的研究涉及数学中的理解。本文介绍了数学理解的基本形式：证明理解。该帐户建立在一个简单的想法之上，即理解证明相当于合理地重建其基本计划。这种特征通过详细说明规划的相关概念和合理重建的相关过程来充实，部分建立在布拉特曼的规划机构理论的基础上。有人认为，所提出的解释可以解释通常与数学家和哲学家的证明理解相关的一系列独特现象。在案例研究的基础上，人们进一步认为，该帐户可以对理解失败进行精确的诊断，并可以提出克服这些失败的方法。反思这里开发的方法，本文最后对如何形成数学和科学理解研究通用的通用方法论进行了一些评论，并重点关注人类能动性。