This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having explanatory power all display an increase of conceptual complexity from the assumptions to the conclusion.

中文翻译：

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数学解释：通过形式证明和概念复杂性进行分析

本文研究内部（或内部）数学解释，即数学定理的证明，这些证明似乎可以解释它们所证明的定理。本文的目标是对这些解释进行严格分析。这将分两步完成。首先，我们将展示如何从数学定理的非正式证明转向涉及证明树及其元素分解的正式演示；其次，我们将证明那些被认为具有解释力的数学证明都表现出从假设到结论的概念复杂性的增加。