Mathematical Explanation in Practice

The connection between understanding and explanation has recently been of interest to philosophers. Inglis and Mejia-Ramos (Synthese, 2019. https://doi-org.proxy.library.nd.edu/10.1007/s11229-019-02234-5) propose that within mathematics, we should accept a functional account of explanation that characterizes explanations as those things that produce understanding. In this paper, I start with the assumption that this view of mathematical explanation is correct and consider what we can consequently learn about mathematical explanation. I argue that this view of explanation suggests that we should shift the question of explanation away from why-questions and towards a "what's going on here" question. Additionally, I argue that when we recognize the connection between understanding and explanation we naturally see how more than just proof can be explanatory. I expand this point by detailing how definitions and diagrams can be explanatory. In all, we see that when we take seriously the connection between understanding and explanation, we get a better sense of how explanation arises within mathematics.