Chris Pincock.  Mathematics and Explanation.

Chris Pincock's book, "Mathematics and Explanation," explores the topic of mathematical explanation and its philosophical implications. Pincock examines both extra-mathematical explanations, where mathematics plays a role in explaining physical phenomena, and intra-mathematical explanations, which involve mathematical reasoning to explain pure mathematical results. The book evaluates various existing accounts of scientific explanation and tests their ability to encompass mathematical explanation. Pincock also discusses the implications of mathematical explanations for broader ontological debates and arguments for mathematical platonism. The text raises important considerations for understanding the nature of mathematical and scientific explanations, including the concept of mapping in mathematics and the uniqueness of systems and structures in mathematical explanations. The author, Pincock, is skeptical of the Enhanced Indispensability Argument (EIA) and argues that it relies on inference to the best explanation (IBE), which is difficult to support in a way that is consistent with scientific realism and mathematical platonism. The text concludes by highlighting objections to Pincock's arguments and discussing the importance of the topic of mathematical explanation. [Extracted from the article]