"Mathematical Explanation: Problems and Prospects"

Abstract: In this talk I have three major aims. The first is to introduce the topic of mathematical explanation by listing a number of problems followed by a reflection on the status of research and prospects for further development. The general discussion in the first part motivates the specific contributions to be presented in the remaining two parts of the talk. In the second part I will draw attention to an important tradition in philosophy of mathematics for which explanation is a concern. Here I discuss Mill, Russell, Gšdel, Lakatos and other philosophers of mathematics on mathematical explanation. The last part of the talk will present a case study of a development in mathematical practice that originates from explanatory concerns, i.e. Alfred Pringsheim's "explanatory" approach to the foundations of complex analysis.
 

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