Do mathematical explanations have instrumental value?
Scientific explanations are widely recognized to have instrumental value by helping scientists make predictions and control their environment. In this paper I raise, and provide a first analysis of, the question whether explanatory proofs in mathematics have analogous instrumental value. I first identify an important goal in mathematical practice: reusing resources from existing proofs to solve new problems. I then consider the more specific question: do explanatory proofs have instrumental value by promoting reuse of the resources they contain? In general, I argue that the answer to this question is “no” and demonstrate this in detail for the theory of mathematical explanation developed by Marc Lange.
KeywordsMathematical explanation Scientific explanation Mathematical practice Proof
I am very grateful to Jeremy Avigad, Michael Friedman, Erich Kummerfeld and Wilfried Sieg for helpful feedback on drafts of this paper. I am also grateful to participants at the 2018 Stanford Workshop on Mathematical Reasoning for their helpful questions and discussions on reuse in mathematics. Finally I am grateful to the anonymous reviewers who provided helpful feedback and suggestions.
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