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MATHEMATICAL EXPLANATION AND THE OPTIMIZATION FALLACYPure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life-cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume facts about mathematical optimality drove selection for the respective traits and explain why they exist. Finally, we show how this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation.
Florida State University