RUI: STS: Standard Research Grant: Mathematical Explanation in Science

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General Audience SummaryThis project will analyze case studies of mathematical explanation in evolutionary biology to inform the philosophical debate about the nature of mathematical explanation in science. It will take place over three consecutive summers, and will make essential use of undergraduate researchers in philosophy, mathematics, and biology; specifically, it will integrate research and education by involving advanced undergraduate students in the project. Doing so will serve to broaden the scope of participation in science by exposing students in mathematics and in philosophy to a collaborative style of research that is often lacking in these disciplines; it will provide a model for institutional interdisciplinarity, fostering intellectual and logistical connections between the natural sciences and the humanities. The results of this project will be widely disseminated through conference presentations and publication of articles in scholarly journals. One overriding goal of the project is to demonstrate that close engagement with the methodology and outputs of scientific practice can yield philosophical insights that are both interesting in their own right and of direct relevance to working scientists.Technical SummaryThe results of the proposed project have the potential to contribute to ongoing philosophical research into the relation between mathematics and the empirical sciences. The particular focus on the explanatory role of mathematics in science is an area of very active current debate in the philosophical literature. The PI has been a leading contributor to these debates. The goal is to produce research outputs that are of relevance to biology and to applied mathematics. Both of the two core examples, periodical cicadas and bee honeycombs, are the subject of ongoing debate among biologists and mathematicians concerning what causal mechanisms are involved, the role played by optimization of different parameters, and what mathematical apparatus, if any, is essentially involved. Thus the project aims not merely to draw on data from several disciplines but to provide research outputs that are of genuine cross-disciplinary interest.