I am working on a survey article on "Philosophy of Mathematics" for the forthcoming Continuum Companion to Philosophy of Science, edited by French and Saatsi. In the article I aim to give philosophers of science some orientation on the debates within philosophy of math that can be intimidating to the uninitiated. But I would also like to highlight some topics that clearly fall into a common area between philosophy of science and philosophy of mathematics, but which are typically pursued in isolation by one specialist or another. Here I am thinking of debates about the role of mathematics within science and what this tells us about mathematics and/or science. A central instance of this is the indispensability argument for platonism about mathematics. While this has been an ongoing debate in philosophy of mathematics for 30 years, the debate is not informed by contemporary philosophy of science. See, for example, the ongoing debate about mathematical explanation of physical phenonomena. At the same time, philosophers of science seem to not have much to say about (i) whether mathematics is indispensable to our best science in some interesting sense or (ii) what this might show about science if it is true.
Any suggestions for other debates in this common area of interest between philosophy of science and philosophy of mathematics? Any suggestions for how to close this gap between two areas of contemporary philosophy?