The applicability of mathematics to science is a fundamental issue in both the philosophy of mathematics and the philosophy of science. In this paper we offer a structuralist approach to this issue which acknowledges the often complex moves which have to be made to bring mathematical and physical structures into na appropriate relationship. Our overall representational framework is that of the partial structure approach of Newton da Costa and we presente as a case study the application of group theory to atomic and nuclear physics. We conclude with some remarks on the implications of our work for realism in both the philosophy of mathematics and the philosophy of science.
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