This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed. – 1. Introduction; – 2. Mathematical Explanations I: Entities; – 3. Mathematical Explanations II: Operations; – 4. Mapping Accounts: Strengths; – 5. Mapping Accounts: Idealizations; 5.1 Pincock and matching models; 5.2 Bueno, Colyvan, and the inferential conception; – 6. Mapping Accounts: Limitations; – 7. Suggestions for a New Approach. – 8. Conclusion. M.-M. V.