In this paper I present a case study of mathematical explanation in science that is new to the philosophical literature, and that arises in the context of estimating the energetic costs of running in bipedal animals. I refer to this as the Bipedal Gait Costs explanation (BGC). I argue that it is important for examples of applied mathematics to be driven not just by philosophical and mathematical concerns but also by scientific concerns. After a detailed presentation of the BGC case study, I discuss ways in which it is different from standard examples of MES. One distinctive aspect of BGC is that substantive mathematics occurs at two different levels. I argue for a distinction to be drawn between the mathematical modeling that occurs at one level, which is non-explanatory, and the mathematical theorem which is applied to results gleaned from these models, which is explanatory. I conclude by drawing some connections with broader indispensability-based arguments for platonism in the philosophy of mathematics.

在这篇论文中，我展示了一个关于科学中数学解释的案例研究，这对哲学文献来说是新的，并且出现在估计双足动物奔跑的能量成本的背景下。我将此称为双足步态成本解释 (BGC)。我认为，重要的是应用数学的例子不仅要受到哲学和数学问题的驱动，还要受到科学问题的驱动。在详细介绍了 BGC 案例研究之后，我将讨论它与 MES 标准示例的不同之处。BGC 的一个独特方面是实体数学发生在两个不同的层次上。我主张区分发生在一个层面上的数学建模，这是非解释性的，以及应用于从这些模型中收集的结果的数学定理，这是解释性的。最后，我将与数学哲学中柏拉图主义的更广泛的基于必要性的论点建立了一些联系。