Structuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mathematics today does. We draw on one calculus textbook, one celebrated analysis textbook, and a monograph on the Navier–Stokes equation to show structural methods like Dedekind’s have long been central to differential equations, and have philosophically respectable ontology and epistemology.

数学哲学中的结构主义主要关注算术、代数和基本分析。一些人怀疑独特的结构工作方法是否会对微分方程等其他领域产生影响。我们证明贝纳塞拉夫提出的狭义结构主义在微分方程中没有实际作用。但戴德金的连续统方法已经不符合这种狭义的含义，今天的数学也很少这样做。我们利用一本微积分教科书、一本著名的分析教科书和一本关于纳维-斯托克斯方程的专着来表明像戴德金这样的结构方法长期以来一直是微分方程的核心，并且具有哲学上值得尊敬的本体论和认识论。