The philosophical problem that stems from the successful application of mathematics in the empirical sciences has recently attracted growing interest within philosophers of mathematics and philosophers of science. Nevertheless, little attention has been devoted to the converse applicability issue of how physical considerations find successful application in mathematics. In this article, focusing on some case studies, I address the latter issue and argue that some successful applications of physics to mathematics essentially depend on the use of conservation principles. I conclude (...) with a short discussion of how the successful interplay between conservation principles and mathematics can be accounted for. (shrink)

Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...) that it is possible for there to be such cases, and provide some toy examples to demonstrate this. I then identify a potential source of scientific case studies as a guide for future work. (shrink)

A lot of philosophical energy has been devoted recently in trying to determine if mathematics can contribute to our understanding of physical phenomena. Not many philosophers are interested, though, if the converse makes sense, i.e., if our cognitive interaction (scientific or otherwise) with the physical world can be helpful (in an explanatory or non-explanatory way) in our efforts to make sense of mathematical facts. My aim in this paper is to try to fill this important lacuna in the recent literature. (...) My answer to the question of this paper is negative. As I will argue, there are serious problems with the main reasons for believing in the first place that it is possible to have physical understanding of mathematical facts. (shrink)

In this paper I present two cases, taken from the history of science, in which mathematics and physics successfully interplay. These cases provide, respectively, an example of the successful application of mathematics in astronomy and an example of the successful application of mechanics in mathematics. I claim that an illustration of these cases has a twofold value in the context of the applicability debate. First, it enriches the debate with an historical perspective which is largely omitted in the contemporary discussion. (...) Second, it reveals a component of the applicability problem that has received little attention. This component concerns the successful application of physical principles in mathematical practice. With the help of the two examples, in the final part of the paper I address the following question: are successful applications of mathematics to physics and successful applications of physics to mathematics two sides of the same problem? (shrink)

Philosophical analysis of mathematical knowledge are commonly conducted within the realist/antirealist dichotomy. Nevertheless, philosophers working within this dichotomy pay little attention to the way in which mathematics evolves and structures itself. Focusing on mathematical practice, I propose a weak notion of objectivity of mathematical knowledge that preserves the intersubjective character of mathematical knowledge but does not bear on a view of mathematics as a body of mind-independent necessary truths. Furthermore, I show how that the successful application of mathematics in science (...) is an important trigger for the objectivity of mathematical knowledge. (shrink)