Applicability of Mathematics in Science

Our understanding of nature, our explanations of natural phenomena, crucially depend on the use and interpretation of mathematics in scientific practice. Mathematics provides a common language for the empirical (i.e., the natural and social) sciences and through its tools we get successful predictions and empirical confirmations that are about the entities and the phenomena of these sciences. When this happens, we say that mathematics successfully applies in science. But the success of mathematics in science prompts the following question: How is it possible for the abstract entities of mathematics (numbers, equations, integrals, and so forth) to say something interesting about phenomena and entities, as for instance nuclear reactions and proteins, that are studied by the empirical sciences and have a completely different nature? The issue is philosophical and the research topic associated to it is known as the Applicability of Mathematics in Science. In this entry, after a short presentation of the topic, I shall offer the reader an overview of some accounts that have been proposed to tackle the philosophical issue. Furthermore, I shall point to some connections that have been established between the study of the applicability of mathematics in science and other debates in philosophy of science and philosophy of mathematics.