Why Is Mathematics So Applicable?

In recent years, many efforts have been made to use mathematics to solve problems outside the field of mathematics. These fields go far beyond the topics traditionally studied in applied mathematics departments. Even parts of mathematics that until recently were too far-fetched to have concrete applications are now successfully used in various fields. The main question of this article is why mathematics is so useful. This is an old question about mathematics, and although it has been discussed a lot, it does not seem to have a concluding answer. Here we examine some features of mathematics that seem to play an important role in all its applications. We will also examine the effect of accepting some philosophical views on this issue. Among these philosophical views, realism and nominalism, Quine's naturalism, and Penelope Maddy's mathematical naturalism can be mentioned. The history of two important areas of mathematics, namely abstract algebra and formal logic, have been examined in detail as examples.