The general consensus among mathematical philosophers (or philosophical mathematicians, for that matter) is that mathematics is a priori – independent of experience. However, a flourishing contemporary branch within the philosophy of mathematics is that of structuralism, which I will explain in detail in a little bit. Advocates of the structuralist approach are e.g. Shapiro  and Resnik , who argue how this approach answers a lot of important philosophical questions, including Resnik’s way of answering how mathematics can have applications in the physical world. There is a catch however: he assumes that mathematics is a posteriori – dependent of experience – contrary to popular belief.