This chapter discusses the relation of mathematics to the world considering two questions: What is the relation of mathematical objects to the world? Why is mathematics applicable to the world? As to the first question, the chapter maintains that mathematical objects are not obtained by abstraction from sensible things, or by idealization from our operations of collecting objects. They are hypotheses we make to solve mathematical problems by the analytic method, several of which have an extra-mathematical origin. As to the second question, the chapter maintains, on the one hand, that the applicability of natural mathematics to the world is due to the fact that natural mathematics fits in certain mathematical properties of the world. On the other hand, the applicability of artificial mathematics to the world is due to several factors, starting with the decision of modern science to confine itself to dealing only with some phenomenal properties of the world, mathematical in kind.