In order to deal with the question of the applicability of mathematics to the world, this article distinguishes between natural mathematics, that is, innate mathematics, and artificial mathematics, that is, mathematics as a discipline. It argues that natural mathematics is applicable to the world because the systems of core knowledge upon which it is based, being a result of biological evolution, fit in certain mathematical properties of the world. On the other hand, the basis for the applicability of artificial mathematics to the world is Galileo’s philosophical revolution, the decision to confine physics to the study of some properties of the world mathematical in character. But, like the applicability of natural mathematics, also the applicability of artificial mathematics depends on our makeup, and hence ultimately on biological evolution.
Keywords: Applicability, conceptualizations, evolution, mathematics, simplicity