The development of ideas about the principles of obtaining new knowledge for natural and social Sciences and Humanities (sociology) is considered. Scientists ' belief in the fundamental difference in the methodologies of these classes of Sciences changed to the opposite point of view due to the transition of science from the classical stage, through the non-classical stage, to the post-non-classical stage. It shows changes in the interpretation of the role of mathematical methods in science, ideas about the principles of their use as a response to this trend. It is argued that these methods are applicable in any science. In particular, mathematics cannot be classified as a natural science. All conclusions are based on the allocation of epistemological the “hypostases” of mathematics and the generalization of measurement principles that are provided for by measurement theory.