Reviewed is development of ideas about principles of obtaining new knowledge in natural and socio-humanitarian sciences (sociology). Scholars’ conviction in principal difference of methodologies of these sciences was replaced by the opposite view owing to the transition of science from the classical stage over the non-classic one to the post-non-classic stage. Changing treatments are shown of the role of mathematical meth ods in the science, of ideas about the principles of their usages as a response to this tendency. It is asserted that these methods are applicable to any science. In particular, mathematics cannot be attributed to natural sciences, all conclusions are based on emphasizing gnosiological facet of mathematics and on generalisations of measurement principles that are provided by the theory of measurings.