The paper examines stages of the university evolution and discusses the problem of how social transformations (transition to knowledge society, fourth industrial revolution) and science and technology (technoscience) development influence the converging changes in science and education. The analysis of the contemporary university model is made in the perspective of social epistemology, since the university is the place for production and translation of knowledge, and epistemology is focused on interpretation of knowledge models. The models of knowledge (knowledge-intuition, knowledge-verification, knowledge-conformity to the pattern, knowledge-information, knowledge-involvement, knowledge-method) defined in classical epistemology and the related educational concepts are analyzed. It is shown that the types of knowledge accentuated in classical epistemology do not represent the whole palette of the semantic variety of knowledge and the ways of its obtaining in the educational process; concretization is required according to cultural and historical specifics. Thus, in the knowledge society, both the knowledge model (Mode-2) and the analysis tool (social epistemology) have changed. It is revealed how knowledge in social epistemology is rethought, where the object is represented by the so-called knowledge society. In traditional epistemology, knowledge was interpreted as the result of cognitive activity; social epistemology emphasizes the dependence of knowledge on the social and humanitarian context. The transition to a knowledge society has become a challenge not only for science, but for education as well. Traditionally, the university was a place of production (science) and translation (education) of knowledge. In a knowledge society, where knowledge has become a competitive resource, special attention is paid to the relationship between knowledge and action. Knowledge management theorists have developed a model of organizational knowledge as of nonformalized knowledge. The contemporary university, being an organization of knowledge producing, has become a place where both strategies for the formation of knowledge are present. Based on the conducted study of the university evolution and the specific features of its being in the knowledge society, the authors come to the conclusion that the genome of the contemporary university represents an indivisible unity of scientific and educational activities. At the same time, with the preservation of the objectives, mechanisms for obtaining and translating knowledge change significantly. Challenges for the contemporary university are conditioned by the formation of a new model of knowledge Mode-2 developed in the knowledge society; digitalization of education, taking place at the stage of development, referred to as the fourth industrial revolution; awareness of the necessity of transition to "complex thinking" as a prerequisite for understanding the supercomplexity of the world that has opened to science today.