In the conditions of science-intensive economy formation, according to the strategy “Kazakhstan-2050” a lot of attention is paid to the formation and development of the science of independent Kazakhstan. The concept of personal knowledge of Michael Polanyi allows making more complex and detailed analysis of trends and processes taking place in the scientific environment of the republic. It is based on the fact that Polanyi’s theory, who is the English chemist, physicist and philosopher, representative of post-positivism, presupposes significant influence of the environment around us in the process of scientific study and research, due to which great discoveries occur, and the cognitive process is generally built. At the first stage, the researcher focuses on certain objects and phenomena, going deeper into the surrounding reality. But by becoming involved more and more, transformations can occur, as a result of which new subjects and objects of research emerge from the environment. And vice versa, the subjects on which the scientist was focused earlier can go out of the attention of his research and take a secondary position in the study environment. In this regard, the concept of personal knowledge has an appliedcharacter in the issue of the formation and development of science in the Republic of Kazakhstan. Thearticle gives many examples based on the concept of M. Polanyi, as well as his own example of choosinga topic and writing a master’s thesis.