The paper presents results of interviews with Russian Foundation for basic research experts using the method of cognitive mapping. Issues of criteria and approaches used in assessing applications for the implementation of research projects are discussed. Expert opinions regarding the value aspects of scientific activity and the organization of science in Russia are clarified. The authors came to the conclusion about existence in the studied group of coinciding views on the criteria for assessing applications, on separation of fundamental science and applied research, on ways to improve situation in Russian sciences.