Features of the scientific reflection and methodological consciousness of mathematicians of XX - the early XXI centuries

The article deals with the specificity of scientific reflection as a fundamental cognitive procedure which defines the logic of scientific research. For further advance of science conscious awareness of the character and specifics of scientific work process is necessary, as well as norms and criteria for evaluation of actions of formation and justification of scientific knowledge. The paper presents the level and structural specifics of scientific reflection as well as the role of the reflection in definition of scientific problems, the analysis of study subjects, research process and the translation of scientific knowledge. The author study various levels of scientific reflection - ontological, epistemological, methodological - in their interrelation. They are shown on the example of professional mathematician community. The paper studies the formation conditions and the subject of scientific reflection of mathematicians of the XX-XXI centuries and analyses its impact on the scientific research...