The purpose of this article is the philosophical analysis of development of mathematical idea in moderneuropian science. The main method of such analysis is the synthesis of historicity and logisticity in science in forming of scientific reality. Such method is added by hermeneutic methodology. In modern times, evolving mathematical idea makes a leap forward. The idea as such, divorced from practical ideas in the V–IV century BC and, having made a hermeneutic circle, overcoming the opposition of pure and applied mathematics, she returns to the practical problems. Since the mathematics is drawn to the study of processes – the transformation of geometric shapes – in the center of her attention is the study of the variables that caused the need for differential and integral calculus discoveries. This has led to the transformation of the object of mathematics: there was a turn from the study of the relationship between the constant values to the relationship between variables, which was the absolute novelty. From this point there is separating algebra from geometry and differentiation arises inside mathematics. The subject of mathematics changes also: if earlier it was the science of numbers and quantities, but now it becomes the science of number and form, ie, the general level of abstraction and generalization has risen to higher level. New perspectives and horizons of knowledge opens. The results, received by authors, can be used in numerous variants of research evolution of scientific reality.