Transforming of mathematical idea in Antiquity as the subject of philosophical analysis

The mathematical idea emerging from the depths of preconceptual thinking, goes through series of development stages, without ever having rigidly fixed, unchanging content. It unfolds in the course of becoming and transforming of mathematical knowledge in the history of human thought. Moduses of development of mathematical ideas are closely tied with changes in the living conditions of society, permanently complicating practices and transforming the nature of mathematical problems. The deployment of mathematical idea means simultaneously multiplying of problems and the forming of the “branched tree” of problematic situations. All stages of transforming of mathematical idea realize perspectives (which it has opened) and discover their dead-ends and their new perspectives. Thus, mathematical idea manifests its essentially incomplete character.