Abstract

The article deals with historical dynamics of implicit and intuitive elements of mathematical knowledge. The author describes historical dynamics of implicit and intuitive elements and discloses a historical and evolutionary mechanism of building up mathematical knowledge. Each requirement to increase the level of theoretical rigor in mathematics is historically realized as a three-stage process. The first stage considers some general conditions of valid mathematical knowledge recognized by the mathematical community. The second one reveals the level of theoretical rigor increasing, while the third one is characterized by explication of the hidden lemmas. A detailed discussion of historical substantiation of the basic algebra theorem is conducted according to the proposed technique.