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Historical Dynamics of Implicit and Intuitive Elements of Mathematical Knowledge

Liberal Arts in Russia. 2012. Vol. 1. No. 1. Pp. 30-35.
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Sultanova L. B.
Bashkir State University


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.


  • • history of mathematics
  • • level of theoretical rigor
  • • three-stage process
  • • hidden lemmas
  • • evolutionary mechanism of mathematical knowledge growth


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  3. Mathematics History since Ancient Times up to the Beginning of XIX century. Moscow: Nauka, 1972. Vol.1–3. Vol.3.
  4. Klein F. Lectures on Mathematics development in XIX century. Vol. I. Moscow: Nauka, 1989. P.69.
  5. Sultanova L. B. Implicit Knowledge in Mathematics. Saarbrücken (Germany): Ed. home LAP LAMBERT Academic Publishing, ISBN 978–3–8433, 2011. 212 p.