ZdzisĹ‚aw Pluta, Tadeusz Hryniewicz, Critics of Existent Theory of Mathematical Pendulum, Part 1, ILCPA Volume 13, International Letters of Chemistry, Physics and Astronomy (Volume 13) https://www.scipress.com/ILCPA.13.113 Abstract: In the framework of this paper a deep critics of existent theory of the simple mathematical pendulum is presented. This work consists of two parts. In the first part of the paper, a thesis is stated to derive a mystification character of the theory. The up-to-date, excerpted from the literature, descriptions of the oscillation motion of the mathematical pendulum, are delivered. This part of the paper is to show that the existent theory describes simply a shadow of the rotating apparent mathematical pendulum. The necessity to re-build the existent theory has been indicated. Keywords: Amplitude, Angular Velocity, Force of Gravity, Force of Inertia, Mathematical Pendulum, Vibration Period