In this paper, we perform a mathematical analysis of the self-compatibility of Einstein's axioms and self geussed definitions of Special Relativity (S.R.), never done previously by Einstein, nor by the literature. In particular, We find a major mathematical contradiction, which refers to "inertial" frames of reference of Special Relativity. S.R. is the theory concerned exclusively with inertial frames, and how information is passed from one inertial frame to another inertial frame, with the so-called Lorentz transformations, in the root of S.R. Though, for the one dimension, the theory has no contradiction for inertial frames, however, for two or three dimensions though, S.R. does so. Therefore, S.R. can not theorize or analyze with no contradiction in the above two or three dimensions. S.R. in the literature systematically considers only the one-dimensional configuration. Generally, it is inaccurate, saying two inertial frames move with constant velocity. Inertial frames are actually frames without the socalled inertial forces and might move in two or more dimension.