Systems of elements of genetic code are studied by their cognitive presentation in a form of mathematical matrices of symbolic and numerical kinds. This cognitive form of data presentation permits to discover new phenomenological rules of evolution of genetic codes, to reveal two branches of evolution within genetic code, to present hidden interrelations between the golden section and parameters of genetic polyplets, to disclose matrices of a hyperbolic turn in genetic matrices, etc. Mysterious sets of structures, realized by the nature in a hierarchical system of genetic codes, can be confronted by a heuristic manner with families of mathematical matrices, which contain elements of these structures. A few rules of degeneracy and segregations of genetic codes are revealed in this direction. A new answer on the fundamental question -"why 20 amino acids?" - is proposed as well.
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