The analysis and the interpretation of the huge quantity of complex experimental data from genetics and molecular biology require a paradigm shift. Mathematical modelling, as the history of physics demonstrate, is the main way for coping with such a situation (see, for example, the birth of quantum mechanics that allowed to explain many different experimental phenomena observed at the atomic and elementary particle level). Mathematical models serve as a reference conceptual framework for interpreting experimental data, suggesting new experiments, and validating predictions. In a dialectic manner, the cross-fertilization between theory and experiments is the basis for improving existing models or for replacing them with better ones.
In this spirit we present a mathematical model of the nuclear genetic code that describes completely its degeneracy distribution. Moreover, the model uncovers many symmetry properties of the code related to the chemical structure of genetic information and allows to analyze genetic sequences from a new point of view. The model can be extended to include the vertebrate mitochondrial genetic code (tesserae model) providing new insights on the difficult problem of the origin of protein synthesis and the biological mechanisms devoted to ensure the quality of genetic coding and decoding.