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Proteins are long chain molecules that fold into beautiful and complicated structures before fulfilling their functions in the living organisms. This talk focus on some mathematical attempts to bring classification of protein native structures from relative comparison to known examples to absolute description of each structure - one step up the scientific evolutionary ladder. In the talk, I will shortly introduce some of the reduced mathematical representations of protein backbones and say a few words on similarity measures on the space of protein structures. The main focus of the talk will be on structural descriptors and on how to use structural descriptors to give the best possible pseudo metric on the space of all known protein folds. In the talk, I will introduce three families of descriptors: The generalized Gauss integrals, that are based on the writhe of an open space curve and come from integral formulas of the Vassiliev knot invariants. The average crossing pattern occurrences, that also generalize the writhe. A new family based on a coloring of the protein backbone and on the distance excess / parabolic section of curves. This family is constructed to be "orthogonal" to the writhe.