Mathematical chemistry illustrations: a personal view of less known results

We have selected to review half a dozen outstanding results of application of mathematics to chemistry, which despite their importance are not well and widely known to chemists. Most of them involve novel mathematical concept or part of mathematics not widely known in chemistry, such as concept of circuits with alternating C=C and C–C bonds within individual Kekulé valence structures, known as conjugated circuits; paths and partial ordering leading to periodic tables of isomers; aromatic sextets in polycyclic benzenoid compounds; local aromaticity derived from ring bond orders based on Pauling CC bond orders; construction of orthogonal molecular descriptors producing stable regression equations; graphical and numerical representation of DNA and proteins; numerical characterization and comparative study of proteomics maps; and finally we will overview the exact solution to the protein alignment problem.