Introduction

Mathematical chemistry nowadays presents a variety of approaches to understanding the mathematical structures which lie behind existing chemical concepts, to establishing and investigating novel mathematical models of chemical phenomena, and applying mathematical ideas and techniques in chemistry. Throughout the entire history of chemistry certain scientists, usually not numerous, were inclined to contemplate connections between mathematics and chemistry and the possibility of using mathematics for deducing known and predicting new chemical facts. Extensive use of mathematical methods is traditional in various branches of physical chemistry, especially in thermodynamics (partial derivatives, proper and improper differentials, path integrals etc.) and chemical kinetics (coupled non-linear differential equations). A real need for mathematics in chemistry appeared, however, only after the discovery, made by physicists in the first three decades of our century, that the basic properties of atoms and molecules can be explained and predicted by means of quantum theory. The awareness that chemistry cannot be understood without a knowledge of quantum physics, including its sophisticated mathematical apparatus, was the actual driving force which led to the introduction of mathematics and mathematical thinking into (or at least not very far from) chemical laboratories.