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Ivan Gutman's Essay - "1500 Scientific Papers and Before"

2023-11-21

This is essay is based on Professor Ivan Gutman's lecture that he delivered at the Kragujevac University.

On the occasion of the publication of my 1500th scientific paper, the Rector of the Kragujevac University invited me to deliver a lecture on this matter. Indeed, my lecture was a brief overview of my 50+ years activity in the area of mathematical chemistry, but at its beginning I wanted to make clear that mathematical research in chemistry has a much older history, and certainly does not begin with me. This introductory part of my lecture may be interesting to a wider audience, and in what follows I briefly repeat it.

1) **2400 years ago**, a scholar in Athens named Aristocles (427-347 BC), nicknamed Plato, studies regular polyhedra , and proves that there are exactly five: tetrahedron, cube, octahedron, icosahedron, and dodecahedron. He then claims that the four elements known at that time (fire, air, water, earth) each consist of particular polyhedra: fire of tetrahedra, air of octahedra, water of icosahedra, and earth of cubes. Celestial bodies would then be made of dodecahedra. Today we see this as an early mathematical model of matter.

2) **1200 years ago**, Jabir ibn Hayyan (712-815), the greatest (al)chemist of his time, claims that the numbers 1, 3, 5, 8, and especially their sum 17, are of great importance, and that everything in the world is determined by 17. In particular, metals have 17 “powers” (qualities).

3) **500-300 years ago**, many alchemists use geometrical constructions in the pursuit of the philosopher’s stone.

4) **250 years ago**, the Russian savant Mihail Lomonosov (1711-1765) writes a booklet entitled “*Elementa Chymiae Mathematicae*” (Elements of Mathematical Chemistry), in which the term “mathematical chemistry” is mentioned for the first time.

5) **150 years ago**, the British mathematician Arthur Cayley (1821-1895) publishes a paper “*On the Mathematical Theory of Isomers*”, first truly scientific work in mathematical chemistry. Another British-American mathematician, James Joseph Sylvester, publishes a paper entitled “*Chemistry and Algebra*”.

6) **90 years ago**, the Hungarian-Swiss-American mathematician Görgy Pólya (1887-1985) solves the problem of enumeration of chemical isomers.

7) **90 years ago**, the German physical chemist Erich Hückel (1896-1980) uses graph spectral theory in the quantum theory of molecules.

8) **50 years ago**, enters Ivan Gutman.

The purpose of the above (brief and imprecise) historical journey was to show how deep the roots of mathematical chemistry are. The concluding statement was the following:

*My contribution to the ocean of science is not a drop of water, but a glass of water.*

*Professor Ivan Gutman is a Fellow of the Core Academy in both Division of Mathematics and Information Sciences and Division of Natural Sciences. *