Gorban has contributed to many areas of fundamental and applied science, including statistical physics, non-equilibrium thermodynamics, machine learning and mathematical biology.

[1] He has founded several scientific schools in the areas of physical and chemical kinetics, dynamical systems theory and artificial neural networks, and is ranked as one of the 1000 most cited researchers of Russian origin.

His father Nikolai Vasilievich Gorban was a historian and writer exiled to Siberia, and his mother was a literature teacher in Omsk Pedagogical Institute.

From 1965 to 1966, he studied at the Specialized Educational Scientific Center on Physics, Mathematics, Chemistry and Biology of Novosibirsk State University (SESC NSU).

In 1967, at the age of 15, he entered Novosibirsk State University but was excluded from it in autumn 1969 because of his participation in January 1968 in political student movements against the convictions of Soviet writers Alexander Ginzburg and Yuri Galanskov.

After studying for a year in a vocational technical school and following an individual extramural program at Omsk Pedagogical Institute, he obtained a master's degree with a thesis entitled Sets of removable singularities in Banach spaces and continuous maps under the supervision of Russian mathematician Vladimir B. Melamed.

A top level view of scientific activity and the future of applied mathematics have been given in his book "Demon of Darwin: idea of optimality and natural selection",[b 1] articles and public lectures.

[4] In functional analysis, Gorban has investigated the properties of analytical Fredholm subsets in Banach spaces, formulated the relevant principle of maximum modulus and proved an analogue of the Remmert-Stein theorem.

In mathematical chemistry, Gorban has investigated the thermodynamical properties of chemical systems based on the analysis of Lyapunov's function trees in the polytope of conservation laws.