When he was still 15 years old Fomin decided that he did not wish to study at school any longer and that he would enter Moscow University at the age of 16. He had no school certificate but he sat the university entrance examination and passed with very high marks. Despite his age he became a student and his first interest was in abstract algebra.
It was not long before Fomin had proved some new results in the theory of infinite abelian groups, examining conditions for such a group to be the direct product of a periodic subgroup and a torsion free subgroup. These results were published in his first paper while he was 19 years old.
Fomin graduated in 1939 and began to undertake research at the University of Moscow under Kolmogorov's supervision. Kolmogorov suggested problems in the theory of dynamical systems for Fomin to investigate, but Fomin was also advised by Aleksandrov to look at some problems in point-set topology and he also began to work in this area.
Aleksandrov and Urysohn had made a conjecture in 1923 concerning necessary and sufficient conditions for a Hausdorff space to be compact and this was not proved until 1935 when M H Stone gave an exceedingly complicated proof using representation theory of Boolean algebras. Aleksandrov asked Fomin to try to find a simpler proof and he succeeded with this task, the result becoming his second publication which appeared in 1940. The authors of  and  write:-
Fomin's topological papers are not numerous, but they are undoubtedly classical pieces of general topology.The work for his papers in topology was still going on when World War II broke out and Fomin was conscripted into the Red Army. Quite how he managed to continue with his mathematical researches under difficult army conditions is almost impossible to understand, but indeed he did continue to work for his doctorate. In 1942 the Red Army gave him an assignment in Kazan which was rather fortunate. At the beginning of World War II the Steklov Mathematical Institute had been moved from Moscow to Kazan and it remained there until the spring of 1943 when it was moved back to Moscow. While Fomin was in Kazan in 1942 he managed to arrange with the Steklov Mathematical Institute for him to defend his thesis and he did so brilliantly.
When the war ended Fomin returned to Moscow University and joined Tikhonov's Department. He was awarded his habilitation for a dissertation On dynamical systems with invariant measure in 1951. Two years later he was appointed professor.
In 1964 Fomin became professor in the Department of the Theory of Functions and Functional Analysis and two years later he was appointed as a professor in the Department of General Control Problems.
We have already mentioned Fomin's work on topology. There are several other areas with which he is associated and in which he made major contributions. One of the areas with which he is particularly associated is ergodic theory. He worked on this early in his career while still influenced by Kolmogorov, publishing a number of important papers such as On dynamical systems in a function space in 1950.
Fomin wrote a couple of papers with Gelfand and in the first of these, also published in 1950, they apply the theory of infinite dimensional representations of Lie groups to the theory of dynamical systems.
In 1959 Fomin began to look at applications to mathematical biology. Although he continued his work at Moscow University, and his research in other areas of mathematics, he was appointed Head of the Laboratory of Mathematical Methods in Biology in 1960. Within mathematical biology he worked in a number of areas: the excitation in nerve fibres; receptors in the visual system; control of the human motor system; and artificial intelligence and robots. In 1973 he published an important text with M B Berkinblit Mathematical problems in biology which included many of his own results in the subject.
While he was carrying out his work in mathematical biology, Fomin was also studying global analysis which he did from 1966 until his death. The reason for his interest in this subject came from another of his many interests, namely quantum physics. In this area he examined the theory of differentiable measures in infinite dimensional spaces and the theory of distributions. He worked with a number of collaborators from 1973 on the writing of a monograph on measure theory and differential equations.
Halmos, who first met Fomin in the spring of 1965, writes:-
Some of the mathematical interests of Sergei Vasilovich were always close to some of mine (measure and ergodic theory); he supervised the translation of a couple of my books into Russian. We had corresponded before we met, and it was a pleasure to shake hands with a man instead of reading a letter. Three or four years later he came to visit me in Hawaii, and it was a pleasure to see him enjoy, in contrast to Moscow, the warm sunshine.A number of important texts written by Fomin ran into several editions and have been translated into English. He wrote Elements of the theory of functions and functional analysis in two volumes. The first appeared in 1954 and covered metric and normed spaces. The second volume on measure, the Lebesgue integral and Hilbert space appeared in 1960. A second revised edition, written with Kolmogorov, was published in 1968, a third edition in 1972, and a fourth in 1976. Concerning this text the authors of  and  write:-
Fomin was a master of mathematical style; he knew how to set out complex mathematical questions simply and explicitly. ... This excellent work is used and will be used for the study of functional analysis by many generations of students.Fomin's interests outside mathematics are described in  and :-
Fomin was a man of high inner culture. His spirit responded in a lively manner to scientific problems, to artistic events, and to human stories. He loved music, literature, and painting; he drew well, played a good game of tennis, was an excellent skier, and to the end of his life did not cease to take part in sport.He died in Vladivostok while taking part in a Mathematical Summer School there.
Article by: J J O'Connor and E F Robertson