Potapov entered Odessa conservatory to study music and for three years he followed the course. At this time, see :-
He was well educated and, although only seventeen, very serious. Whatever he did, he did in a very serious fashion, he walked and spoke slowly, and had his own opinion about everything. Even his teachers at the conservatory respected his profundity and thoroughness and called him 'professor'. And, as time proved, they were not mistaken.However he did not complete the four year course, transferring instead to the Faculty of Physics and Mathematics at Odessa University.
At Odessa University, Potapov was a student of Livsic and he was also taught by Livsic's teacher Krein. After graduating in 1939 he began to work for his doctorate on the problem of divisors of almost periodic polynomials. Europe was disrupted by World War II soon after he began his doctoral work but due to poor eyesight Potapov did not have to undertake military duties. He was sent to the Odessa Institute of Marine Engineer, however, to undertake mathematical work in keeping with the war effort.
In 1941 Potapov was evacuated from Odessa which is in south-western Ukraine on the Black Sea coast. He taught at a school in Fari but was allowed to return to Odessa in 1944 and, much delayed by the war, submitted his doctoral thesis to Odessa University in 1945.
When the war was over people of Jewish descent were victimised. In particular Jewish lecturers at Odessa such as Krein and Livsic were dismissed from their posts. Potapov was not Jewish but he wrote an article attacking the policy of dismissing Jewish lecturers:-
The leaders of the university have to correct their mistakes and to revive immediately the famous traditions of the Odessa School of Mathematics. The Faculty of Physics and Mathematics has to become active again, as a really creative centre of scientific and mathematical thought in our city ....He did not stop at an article as is explained in :-
During the forties and fifties V P Potapov made many unsuccessful attempts to bring M G Krein and his students back to the university. The leaders of the Faculty of Physics and Mathematics could not forgive him for this. In fact they prohibited the use of any subject connected with Potapov's investigations as a theme for a diploma.In 1948 Potapov was invited to the Pedagogical Institute at Odessa. He soon became Head of Mathematics and, from 1952, Dean of the Faculty of Physics and Mathematics. He used his position to invite Livsic and others to the Institute.
During the 1950s Potapov worked on the theory of J-contractive matrix functions and the analysis of matrix functions became his main work. He published papers on the multiplicative theory of analytic matrix functions in the years 1950-55 which contain work from his doctoral thesis. He also worked on interpolation problems.
From 1974 Potapov lectured at Odessa Institute of National Economy, then he went to Kharkov to head the Department of Applied Mathematics at the Institute for low temperature physics.
Article by: J J O'Connor and E F Robertson