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In 1942 Shtokalo was appointed to the Institute of Mathematics of the Academy of Sciences of Ukraine in Kiev. In 1944 he also received an appointment at Kiev University. Then in 1949 he went to Lvov when he became the Chairman of branch of the Academy of Sciences of Ukraine.

In 1956 Shtokalo returned to Kiev where he again took up his posts at the Institute of Mathematics of the Academy of Sciences of Ukraine and his chair at Kiev University. At the Institute of Mathematics Shtokalo set up a seminar on the history of mathematics. In 1963, while retaining his position at Kiev University he moved from the Institute of Mathematics to the Institute of History of the Academy of Sciences of Ukraine in Kiev.

Shtokalo worked mainly in the areas of differential equations , operational calculus and the history of mathematics. Petryshyn , writing in describes Shtokalo's work:

After 1945 he became particularly interested in the qualitative and stability theory of solutions of systems of linear ordinary differential equations in the Lyapunov sense and in the 1940s and 1950 published a series of articles and three monographs in these areas.

Shtokalo's work had a particular impact on linear ordinary differential equations with almost periodic and quasi-periodic solutions. He extended the applications of the operational method to linear ordinary differential equations with variable coefficients.

In Petryshyn describes Shtokalo's work on the history of mathematics:

He is regarded as one of the founders of the history of Soviet mathematics and particularly of the history in Ukraine and articles about M Ostrogradski and H Voronoy , he edited the three volume collections of Voronoy 's (1952-3) and Ostrogradski 's works (1959-61), a Russian-Ukrainian mathematical dictionary (1960) and approximately eighteen other Russian-Ukrainian terminology dictionaries.

Shtokalo received the prestigious Koyré award from the International Academy of the History of Sciences in 1970.

Source:School of Mathematics and Statistics University of St Andrews, Scotland