It is suggested that Smirnov was influenced by the works of Velimir Khlebnikov, who had emphasized that the most fruitful results in arts and humanities could be achieved only after thoroughly understanding the natural sciences.

According to the testimony of a friend, the artist S. P. Isakov, Smirnov, following this advice, entered Moscow State University after his discharge from the army in 1921 and focused his attention to the study of mathematics.

Smirnov's initial period of research ended in 1938 with the defense of his doctoral dissertation "On approximation of the distribution laws of random variables" (Russian: Об аппроксимации законов распределения случайных величин), which served as the foundation for his work on nonparametric tests for which he was later renowned.

His sudden, unexpected death left him unable to complete his research in mathematical genetics, to which he had returned in the final years of his life with the intention to publish several works.

Smirnov made great efforts to popularize and widely disseminate methods of mathematical statistics in the natural sciences and engineering.