Showing an early talent for mathematics, Naimark enrolled in a technical college at the age of fifteen in 1924 soon after the Russian Civil War had ended.
[2] In 1941 Hitler invaded the Soviet Union, and in the same year the Romanian and German occupation of Ukraine led to a massacre in Naimark's hometown.
Naimark joined special duty (called "home-guard") during the war and worked on the labor front, moving to Tashkent with the Seismological Institute at the end of 1941 as the Nazi army advanced on Moscow, where he remained until 1943.
He was appointed a professor at the Steklov Institute of Mathematics in 1962, where he stayed for the remainder of his career, and supervised seven doctoral students.
During his service in World War II Naimark wrote several papers on seismology and helped to develop the Spectral theory of ordinary differential equations.
In 1956 Naimark published his monograph Normed Rings which gave the first comprehensive treatment of Banach algebras and was enormously influential in the development of the field.