Naumov studied until 1950 at the Moscow Conservatory with Heinrich Neuhaus piano and composition with Vissarion Schebalin and Anatoly Alexandrov. Naumov immediately began to teach at the Conservatory because he his ideal work did not look artistic and nervous reasons in the concert hall. From 1955 he was one of the three assistants of Heinrich Neuhaus (next Neuhaus ' son of Stanislaw and Yevgeny Malinin ), 1967, he received an own piano class. In 1976 he became a professor in 1980, he took over after Stanislaw Neuhaus ' death also his pupil. His memories of Neuhaus he reached the age in the book " Under the sign of Neuhaus " together. Until his death, he taught 50 years at the Moscow Conservatory. Naumov has produced numerous well-known artists, 70 of which won first prizes at international competitions. Mention may be made, for example, Andrei Gavrilov, Alexander Toradze, Alexander Kobrin, Vassily Lobanov, Andrei Hoteev. and Konstantin Scherbakov.
Naumows compositions are little known; among other things, he wrote a symphony, a cantata, a string quartet, a piano sonata and several song cycles.