Mazurov's parents Daniil Petrovich and Evstolia Ivanovna were teachers.
He then moved to Sverdlovsk (now Yekaterinburg) to study mathematics in Ural State University.
After graduating in 1965, they moved to Novosibirsk where Mazurov joined the research staff of the Sobolev Institute of Mathematics (Russian: Институт математики СО РАН).
Mazurov is an editor (with Evgenyj Khukhro) of the "Kourovka Notebook",[3] a periodically updated collection of over 1,000 open problems in Group Theory.
Mazurov obtained several results that contributed to the proof of the classification of finite simple groups, also known as the Enormous Theorem[4] and considered one of the greatest achievements in mathematics of the 20th century.