He received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai.

He was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept it in person, allegedly due to antisemitism against Jewish mathematicians in the Soviet Union.

"[8] Margulis's early work dealt with Kazhdan's property (T) and the questions of rigidity and arithmeticity of lattices in semisimple algebraic groups of higher rank over a local field.

Margulis proved that under suitable assumptions on G (no compact factors and split rank greater or equal than two), any (irreducible) lattice Γ in it is arithmetic, i.e. can be obtained in this way.

The affirmative solution for n ≥ 4, which was also independently and almost simultaneously obtained by Dennis Sullivan, follows from a construction of a certain dense subgroup of the orthogonal group that has property (T).

In 1986, Margulis gave a complete resolution of the Oppenheim conjecture on quadratic forms and diophantine approximation.