Sapir received his undergraduate degree in mathematics (diploma of higher education) from the Ural State University in Yekaterinburg (then called Sverdlovsk), Russia, in 1978.
[3] He gave an AMS Invited Address at the American Mathematical Society Sectional Meeting in Huntsville, Alabama in October 2008.
The first paper provided an essentially complete description of all the possible growth types of Dehn functions of finitely presented groups.
[17] Sapir was also known for his work, mostly joint with Cornelia Druţu, on developing the asymptotic cone approach to the study of relatively hyperbolic groups.
[20] Sapir also introduced, in a 1993 paper with Meakin,[21] the notion of a diagram group, based on finite semigroup presentations.