Originally it was built in XIXth century for Bestuzhev Courses, the largest and most prominent women's higher education institution in Imperial Russia. After the revolution the courses were reorganized as the Third University of Petrograd, which was merged into the Petrograd University in September 1919.
For many years, until 1979, when mat-mex moved to Peterhoff, this was the main center of mathematical activities in Leningrad. In mornings and early afternoons it was full of students, three large lecture halls were occupied by regular lectures to undergraduate students. Two large lecture halls were located on the third floor, their large windows are seen on the pictures (the leftmost two and rightmost two on the top floor). Smaller halls accomodated nemrous recitation sessions.
At 5pm the time of research seminars and advanced courses started. Some lectures finished at 10pm. Rokhlin's lectures of his large two year Topology course were in one of the large halls on Mondays 8pm-10pm. Rokhlin's topological seminar gathered on Mondays at 5pm-7pm.
This building was also a place for Leningrad mathematical olympiads. Lots of mathematical circles for high school students (Yu M Sh - the school for young mathematicians) occupied small rooms in the evening hours.
This center was killed when mat-mex moved to a new campus in Peterhoff. A train travel of about 40 minutes long and empty cold environment did not encourage to relocate evening classes and seminars to the new building. It is dead empty after hours.
The mahematical life moved to the building of LOMI (Leningrad branch of the Matheamtics Institute of the Academy - Steklov Institute) in center of city, but could never recover, because there was not enough space for seminars and lectures.
The old mat-mex building on 10th linia of Vassilievskij Ostrov belongs now to the Faculty of Geography and Geoecology of the St.Petersburg University. When I came to there, it feeled sleepy.