There he became a student of Lyapunov and, after a highly successful university career, he graduated in 1887. Steklov remained at Kharkov University working towards becoming a university teacher.
Doon siya ay naging isang mag-aaral ng Lyapunov at, matapos ang isang lubhang matagumpay na unibersidad karera, siya ay nagtapos sa 1887. Steklov naiiwan sa Kharkov University nagtatrabaho patungo sa pagiging isang guro ng unibersidad.