Being a talented mentor and professor, Shahinian was a teacher and research supervisor for many young gifted mathematicians.

He is the founder of the Armenian research mathematical school, which already in the 1940s and early 1950s was known internationally.

Some known Armenian poets, writers, and painters of the time have witnessed that Shahinyan had professional level knowledge in poetry, history, and arts.

Among the first students of Academician Shahinian were Sergey Mergelyan, Mkhitar Djrbashian, Rafayel Alexandryan, Alexander Talalyan, and Norair Arakelian, who became famous mathematicians, academicians, and the next leaders of the Armenian mathematical school.

Shahinian held several positions, including Head of Chair of Yerevan State University (1944–1978), Dean (1939–1942), Head of the Mathematics and Mechanics Department of the Academy of Sciences of the Armenian SSR (1945–1955), Director of the Institute of Mathematics and Mechanics (1955–1959), Academy-secretary of the Department of Physics-Mathematical Sciences (1950–1963).