Studies in contemporary mathematics in Armenia date back to 1944, when a Section for Mathematics and Mechanics was created within the newly born Armenian Academy of Sciences. The section later developed into an Institute of Mathematics and Mechanics of the Armenian Academy of Sciences whose first Director was Academician Artashes Shahinian well known for his results in complex analysis.

The Institute of Mathematics of the Armenian Academy of Sciences separated from the latter Institute in 1971. The bearers of the office of the Director of Institute have been Academician Mkhitar Djrbashian (1971-1989, 1989-1994 Honorary Director), Academician Norair Arakelian (1989-1991, 1997-2006), Academician Alexandr Talalyan (1991-1997), professor Bagrat Batikyan, corresponding member of NAS RA Valery Martirosian (2011-2012), Dr Rafayel Barkhudaryan (2014-2019), professor Grigori Karagulyan (2019-2022). The Academicians Sergei Mergelian, Raphayel Alexandrian, Ruben Ambartzumian and Anry Nersesyan also have greatly influence the formation of the scientific profile of the Institute.

In the early years the investigations carried out in the Institute concentrated on Function Theory. Gradually the sphere of investigations expanded and now includes Differential and Integral Equations, Functional Analysis, Probability Theory and Mathematical Statistics, Mathematical Physics.

At present the Institute has about 25 main researchers as well as a number of associate researchers from Yerevan State University. The essential volume of the research results obtained in the Institute has been published in the Journal "Izvetija Academii Nauk Armenii, Matematika" of the Armenian Academy of Sciences. This journal was founded in 1966 and since 1979 the cover-to-cover translation of this journal named "Journal of Contemporary Mathematical Analysis" is published by Allerton Press Inc. in USA.