The institute was founded by a government decree in 1950 as the Institute for Applied Mathematics of the Hungarian Academy of Sciences. Its first director was Alfréd Rényi, who headed the Institute till his early death in 1970. Successive directors were László Fejes Tóth (1970-1982), András Hajnal (1982-1992), Domokos Szász (1993-1995), Gyula O. H. Katona (1996-2005), Péter Pál Pálfy (2006-2018) and András Stipsicz (2019-).
The research staff of the Institute consists of about 120 members, but at any time a considerable part of them (typically 20-30 p.c.) are on leave, fulfilling longer term invitations/temporary positions at various universities or research centers abroad.
The research staff of the Institute forms research teams covering the following research topics: algebra, algebraic geometry, algebraic logic and computer science, approximation theory, differential equations, discrete mathematics, functional analysis, geometry, information theory, mathematical statistics, number theory, probability theory, set theory, statistical physics, topology. The scientific output of the Institute is well certified by the research papers published by its staff in leading international journals. The members of the Institute play an important part in organizing the conferences of the János Bolyai Mathematical Society, the proceedings of which are also well known by the international mathematical community. In 2001 the Institute was granted the title Centre of Excellence of the European Union.
Beside the research work another important duty of the Institute is the active support of mathematics teaching at various levels from undergraduate to postgraduate. This is partly done by undertaking teaching duties at various universities of the country, by organizing graduate and postgraduate courses in the topics mentioned above, and by tutoring PhD students. From the academic year 2001/2002 to 2019/2020 a new PhD program has been launched jointly with Cental European University.
The Institute welcomes visiting researchers both at postgraduate and senior levels from Hungary as well as from abroad. Colleagues who wish to pay a short term visit to the Institute in order to establish or promote scientific contacts are also welcome.