Keldysh Institute of Applied Mathematics (Russian Academy of Sciences) was founded in 1953 to solve complex mathematical problems involved in national projects of space exploration, atomic and thermonuclear energy application, etc. This goal was meant to be achieved by developing and using appropriate computer hardware and software facilities. The Institute founder and first director (1953–1978 ) was President of the USSR Academy of Sciences Mstislav Keldysh

Since its first years the Institute activity oriented to solving large scale applied problems is based on the results of fundamental scientific research in mathematics, mechanics, cybernetics, informatics, etc. which is carried out by the Institute scientists. Among them are four academicians, five corresponding members of the Russian Academy of Sciences, 74 doctors of sciences and 224 candidates of sciences, including 14 laureates of Lenin prize, 30 laureates of State prize, 5 laureates of the USSR Soviet of Ministers prize.

Since the launch of the first satellite the Ballistic Center of the Institute has been engaged in navigational support of unmanned and manned space missions including those of long-term orbital stations "Salyut" and "Mir", Soviet space shuttle "Buran", spacecraft "Luna", "Venera", "Mars", etc. It also takes part in some international space projects.

The studies carried out at the Institute on algorithmic and software support of locomotive machines (walking robots), automation of manual operations for assembling machine parts by adaptable robots have been widely recognized throughout the world.

The Institute is one of the first scientific organizations in this country where a new technique to carry out theoretical studies has been developed and widely recognized.This is a computational experiment based on using perfect mathematical models, efficient computational codes and high performance computers.

The Institute has been an initiator in utilizing computer facilities in the USSR. The first mass-production computer was installed at the Institute and the first team of soviet engineers was formed to perform pioneer work in the development of computer software. In 1963 the Algol-60 translator (one of the first from the complete language version) and the IS-2 (the first mini-OS) were developed and implemented by the Institute specialists. This trend in the software development was further continued in the full scale operational systems DISPAK and OS IPM, an optimizing compiler from FORTRAN, the program package GRAFOR for graphic data representation, in the studies on supercomputer architecture and software, manymachine complexes and networks. An important role in the Institute activity is given to the system studies of applied problems such as: programming and debugging systems for the Buran space shuttle, the real-time control system, the information retrieval systems for different applications, CAD/ CAM systems, software tools for constructing applied packages.

Much attention is attached to educational and training issues. The Institute acts as a basis for Moscow State University, Moscow Engineer and Physical Institute and Moscow Aviation Institute. The Faculty of Applied Mathematics of the Moscow Physical and Technical Institute is set up at the Institute.

The Keldysh Institute is a head investigator in a number of leading studies in applied mathematics. The results obtained by the Institute scientists have been recognized in Russia and abroad. At different times several research organisations such as the Computing Center, the Institute of Space Research, the Institute of Mathematical Modelling had sprung from the Keldysh Institute and become leading scientific centers of the Russian Academy of Sciences.