The Sverdlovsk Branch of the Steklov Institute of Mathematics of the USSR Academy of Sciences was established in 1956. The branch in Sverdlovsk was founded due to the desire of the administrations of the USSR Academy of Sciences (president, Academician M. V. Keldysh) and the Institute of Mathematics (director, Academician I. M. Vinogradov) to create in the Urals, which is a large industrial and scientific region of Russia, an institution aimed to coordinate fundamental and applied research in mathematics and mechanics. Along with the foundation of the Institute, it was planned to create on its premises a high-performance computing center for collective use that would largely satisfy the computing power needs of research institutions, universities, and industrial enterprises of Sverdlovsk.

Professor S. B. Stechkin  was appointed as the first Deputy Director for the Sverdlovsk Branch at the Steklov Institute of Mathematics of the USSR Academy of Sciences.

In 1970, the Sverdlovsk Branch of the Steklov Institute of Mathematics of the USSR Academy of Sciences was transformed into the Institute of Mathematics and Mechanics of the USSR Academy of Sciences. Academician N. N. Krasovskii became the first director of the IMM.

Since March 1971, the IMM has been part of the Ural Scientific Center of the USSR Academy of Sciences. In connection with the reorganization of the Ural Scientific Center in February 1987, the Institute became part of the Ural Branch of the USSR Academy of Sciences. In December 1991, with re-establishment of the Russian Academy of Sciences, the Institute became part of the Ural Branch of the Russian Academy of Sciences. By resolution of the Presidium of the Russian Academy of Sciences No. 101 of 05.15.2012, the Institute was named after Academician N. N. Krasovskii “in order to perpetuate the memory of the leading scientist in the field of the motion stability theory and mathematical optimal control theory.”

The main objective of the Institute is to conduct of research in the fields of mathematics and mechanics and the develop solutions to applied problems based on high-performance computing.

IMM UB RAS is one of the leading academic institutions of the country with highly qualified personnel and developed infrastructure working in a wide range of fields of mathematics and related sciences. The Institute plays a systemic role in the development of mathematical and computer sciences and high-performance computing in the Ural region. The Institute’s supercomputer center provides computational and telecommunication support for the scientific and educational organizations of the Urals.

Scientific divisions of the Institute: Department of Approximation and Applications; Department of Dynamic Systems; Department of Optimal Control; Department of Differential Equations (includes the Scientific Information Resources Laboratory); Department of Function Approximation Theory (includes the sector of mathematical modeling in cardiology); Department of Applied Optimal Control; Department of Algebra and Topology; Department of Mathematical Programming; Department of Applied Problems; Department of Ill-posed Analysis and Application Problems (includes the Laboratory of Inverse Problems of Atmospheric Sounding and Climatology); Department of Control Systems; Department of Equations of Mathematical Physics; Department of Algorithmic Topology; Department of Computing Systems (includes the Complex Systems Analysis); System Support Department; and Department of Mathematical Methods of Nonlinear Dynamics.

Main research areas: mathematical optimal control theory, differential equations, function theory, algebra, discrete mathematics, topology, mathematical programming and theoretical informatics, mechanics, mathematical physics, ill-posed and inverse problems, mathematical modeling, high-performance computing systems, information and telecommunication support of research.

More than 300 employees work at the IMM UB RAS, including 5 academicians of the RAS, 7 corresponding members of the RAS, 3 professors of the RAS, 2 honored scientists of the Russian Federation, 60 doctors of physical and mathematical sciences, 89 candidates of sciences. There are three candidate and doctoral dissertation defense boards at the Institute, which work in the following subjects: Differential Equations, Dynamical Systems, and Optimal Control; Theoretical Mechanics; Real, Complex and Functional Analysis; Computational Mathematics; Discrete Mathematics and Mathematical Cybernetics; Mathematical Logic, Algebra and Number Theory. The Institute prepares highly qualified scientific and pedagogical personnel; on average, there are 10–15 graduate students in 4–5 subjects in the fields of mathematics and mechanics; computer and information sciences; and computer science and computer engineering.

Scientific schools. The Institute is home to several established scientific schools in a number of important areas of modern and classical mathematics:

School of Academician N. N. Krasovskii on the mathematical theory of optimal control and the theory of differential games (currently the leaders of the school in Yekaterinburg are corresponding members of the RAS V. N. Ushakov, A. G. Chentsov, N. N. Subbotina, and N. Yu. Lukoyanov),

School of Academician A. B. Kurzhanskii on assessing the states and parameters of dynamic systems and the synthesis of controls for incomplete data,

School of Academician Yu. S. Osipov on the control of multidimensional and infinite-dimensional systems, differential equations, and their applications,

School of Professor S. B. Stechkin on the theory of approximation of functions and operators, extremal problems for polynomials, splines, wavelets, and geometric approximation problems (currently the leaders are Academician V. I. Berdyshev and Corresponding Member of the RAS Yu. N. Subbotin),

School of Academician I. I. Eremin on mathematical programming, operations research, and pattern recognition (the school presently is headed by Professor of the RAS, Dr. Sc. M. Yu. Khachai),

School of Academician A. F. Sidorov on analytical and numerical methods for solving problems of continuum mechanics (present head is Dr. Sc. A. I. Korotky),

School of Academician A. M. Ilyin on the study of partial differential equations and their systems with small parameter (currently, the leader of the school in Yekaterinburg is Dr. Sc. A. R. Danilin),

School of Corresponding Member V. K. Ivanov on ill-posed problems and solving applied inverse problems from geophysics, sensing the atmosphere, hydro- and radiolocation (currently, the leader is Corresponding Member of the RAS V. V. Vasin),

Scientific school on algebra and combinatorics (the school originates from Professor S. N. Chernikov, now it is headed by Corresponding Member of the RAS A. A. Makhnev),

School of Academician S. V. Matveev on small-dimensional topology.

Journals. Since 1992, the Institute has been publishing the journal Proceedings of the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (since 2018 it has been indexed by WoS). Since 2015, together with the Ural Federal University, the online Ural Mathematical Journal has been published in English (since 2019 it has been indexed by Scopus).

Cooperation.

IMM UB RAS plays an important role in the integration of mathematical sciences and education in the Urals. In universities of the Urals, mainly in the Ural Federal University, more than 100 employees of the Institute teach. An important role in the training of personnel for research in the fields of mathematical modeling, high-performance computing, and system programming is played by the Chair of High-Performance Computer Technologies, created jointly with the Ural Federal University. A regional part-time school in mathematics and computer science for school students has been operating under the auspices of the Institute for 25 years. IMM UB RAS cooperates with Russian universities (Moscow State University, Ural Federal University, Chelyabinsk State University, South Ural State University, Tula State University, Udmurt State University), academic institutes (Steklov Mathematical Institute; Sobolev Institute of Mathematics SB RAS; Ishlinsky Institute for Problems in Mechanics; V. A. Trapeznikov Institute of Control Sciences; Institute of Continuous Media Mechanics UB RAS; Institute of Thermal Physics UB RAS; Institute of Engineering Science UB RAS; Institute of Solid State Chemistry UB RAS; Institute of Economics UB RAS).

IMM UB RAS is a member of the Ural Scientific and Educational Consortium of Biomedicine, Pharmacy, and Medical Engineering. The Institute is the coordinator and participant in research programs of the RAS. The Institute’s employees are members of Russian and international professional associations such as RuORS, IFAC, IIASA, IFIP, AMS, IPACS, EUROMECH, and others, members of expert councils and commissions of the RAS, Ministry of Science and Higher Education, Russian Science Foundation, Russian Foundation for Basic Research, etc. They are also on the editorial boards of scientific journals and program and organizational committees of scientific conferences.

Conferences. The Institute organizes and conducts regular international scientific conferences, seminars, youth schools (N. N. Krasovskii and A. I. Subbotin memorial conference on the mathematical optimal control theory and related; S. B. Stechkin school-conference on function theory; A. F. Sidorov conference “Actual Problems of Applied Mathematics and Mechanics”; I. I. Eremin “Mathematical Programming and Applications” conference; annu