# Institute of Mathematics of the National Academy of Sciences of Ukraine

**Institute of Mathematics of the National Academy of Sciences of Ukraine **(Інститут математики НАНУ; Instytut matematyky NANU). A scientific research institute at the National Academy of Sciences of Ukraine in Kyiv. It was established in 1934 out of three former departments of the natural science–technical section of the All-Ukrainian Academy of Sciences chaired by Dmytro Grave (applied mathematics), Heorhii Pfeiffer (pure mathematics), and Mykhailo Kravchuk (mathematical statistics). Since that time it has been the main center of mathematical research in Ukraine.

Under its first director, Dmytro Grave (1934–9), the institute was the center of Soviet algebraic studies. The priority areas of study at that time was algebra and number theory, mathematical and functional analysis, theory of integral and differential equations, probability theory and mathematical statistics, function theory, applied mathematics, and mechanics. The institute published *Zhurnal Instytutu matematyky* (1934–6). It lost several of its leading scientists to the Stalinist terror of the 1930s. Among them was the institute’s scholarly secretary Mykhailo Orlov and the research associate in the department of mathematical statistics Volodymyr Mozhar, who were executed in 1936 and 1937 respectively. Several other mathematicians were arrested, including academician Mykhailo Kravchuk, who perished in the GULAG in 1942. Under its second director, Mikhail Lavrentev (1939–41), the institute was reorganized and now included 6 departments: theory of functions of a complex variable and its application; mathematical analysis; mechanics; applied mathematics; algebra and functional analysis; and Lviv department of functional analysis of the Institute of Mathematics. The latter consisted of several distinguished Polish mathematicians of the well-known Lviv school (eg, Stefan Banach and his students, S. Mazur, W. Orlicz, and J. Schauder) that became affiliated with the institute after the Soviet occupation of Western Ukraine. During the Second World War the institute was directed by Heorhii Pfeiffer (1941–4) and was evacuated to Ufa (where it was united with the Institute of Physics of the Academy of Sciences of the Ukrainian SSR) and then Moscow. It was re-established in Kyiv in the fall of 1944 under its former director Lavrentev (1944–9). Mykola Krylov’s and Nikolai Bogoliubov’s earlier joint work in non-linear mechanics was further developed after the war by Bogoliubov, his students Ostap Parasiuk and D. Shirkov, and Yurii Mytropolsky and Yosyp Shtokalo.

Under the directors Aleksandr Ishlinsky (1949–55), Borys Hniedenko (1955–8), and Yurii Mytropolsky (1958–88), research concentrated on the theory of asymptotic methods in non-linear mechanics (Nikolai Bogoliubov, Mytropolsky, Anatolii Samoilenko), mathematical physics and mathematical methods in quantum field theory (Bogoliubov, Mytropolsky, Ostap Parasiuk, Dmytro Petryna, Vilhelm Fushchych, Samoilenko), asymptotic and operational methods for special classes of linear and non-linear equations with slowly varying coefficients (Yosyp Shtokalo, I. M. Rapoport, Stepan Feshchenko, Ivan Lukovsky), functional analysis (Stefan Banach, Marko Krein, Yurii Berezansky, Ihor Skrypnyk, Myroslav Horbachuk, Samoilenko), differential equations and dynamic systems (Mykhailo Kravchuk, Yurii Sokolov, Samoilenko, Oleksandr Sharkovsky), probability theory and mathematical statistics (Hniedenko, Anatolii Skorokhod, Volodymyr Koroliuk, Mykola Portenko), function theory and approximation methods (Mikhail Lavrenev, Mykola Korneichuk, Vladyslav Dziadyk, Oleksandr Stepanets), complex variables, the theory of conformal maps, the application of analysis methods, mechanics theory and computational mathematics (Sharkovsky, Ishlinsky, Lukovsky, Volodymyr Makarov), and elasticity theory (Hurii Savin, Ishlinsky, Mikhail Leonov). Some work was done in such areas of pure mathematics as algebraic and differential topology, differential geometry, and contemporary abstract algebra (Viktor Hlushkov, Sergei Chernikov, Volodymyr Sharko, Yurii Drozd).

Among the institute’s other achievements was the work on the creation of a universal computer ‘Kyiv’ (began in 1956 in the laboratory of computational mathematics and technology, under the direction of Borys Hniedenko, and completed under the guidance of Viktor Hlushkov in the computing center created on the basis of this laboratory). In 1962, the computing center was transformed into the Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR. In 1965, the institute’s director Yurii Mytropolsky was awarded the Lenin Prize (the most prestigious award in the USSR for accomplishments in arts and sciences) for a series of works devoted to the essential development and strict mathematical substantiation of the theory of nonlinear oscillation. In 1978, Mykola Korneichuk was awarded the State Prize of the USSR for the development of effective methods of the approximation theory. The same year, the Lviv branch of the Institute of Mathematics became the Institute of Applied Mathematics and Mechanics of the Academy of Sciences of the Ukrainian SSR. The period between 1980 and 1989 was marked by the efforts of the institute’s scientists to increase the efficiency of mathematics’ use for applied purposes. At the same time, several priority areas of fundamental research were established, including asymptotic and qualitative methods in the theory of differential equations, analytical methods of the theory of random processes, functional analysis, theory of approximation of functions, and dynamics and stability of special multidimensional systems. The institute’s scientists were awarded the State Prize of the Ukrainian SSR in 1970, 1975, 1978, 1980, 1982, 1983, 1985, and 1987.

In the early 1990s the institute had 18 scientific departments and 10 structural laboratories. In 1994 it received its present name: the Institute of Mathematics of the National Academy of Sciences of Ukraine. The institute has remained a leader in mathematical research under the directors Anatolii Samoilenko (1988–2020) and Oleksandr Tymokha (2020–). In the 1990s, several of its leading scientists were awarded the State Prize of Ukraine in Science and Technology—the highest award given by the Government of Ukraine for accomplishments in science and technology. For instance, in 1994, the institute’s veteran mathematician Mykola Korneichuk was awarded the prize for the cycle of works titled ‘The theory of splines and its application in optimization of approximations.’ In 1996, Yurii Mytropolsky, Anatolii Samoilenko, and several of their colleagues were awarded the prize for the cycle of works titled ‘New mathematical methods in nonlinear analysis.’ In 1998 another group of mathematicians was awarded the prize for the cycle of works titled ‘New methods in the theory of generalized functions and their application to mathematical physics.’ More state prizes of Ukraine were awarded to the institute’s scientists over the next two decades (2001, 2003, 2005, 2007, 2010, 2012, 2018, and 2020). Of particular importance were also the accomplishments of individual mathematicians, among them Volodymyr Koroliuk’s research into the boundary theorem of the averaging type, diffusive and Poisson approximation of semi-Markov random evolution, and diffusive approximation of stochastic systems (1990–2018); Yurii Berezansky’s continued research into the theory of spaces with positive and negative norms and its application in mathematical physics; Promarz Tamrazov’s solution of a series of extremal problems for conformal maps and those related to the capacity of capacitor (1980–2010); Yurii Samoilenko’s mathematical models of planetary magnetism (2000–8); and Volodymyr Sharko’s contribution to the creation of the Kyiv school of topology (1975–2014).

The institute has 11 departments (algebra and topology; theory of dynamical systems and fractal analysis; differential equations and oscillation theory; complex analysis and potential theory; mathematical problems of mechanics and control theory; mathematical physics; nonlinear analysis; numerical mathematics; theory of random processes; theory of functions; and functional analysis), 5 laboratories (differential equations with partial derivatives; boundary value problems of differential equations theory; optimal methods for inverse problems; topology; and fractal analysis), and employs 148 scientists, including 6 academicians of the National Academy of Sciences of Ukraine (in 2019). It has published the journals *Zhurnal Instytutu matematyky AN URSR* (1934–8), *Zbirnyk prats' Instytutu matematyky AN URSR* (1938–48), *Ukrainskii matematicheskii zhurnal*/*Ukraїns'kyi matematychnyi zhurnal* (74 vols, 1949–), *Neliniini kolyvannia/Journal of Mathematical Sciences* (25 vols, 1998–), *Ukraїns'kyi matematychnyi visnyk* (19 vols, 2004–), *Methods of Functional Analysis and Topology* (28 vols, 1995–), *Zbirnyk naukovykh prats' Instytutu matematyky NAN Ukraїny* (18 vols, 2004–), *Theory of Stochastic Processes* (20 vols, 199'-), and *Symmetry, Integrability, and Geometry: Methods and Applications* (18 vols, 2005–).

BIBLIOGRAPHY*Instytut matematyky* (Kyiv 1988)

Samoilenko, A., Strok, V., Sukretnyi, V., *Khronika* –* 2005. Storinky z istoriї Instytutu matematyky* (Kyiv 2005)*Do istoriї Instytutu matematyky NAN Ukraїny (Istorychni narysy)* in *Zbirnyk prats' Instytutu matematyky NAN Ukraїny*, vol. 13 (2016), no. 16

The institute’s official website: https://imath.kiev.ua/

Serhiy Bilenky, Wolodymyr Petryshyn

[This article was updated in 2022.]