Nikolay Nikolayevich Bogolyubov^{[a]}^{[1]} (Russian: Никола́й Никола́евич Боголю́бов; Ukrainian: Микола Миколайович Боголюбов, romanized: Mykola Mykolaiovych Bogoliubov; 21 August 1909 – 13 February 1992) was a Soviet, Ukrainian and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal.
Nikolay Bogolyubov  

Николай Боголюбов, Микола Боголюбов  
Born  
Died  13 February 1992  (aged 82)
Nationality  Soviet, Ukrainian, Russian 
Known for 

Awards  Stalin Prize (1947, 1953) USSR State Prize (1984) Lenin Prize (1958) Heineman Prize (1966) Hero of Socialist Labor (1969, 1979) Max Planck Medal (1973) Lomonosov Gold Medal (1985) Dirac Prize (1992) 
Scientific career  
Fields  Theoretical physics, mathematical physics, mathematics 
Institutions  Kyiv University Steklov Institute of Mathematics Lomonosov Moscow State University Joint Institute for Nuclear Research 
Doctoral advisor  Nikolay Krylov 
Doctoral students  Dmitry Zubarev Yurii Mitropolskiy Sergei Tyablikov Dmitry Shirkov 
Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music.
Six months after Mykola's birth, the family moved to Nizhyn, city of Chernihiv Oblast, Ukraine, where his father taught until 1913.
From 1913 to 1918, the family lived in Kyiv. Mykola received his initial education at home. His father taught him the basics of arithmetic, as well as German, French, and English. At the age of six, he attended the preparatory class of the Kyiv Gymnasium. However, he did not stay long in the gymnasium—during the years of the Ukrainian War of Independence from 1917 to 1921, the family moved to the village of Velyka Krucha (now in Poltava Oblast, Ukraine). From 1919 to 1921, he studied at the Velykokruchanska sevenyear school – the only educational institution he graduated from.^{[2]}
The family soon moved to Kyiv in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923.^{[3]} After finishing the sevenyear school, Bogolyubov independently studied physics and mathematics, and by the age of 14, he was already participating in the seminar of the Department of Mathematical Physics at Kyiv University under the supervision of Academician Dmitry Grave.
In 1924, at the age of 15, Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925 he entered Ph.D. program at the Academy of Sciences of the Ukrainian SSR under the supervision of the wellknown contemporary mathematician Nikolay Krylov and obtained the degree of Kandidat Nauk (Candidate of Sciences, equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of Doktor nauk (Doctor of Sciences, equivalent to Habilitation), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field.
This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the calculus of variations, the theory of almost periodic functions, methods of approximate solution of differential equations, and dynamical systems. This earlier research had already earned him recognition. One of his essays was awarded the Bologna Academy of Sciences Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics. This was the period when the scientific career of the young Nikolay Bogolyubov began, later producing new scientific trends in modern mathematics, physics, and mechanics.
Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kyiv school of nonlinear oscillation research", where their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947) leading to a creation of a large field of nonlinear mechanics.
And this can explain, as the authors believe, the need to shape the collection of problems of nonlinear perturbation theory into a special science, which could be named NONLINEAR MECHANICS.
— N. M. Krylov and N. N. Bogolyubov, New methods in nonlinear mechanics, ONTI GTTI, MoscowLeningrad, 1934
Distinctive features of the Kyiv School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a control engineering point of view, the key achievement of the Kyiv School was the development by Krylov and Bogolyubov of the describing function method for the analysis of nonlinear control problems.
In 1936, M. M. Bogolyubov was awarded the title of professor, and from 1936 to 1940, he chaired the Department of Mathematical Physics at Kyiv University In 1939, he was elected a corresponding member of the Academy of Sciences of the Ukrainian SSR (since 1994 – National Academy of Sciences of Ukraine). In 1940, after the reunification of Northern Bukovyna with Ukraine, Nikolay Bogolyubov was sent to Chernivtsi to organize mathematical departments at the Faculty of Physics and Mathematics of Chernivtsi State University.
After the German attack against the Soviet Union on 22 June 1941 (beginning of the Eastern front of World War II), most institutes and universities from the western part were evacuated into the eastern regions, far from the battle lines. Nikolay Bogolyubov moved to Ufa, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University and at Ufa Pedagogical Institute, remaining on these positions during the period of July 1941 – August 1943.
In autumn 1943, Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the Moscow State University (MSU). At that time the Head of the Department was Anatoly Vlasov (for a short period in 1944 the Head of the Department was Vladimir Fock). Theoretical physicists working in the department in that period included Dmitri Ivanenko, Arseny Sokolov, and other physicists.
In the period 1943–1946, Bogolyubov's research was essentially concerned with the theory of stochastic processes and asymptotic methods. In his work^{[citation needed]} a simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker–Planck equation, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian, and in the general case as a nonMarkov process. This work was the first to introduce the notion of time hierarchy in nonequilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a oneparameter integral manifold for a system of nonlinear differential equations. He investigated periodic and quasiperiodic solutions lying on a onedimensional manifold, thus forming the foundation for a new method of nonlinear mechanics, the method of integral manifolds.
In 1946, he published in JETP two works on equilibrium and nonequilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics (Moscow, 1946).
On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.
In 1947, Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the Steklov Institute of Mathematics. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics (Head Vasily Vladimirov), of Statistical Mechanics, and of Quantum Field Theory (Head Mikhail Polivanov). While working in the Steklov Institute, Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory, renormalization group, axiomatic Smatrix theory, and works on the theory of dispersion relations.
In the late 1940s and 1950s, Bogolyubov worked on the theory of superfluidity and superconductivity, where he developed the method of BBGKY hierarchy for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on quantum field theory, where introduced the Bogoliubov transformation, formulated and proved the Bogoliubov's edgeofthewedge theorem and Bogoliubov–Parasyuk theorem (with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the quark model of hadrons; in 1965 he was among the first scientists to study the new quantum number color charge.
In 1946, Nikolay Bogolyubov was elected as a Corresponding Member of the Academy of Sciences of the Soviet Union. He was elected a full member (academician) of the Academy of Sciences of the Ukrainian SSR and in full member of the Academy of Sciences of the USSR in 1953.
Since 1956, he worked in the Joint Institute for Nuclear Research (JINR), Dubna, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of the Laboratory of Theoretical Physics. This laboratory, where Nikolay Bogolyubov worked for a long time, has traditionally been the home of the prominent Russian schools in quantum field theory, theoretical nuclear physics, statistical physics, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966–1988.
In the postwar years, M. M. Bogolyubov worked as the dean of the Faculty of Mechanics and Mathematics at Kyiv University and headed the Department of Probability Theory at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (now – NASU Institute of Mathematics). His first students in nonlinear mechanics were Yurii Mitropolskyi and Yu. V. Blagoveshchensky, and in probability theory and mathematical statistics, I. I. Gikhman.
In the first half of the 1960s, Bogolyubov worked on organizing the Institute for Theoretical Physics of the Academy of Sciences of the Ukrainian SSR (now – Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine) and from 1966 to 1973, he served as its director.^{[4]} When the institute was established in 1966, it consisted of three departments: Mathematical Methods in Theoretical Physics (Head: Academician Ostap Parasyuk), Theory of the Nucleus (Head: Oleksandr Davydov), and Theory of Elementary Particles (Albert Tavkhelidze). In 1968, the institute organized the Department of Nuclear Reaction Theory (Head: Oleksiy Sytenko).
Nikolay Bogolyubov was married (since 1937) to Evgenia Pirashkova.^{[5]} They had two sons – Pavel and Nikolay (jr). Nikolay Boglyubov (jr) is a theoretical physicist working in the fields of mathematical physics and statistical mechanics. Pavel was a theoretical physicist, Doctor of Physical and Mathematical Sciences, senior researcher, and head of the sector at the Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research.^{[6]}
Nikolay Bogolyubov was a scientific supervisor^{[7]} of Yurii Mitropolskiy, Dmitry Shirkov, Selim Krein, Iosif Gihman, Tofik Mamedov, Kirill Gurov, Mikhail Polivanov, Naftul Polsky, Galina Biryuk, Sergei Tyablikov, Dmitry Zubarev, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warm atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogolyubov approach".
Nikolay Bogolyubov received various high USSR honors and international awards.
Institutions, awards and locations have been named in Bogolyubov's memory:
In 2009, the centenary of Nikolay Bogolyubov's birth was celebrated with two conferences in Russia and Ukraine:
Fundamental works of Nikolay Bogolyubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.
He built a new theory of scattering matrices, formulated the concept of microscopical causality, obtained important results in quantum electrodynamics, and investigated on the basis of the edgeofthewedge theorem the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.
Mathematics and Nonlinear Mechanics:
Statistical Mechanics:
Quantum Field Theory: