# Serge Mikhalovich Nikolski

### Quick Info

Born
30 April 1905
Zavod Talitsa, Perm Province, Russian Empire
Died
9 November 2012
Moscow, Russia

Summary
Serge Nikolski was a Russian mathematician who worked in functional analysis and partial differential equations.

### Biography

Perhaps the first comment we should make at the beginning of this biography is to say that we have not made an error in giving Serge Mikhalovich Nikolski's dates of birth and death above; he really did live to be 107 years old. The second comment is to say that his name appears in various different transliterations, the most common versions of his first name being Serge and Sergey while that of his family name is Nikol'ski, Nikolski, Nikolski, and Nikolsky. We have never seen anything other than Mikhalovich for his patronymic. His place of birth, the small Zavod Talitsa settlement in Perm Province, is now the city of Talitsa in the Sverdlovsk Region. The final comment to make about the data in our heading regards the date of his birth. When he was born in 1905 the Russians were still using the Old Style Julian Calendar. Only on 31 January 1918 did the Bolshevik government adopt the Gregorian Calendar which required 13 days to be added. For this reason his date of birth sometimes appears as 17 April 1905 (correct at the time of his birth) and, at other times, 30 April 1905 (the corrected date in the Gregorian Calendar).

Serge Mikhalovich Nikolski was the son of Mikhal Dmitrievich Nikolski and Lyudmila Mikhalovna Fedorova. Mikhal Dmitrievich was a forester who had been trained at the St Petersburg Forestry Institute. As well as being an active forester, he also taught forestry at a specialist school. Lyudmila Mikhalovna was a teacher in a country school. Serge Mikhalovich was the fourth of his parents' six children and he spent his early years in the region of Poland which had become part of the Russian Empire in 1795 when its lands were divided between Prussia, the Austrian Empire and the Russian Empire. Soon after Sergei's birth his father began working at the Augustow forest, near the Prussian border, and the young boy began his education in the city of Suwalki. This town was really Polish but formally part of the Russian Empire.

At the end of July 1914 France began mobilizing its troops and, on 1 August, Germany declared war on Russia, declaring war on France two days later. With the outbreak of war, the Nikolski family moved to Chernigov (now known as Chernihiv in Ukraine), where Sergei Mikhalovich continued to study at the gymnasium. In 1918, after the start of the Russian Civil War, the family moved to the Voronezh region in the same year that a forestry department was opened as part of Voronezh Agricultural Institute. Mikhal Dmitrievich worked as a forester at the Shipov Forestry Management Enterprise in the Shipov forest near the village of Livenki in the Pavlovsk district.

At the age of fourteen Serge Mikhalovich began working as a forester but also had a job as an observer at the Krasnyi Kordon meteorological station, one of around twenty large and well-equipped meteorological stations then existing in Russia. He then worked as an assistant gardener in the nursery of the Livensky state farm. In 1919 he began his studies in Buturlinovka and continued them in Pavlovsk, graduating from the school there in 1921. His father was fond of mathematics and had taught Serge the basic properties of the differential and integral calculus. At this time he read his first mathematical book, Elements of Mathematical Analysis which was written in a very intuitive way. By 1921 Serge's father Mikhal Dmitrievich, seeing that his son was a talented mathematician, thought that Serge should become an engineer. Mikhal Dmitrievich was murdered, however, in late 1921 by bandits who came to the Shipov Forest [9]:-
There is now a granite monument in the forest at the spot of his murder. The bandits also destroyed the meteorological station, turning it into a pile of glass and metal. It was not reconstructed in its previous distinctive form.
After Mikhal Dmitrievich's murder, Serge, his siblings and his mother returned to Chernigov where Serge worked at the Professional School of the Local Department of Political Education. He studied on his own, taking examinations at the Chernigov technical school without attending classes. He decided in 1925 that he wanted to study higher education, which he could not do in Chernigov, but this was not easy for a young man unless he had the right connections [9]:-
In 1925 Nikolski decided to go to another town in order to attend an institute of higher education. But at the time such institutes admitted students only by recommendations from social organisations. He could not get a recommendation to a technical institute. Nikolski tried in 1925 to enter the Kiev Polytechnical Institute without a recommendation, but he was rejected, not even given an examination. A trade union offered him a recommendation to Ekaterinoslav University, then called the Institute of National Education, and he went there. Thus, Nikolski found himself in Ekaterinoslav (now Dnepropetrovsk).
Nikolski's family were not able to give him financial support so when he arrived in Ekaterinoslav, in addition to full time study, he took a labouring job in a metallurgical factory. At this stage he was still intending to become an engineer as his father had wanted, so his initial plan was to spend a year at Ekaterinoslav University in the Physics and Mathematics Faculty and then transfer to a technical institute. He soon changed his plan, however, when he discovered his deep love of mathematics. A major factor in this was certainly the lectures of Grigory Alekseevich Gruzintsev (1881-1929).

Grigory Alekseevich was the son of Aleksii Petrovich Gruzintsev, the professor of physics at Kharkov University. He graduated from a gymnasium in 1898 and began his studies in the Physics and Mathematics faculty of Kharkov University. He was sent away from the university in 1901 and given no right to return. He became acquainted with Sergi Bernstein and attended seminars of such famous mathematicians as Felix Klein, David Hilbert and Hermann Minkowski. Gruzintsev graduated with an external degree from Kharkov University in 1908 and, in 1910, he was appointed as a docent at that university [44]:-
Not long before the 1914 war Gruzintsev, then a lecturer at Kharkov University, was sent to Göttingen to complete his education in the sciences. There he attended a seminar of Hilbert. However, the imperialistic war began, and Gruzintsev had to move to Switzerland and then to Italy, where he was at universities during the whole war, and only after the 1917 revolution did he return to Russia, having been appointed to the post of professor at the recently opened Ekaterinoslav University. There he taught courses in mathematical analysis and foundations of geometry. A serious illness (tuberculosis) did not allow him to implement his research ideas in the area of the foundations of mathematics, but the influence on students of his lectures and seminars, which were infrequent because of sickness, was enormous. He died in 1929.
We have given quite a few details about Gruzintsev since we believe that he was important in changing Nikolski from a career in engineering to one in mathematics.

Let us explain at this point that the city of Ekaterinoslav was renamed Dnipropetrovsk in 1926. The name change followed the Ukrainian War of Independence (1917-1921) after which Ukraine became part of the Soviet Union. The name Dnipropetrovsk was chosen so that the city was named for Grigory Petrovsky, the Communist leader of the country. Ekaterinoslav University was founded in 1918, but renamed Ekaterinoslav Institute of Education in 1920. After the city changed its name, the Institute became Dnipropetrovsk Institute of Education but in 1933 it became Dnipropetrovsk State University. Let us, for simplicity, just refer to it as Dnipropetrovsk University.

Nikolski graduated from Dnipropetrovsk University in 1929 and began teaching at the University as an assistant professor. He also taught mathematics and physics at a workers' school in Kamenskoe immediately after he graduated. We note that again there were changes of name and Kamianske was renamed Dniprodzerzhynsk in 1936 but, in 2016, it reverted to its original name of Kamianske. In 1930 several new educational establishments were set up in Dnepropetrovsk, such as the Institute of Railway Transport Engineers and the State Academy of Civil Engineering and Architecture. Nikolski taught mathematics courses at several of these new educational establishments.

After Aleksii Petrovich Gruzintsev died in 1929, Isaak E Ogievetskii was appointed to the chair of mathematics at Dnipropetrovsk. He was very successful obtaining grants from different institutes to allow him to invite leading mathematicians to lecture at Dnipropetrovsk. Pavel Sergeevich Aleksandrov, Benjamin Fedorovich Kagan, Ivan Georgievich Petrovsky and Andrei Nikolaevich Kolmogorov made frequent visits and gave lectures at Dnipropetrovsk. Kolmogorov, who had been appointed a professor at Moscow University in 1931, was very impressed by Nikolski's work and began to advise him on writing a Candidate's thesis (equivalent to a Ph.D.).

Nikolski married Nina Ivanovna Shlepkina (20 August 1910 - 23 January 1998) who was born in a small town of Kulebaki, which is located on the Oka river and is famous for metallurgical production. She had graduated from the University of Dnipropetrovsk. They had a son Yuri born 20 March 1934, a son Mikhail born 12 October 1941 who became a mathematician, and a daughter Natalia born in 1946.

Nikolski was allowed to spend 1934-35 as a graduate student at Moscow State University where he attended lecture courses on functional analysis by Abraham Ezechiel Plessner and Lazar Aronovich Lyusternik (1899-1981), as well as seminars by Kolmogorov and Igor' Nikolaevich Khlodovskii (1903-1951) on approximation theory. Nikolski submitted his Candidate's Thesis Linear equations in Banach space in 1935 and, after defending his thesis, was awarded the degree. He continued teaching at Dnipropetrovsk until late 1940 when he moved, with his wife and son Yuri, to Moscow. In Moscow he studied for his doctorate (equivalent in level to the habilitation or D.Sc.) at the at the Institute of Mathematics, which was later named the Steklov Mathematical Institute of the Russian Academy of Sciences. In January 1941, he moved with his wife and son to the Ukhtomskaya suburbs of Moscow.

World War II broke out on 1 September 1939 when German troops entered Poland. On 22 September, Russian troops entered Poland occupying Bialystok and five days later Warsaw fell to the Germans and, following the Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union, Poland was partitioned between these two powers. The Molotov-Ribbentrop non-aggression pact meant that the initial years of the World War II had little effect on life in Russia and, in particular, none on Nikolski. Things changed dramatically on 22 June 1941 when Germany broke the non-aggression pact and invaded the Soviet Union. German armies advanced towards Moscow and Nikolski played his part in defending the city by working for the Moscow fire brigade and also, along with Alexey Andreevich Lyapunov (1911-1973) (a mathematician working at the Steklov Mathematical Institute), helped with constructing anti-tank fortifications in Maloyaroslavets about 125 km south west of Moscow. The German army captured Maloyaroslavets on 18 October 1941. Nikolski was later awarded the medal "For the Defence of Moscow".

In late 1941 members of the Russian Academy of Sciences in Moscow were evacuated to Kazan where they were housed in Kazan University and Nikolski was one of those evacuated. He defended his doctoral thesis On the theory of the approximation of functions by polynomials in January 1942, while in Kazan, before a committee consisting of Aleksandr Osipovich Gelfond, Boris Mikhailovich Gagaev (1897-1975) and Abraham Ezechiel Plessner. Returning to Moscow, he continued to undertake research at the Steklov Mathematical Institute but also worked as Head of the Department of Mathematics at the Moscow Automobile and Road Institute.

In 1947 Nikolski was appointed as a professor at the Moscow Institute of Physics and Technology (MIPT). This Institute was founded on 25 November 1946 as a Department of Moscow State University but enjoyed considerable autonomy within the University. In the summer of 1951, it was closed down as a Department in Moscow State University. Various leading academics immediately attempted to have MIPT re-established and put their case before Stalin. They succeeded in obtaining Stalin's approval and, on 17 September 1951, a government decree re-established it as the Moscow Institute of Physics and Technology, a separate Institute not part of Moscow State University. Over the following fifty years, Nikolski worked at the Faculty of Mechanics and Mathematics of Moscow State University, at the Steklov Mathematical Institute, and at MIPT.

In September 1954 the International Congress of Mathematicians was held in Amsterdam. Nikolski was a plenary speaker delivering the lecture Einige Fragen der Approximation von Funktionen durch Polynome . For an English translation of the Introduction to Nikolski's lecture, see THIS LINK.

To gain an overview of Nikolski's mathematical work we quote from [55]:-
The solutions of many problems in analysis make use either of the fact that certain functions can be represented by means of an integral involving some of its derivatives (or differences) or of the fact that its derivatives have an integral representation (or approximation) involving the original function and an appropriate kernel. The fundamental theorem of the calculus is the prototype of such integral representations. The possibility of obtaining such formulas leads to the study of various function spaces, defined in terms of certain Hölder conditions (usually called Lipschitz or Besov spaces) and differentiability conditions, and the relations among them.

Such studies have been carried out by many investigators in several countries. The Russian school in this subject, which is now led by Nikolski, has been particularly active during the past two decades. Nikolski's book 'Approximation of Functions of Several Variables and Imbedding Theorems' (Springer-Verlag, 1975) presented the work of his school done prior to the seventies, which involved, mainly, the study of functions defined in all of $\mathbb{R}^{n}$.

As we noted right at the start of this biography, Nikolski lived to be 1907 years old. In fact he began teaching at the Moscow Institute of Physics and Technology in 1947, at the age of 42, and taught there until 1997, when he was age 92. When he was asked to tell people what was his secret of long life, he said he could not explain it rationally, particularly since none of his relations were long-lived, none living to over 75. As a young boy he was not very healthy, suffering very painful sore throats. When he was a student he developed polyarthritis. He said he was not a vegetarian but he always had small helpings of food which he took his time eating. He was a smoker in his youth but gave up when he was 90 years old. He was very active throughout his life, enjoyed swimming and rowing, and went skiing every winter. He enjoyed taking long walks every day. Even when he was over 100, he kept up his interests by watching television, reading newspapers and continuing to enjoy mathematics.

He died in Moscow and was buried in the Troekurovsky cemetery on 14 November 2012.

### References (show)

1. L D Kurdryavtsev, O V Besov, V A Ilin, P I Lizorkin, S I Pokhozhaev and S B Stechkin (eds.), Theory and Applications of Differentiable Functions of Several Variables: Collection of Papers : Dedicated to Academician Sergei Mikhailovich Nikolskii on His Eighty-fifth Birthday (American Mathematical Society, Providence, R.I., 1994).
2. S M Nikolskii, Recollections (Russian), Rossiiskaya Akademiya Nauk, Matematicheskii Institut im. V A Steklova (MIAN) (Moscow, 2003).
3. A A Rusakov and V N Chubarikov, Sergei Mikhailovich Nikolskij, Legend of Century, Modern Problems of Teaching Mathematics and Computer Science (Fazis, Moscow, 2005).
4. B G Bakulov, N K Karapetyants, Yu F Korobeinik, A G Kusraev and S G Samko, Sergei Mikhailovich Nikolskii (on the occasion of his hundredth birthday) (Russian), Vladikavkaz. Mat. Zh. 7 (2) (2005), 5-10.
5. O V Besov, On the works of S M Nikolskii in the theory of function spaces and its applications (Russian), Tr. Mat. Inst. Steklova 232 (2001), 25-30.
6. O V Besov, On the works of S M Nikolskii in the theory of function spaces and its applications, Proc. Steklov Inst. Math. 2001 (1)(232) (2001), 19-24.
7. O V Besov, E A Volkov, V K Dzyadyk, N P Korneichuk, L D Kurdryavtsev and P I Lizorkin, Sergei Mikhailovich Nikolskii (on his eighty-fifth birthday), in L D Kurdryavtsev, O V Besov, V A Ilin, P I Lizorkin, S I Pokhozhaev and S B Stechkin (eds.), Theory and Applications of Differentiable Functions of Several Variables: Collection of Papers : Dedicated to Academician Sergei Mikhailovich Nikolskii on His Eighty-fifth Birthday (American Mathematical Society, Providence, R.I., 1994), 1-9.
8. O V Besov, E A Volkov, V K Dzyadyk, N P Korneichuk, L D Kurdryavtsev and P I Lizorkin, Sergei Mikhailovich Nikolskii (on his eighty-fifth birthday) (Russian), Trudy Mat. Inst. Steklov 201 (15) (1992), 3-13.
9. O V Besov, E A Volkov, V K Dzyadyk, N P Korneichuk, L D Kurdryavtsev and P I Lizorkin, Sergei Mikhailovich Nikolskii (on his eighty-fifth birthday), Proc. Steklov Inst. Math. 1994 (2)(201) (1994), 1-9.
10. O V Besov, S V Bochkarev, E A Volkov, et al., His mathematical century (in memory of Sergei Mikhailovich Nikolskii) (Russian), Uspekhi Mat. Nauk 68 (3)(411) (2013), 205-207.
11. O V Besov, S V Bochkarev, E A Volkov, et al., His mathematical century (in memory of Sergei Mikhailovich Nikolskii), Russian Math. Surveys 68 (3) (2013), 591-594.
12. O V Besov, S V Bochkarev, V S Vladimirov, et al., Sergei Mikhailovich Nikolskii (on the occasion of his ninetieth birthday) (Russian), Uspekhi Mat. Nauk 50 (6)(306) (1995), 223-228.
13. O V Besov, S V Bochkarev, V S Vladimirov, et al., Sergei Mikhailovich Nikolskii (on the occasion of his ninetieth birthday), Russian Math. Surveys 50 (6) (1995), 1321-1327.
14. O V Besov and V I Burenkov, To the memory of Academician Sergei Mikhailovich Nikolskii, Eurasian Math. J. 3 (4) (2012), 6-9.
15. O V Besov, V A Sadovnichii and S A Telyakovskii, On the scientific activity of S M Nikolskii (Russian), Uspekhi Mat. Nauk 60 (6)(366) (2005), 5-20.
16. O V Besov, V A Sadovnichii and S A Telyakovskii, On the scientific activity of S M Nikolskii, Russian Math. Surveys 60 (6) (2005), 1005-1020.
17. A N Kolmogorov and S B Stechkin, Sergei Mikhailovich Nikolskii (on his fiftieth birthday) (Russian), Uspekhi Mat. Nauk 11 (2)(68) (1956), 239-244.
18. V K Dzyadyk, A N Kolmogorov and L D Kurdryavtsev, Sergei Mikhailovich Nikolskii (on his sixtieth birthday) (Russian), Uspekhi Mat. Nauk 20 (5)(125) (1965), 275-287.
19. V K Dzyadyk, A N Kolmogorov and L D Kurdryavtsev, Sergei Mikhailovich Nikolskii (on his sixtieth birthday), Russian Math. Surveys 20 (5) (1965), 193-205.
20. V K Dzyadyk, A N Kolmogorov and L D Kurdryavtsev, Sergei Mikhailovich Nikolskii (on his seventieth birthday) (Russian), Uspekhi Mat. Nauk 30 (4) (184) (1975), 271-280.
21. V K Dzyadyk, A N Kolmogorov and L D Kurdryavtsev, Sergei Mikhailovich Nikolskii (on his seventieth birthday), Russian Math. Surveys 30 (4) (1975), 193-202.
22. V K Dzyadyk, A N Kolmogorov, L D Kurdryavtsev and S L Sobolev, Sergei Mikhailovich Nikolskii (on his eightieth birthday) (Russian), Uspekhi Mat. Nauk 50 (5)(245) (1985), 269-278.
23. V K Dzyadyk, A N Kolmogorov, L D Kurdryavtsev and S L Sobolev, Sergei Mikhailovich Nikolskii (on his eightieth birthday), Russian Math. Surveys 40 (5) (1985), 251-263.
24. S I Grozdev, A A Rusakov and B I Sendov, Distinguished mathematician and educator S M Nikolskij, J. Bulg Acad Sci. 1 (2013), 63-65. S I Grozdev, A A Rusakov and B I Sendov, A life a model example, J. Bul. Acad. Sci. 1 (2011), 31-39.
25. In memory of Sergei Mikhailovich Nikolskii (Russian), Tr. Mat. Inst. Steklova 279 (2012), 7-8.
26. In memory of Sergei Mikhailovich Nikolskii, Proc. Steklov Inst. Math. 279 (1) (2012), 1-2.
27. M K Kerimov, Sergei Mikhailovich Nikolskii (on the occasion of his hundredth birthday) (Russian), Zh. Vychisl. Mat. Mat. Fiz. 46 (3) (2006), 363-371.
28. M K Kerimov, Sergei Mikhailovich Nikolskii (on the occasion of his hundredth birthday), Comput. Math. Math. Phys. 46 (3) (2006), 345-353.
29. N P Korneichuk, S M Nikolskii and the development of investigations in the theory of approximation of functions in the USSR (Russian), Uspekhi Mat. Nauk 40 (1)(241) (1985), 71-131.
30. N P Korneichuk, S M Nikolskii and the development of investigations in the theory of approximation of functions in the USSR, Russian Math. Surveys 40 (5) (1985), 83-156.
31. N P Korneichuk, S M Nikolskii and the Soviet school of approximation theory (Russian), Trudy Mat. Inst. Steklov 180 (1987), 3-12.
32. N P Korneichuk, S M Nikolskii and the Soviet school of approximation theory, Proc. Steklov Inst. Math. 1989 (3)(180) (1989), 1-10.
33. L D Kurdryavtsev, On the work of S M Nikolskii in the theory of differentiable functions of several variables (Russian), Trudy Mat. Inst. Steklov 180 (1987), 12-22.
34. L D Kurdryavtsev, On the work of S M Nikolskii in the theory of differentiable functions of several variables, Proc. Steklov Inst. Math. 1989 (3)(180) (1989), 11-21.
35. List of publications of S M Nikolskii (Russian), Tr. Mat. Inst. Steklova 248 (2005), 8-25.
36. List of publications of S M Nikolskii, Proc. Steklov Inst. Math. 2005 (1)(248) (2005), 2-20.
37. List of publications of S M Nikolskii (Russian), Tr. Mat. Inst. Steklova 232 (2001), 31-32.
38. List of publications of S M Nikolskii (Russian), Proc. Steklov Inst. Math. 2001 (1)(232) (2001), 25-26.
39. P I Lizorkin, Sergei Mikhailovich Nikolskii, The Great Soviet Encyclopaedia (1979).
40. L G Mikhailov, On the eightieth birthday of Academician S M Nikolskii (Russian), Izv. Akad. Nauk Tadzhik. SSR Otdel. Fiz.-Mat. Khim. i Geol. Nauk 1986 (2)(100) (1986), 128.
41. S M Nikolskii, About teaching the subject of algebra at school (Russian), Uspekhi Mat. Nauk 40 (4)(244) (1985), 77-78.
42. S M Nikolskii, Some Words about Myself, Trudy Mat. Inst. Steklov 2001 (232) (2001), 8-18.
43. A A Rusakov, S M Nikolskii: mathematician and teacher (on the occasion of his hundredth birthday) (Russian), Chebyshevskii Sb. 6 (3)(15) (2005), 5-10.
44. A A Rusakov, The First Student of Andrei Nikolaevich Kolmogorov, in V Mityushev and M V Ruzhansky (eds.), Analytic Methods in Interdisciplinary Applications (Springer 2015), 125-152.
45. A A Rusakov, S M Nikolskii: mathematician and teacher (on the occasion of his hundredth birthday) (Russian), Chebyshevskii Sb. 6 (3)(15) (2005), 5-10.
46. A A Rusakov and Yu P Nikolaev, Sergei Mikhailovich Nikolskij in school named after A N Kolmogorov, in A A Rusakov (ed.), Proceedings of the International Scientific-Methodology Conference. Informatization of Education (Tula University, 2006), 133-135.
47. A A Rusakov and V N Rusakova, Books and pedagogical ideas by S M Nikolskij in study of mathematics at school, All-Russian Scientific Conference, "Actual Problems of Mathematics Education" (Adygeysky University Publ, Maikop, 2010), 180-184.
48. Sergey Mikhailovich Nikolsky, Prabook. https://prabook.com/web/sergey_mikhailovich.nikolsky/3750191
49. S A Telyakovskii, The works of S M Nikolskii in the theory of the approximation of functions (Russian), Tr. Mat. Inst. Steklova 232 (2001), 19-24.
50. S A Telyakovskii, The works of S M Nikolskii in the theory of the approximation of functions, Proc. Steklov Inst. Math. 2001 (1)(232) (2001), 13-18.
51. S M Nikolskii (on the occasion of his hundredth birthday) (Russian), Mat. Zh. 5 (2)(16) (2005), 94.
52. Ya A Vagramenko and A A Rusakov, Outstanding mathematician and educator Nikolskij, Edu. Inform. 4 (2012), 3-7.
53. V S Vladimirov, V K Dzyadyk, N P Korneichuk and L D Kudryavtsev, Sergei Mikhailovich Nikolskii (on the occasion of his eightieth birthday) (Russian), Uspekhi Mat. Nauk 46 (3)(279) (1991), 207-214.
54. V S Vladimirov, V K Dzyadyk, N P Korneichuk and L D Kudryavtsev, Sergei Mikhailovich Nikolskii (on the occasion of his eightieth birthday), Russian Math. Surveys 46 (3) (1991), 241-250.
55. G Weiss, Review: Integral Representations of Functions and Imbedding Theorems, by Oleg V Besov, Valentin P Il'in, Sergei M Nikolskii and Mitchell H Taibleson, American Scientist 67 (6) (1979), 729-730.