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Sergei Borisovich Stechkin

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Born
6 September 1920
Moscow, USSR
Died
22 November 1995
Moscow, Russia
Summary
Sergei Stechkin was a Russian mathematician who obtained deep results in the theory of trigonometric series, the theory of approximations for functions and operators, in the study of approximation properties of sets in Banach spaces, and in number theory.
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Biography

Sergei Borisovich Stechkin was the son of Boris Sergeevich Stechkin (1891-1969) and Irina Nikolaevna Shilova (1898-1958). Boris Sergeevich was born on 20 July 1891 (new calendar 5 August) in Trufanovo, Tula, Russia. His father Sergei Yakovlevich Stechkin (1864-1913) was a journalist and science fiction writer who wrote under the name Sergei Solomin. Boris Sergeevich's uncle was the famous scientist Nikolai Egorovich Zhukovsky who did pioneering work on aerodynamics.

Boris Sergeevich was brought up by his mother and, after studying at the Oryol Bakhtin Cadet Corps (1901-1908), he entered the Moscow Higher Technical School where he attended lectures by his uncle Zhukovsky. In 1918 he received a diploma in mechanical engineering and was appointed as head of the propeller-engine department at the Central Aerohydrodynamic Institute. This newly created Institute was headed by Zhukovsky. He worked at the Zhukovsky Institute of Engineers and the Lomonosov Institute. He quickly gained an international reputation publishing articles on the theory of aircraft engines. In 1926 his study of the Biot-Savart theorem was published by the Paris Academy of Sciences. Boris Sergeevich married Irina Nikolaevna Shilova whose father Nikolai Aleksandrovich Shilov (1872-1930), was a professor of chemistry at Moscow University who studied reactions, catalysis, and induction and was the founder of physical chemistry in Russia. Irina Nikolaevna was also a chemist and taught in the chemistry department of Moscow State University.

Sergei Borisovich, born in Moscow on 6 September 1920, received his primary education in the family and with home tutors, and then went straight into the third grade of the 59th Moscow school. This school had been founded in 1902 as the Medvednikovskaya gymnasium and had an excellent reputation. The family suffered a shock in 1930, however, when Boris Sergeevich Stechkin was arrested in the "Prompartiya" case. This was a show trial in which several Soviet scientists and economists were accused and convicted of plotting a coup against the government of the Soviet Union. He was sentenced to three years in prison but, after Sergei Alekseevich Chaplygin, who also worked in work in hydrodynamics and aerodynamics, bravely supported him arguing that Boris Sergeevich had not been involved in a coup against the government, he was released in 1931. In December 1937, when Sergei Borisovich was in his final year at the 59th Moscow school, his father was arrested again. The Moscow trials were a series of show trials held by the Soviet Union between 1936 and 1938 at the instigation of Joseph Stalin. They were nominally directed against "Trotskyists". Sergei Borisovich's father was imprisoned and was not released until 1943. This created problems for his son's education.

During his first few years at the 59th Moscow school Sergei Borisovich Stechkin's main passion had been for chess. By the age of fourteen he had become interested in mathematics and during his final year at the school, 1937-38, he took all his chess books to a second-hand bookseller and exchanged them for mathematics books. He graduated from the 59th Moscow school in 1938 having been awarded a gold certificate. This certificate meant that he could enrol in any Soviet university without sitting entrance examinations. He wanted to study mathematics at Moscow State University which had world class mathematics professors and was recognised as providing the best courses on this topic. He was refused entry to Moscow State University, however, officially "due to lack of space and health reasons", but the real reason was that his father was in prison. Stechkin went to Gorky in 1938 where he completed the first year course in mathematics and physics at the university.

Sergei Alekseevich Chaplygin, who worked in Moscow State University, knew the Stechkin family well and understood Sergei Borisovich Stechkin's potential to become a leading mathematician. He appealed to the authorities of Moscow State University to allow Stechkin to study there and in 1939 he was permitted to enter the second year of the mathematics and physics course. Although World War II started in September 1939 with the German and Russian invasion of Poland, this had little effect on Moscow State University. However, on 22 June 1941 the German armies invaded their former ally pushing rapidly east into Soviet lands. They advanced along a broad front from the Baltic to the Black Sea bringing hardship to everyone. In July 1941 Stechkin became a fire fighter in the university fire brigade and on the night of 23-24 July he took part in extinguishing incendiary bombs that fell on the P K Sternberg Institute. This Astronomical Institute was named after astronomer Pavel Karlovich Sternberg. It was founded in 1931 as an Institute of Moscow State University.

At Moscow State University, Stechkin took lecture courses from several leading mathematicians but the lecturer who made the greatest impression on him was Aleksandr Yakovlevich Khinchin. When in the fourth year of the course, in October 1941 he was sent to the Steklov Mathematical Institute to undertake computational work. In 1943 Stechkin was overjoyed when his father was released from prison. This came about when the aircraft engine designer Aleksandr Aleksandrovich Mikulin (1895-1985) developed a ramjet engine and wanted to create a plant to produce prototypes. He met with Joseph Stalin who approved the idea. Mikulin convinced Stalin that he needed Boris Sergeevich Stechkin as his deputy and, in March 1943, Sergei Borisovich's father was released from prison.

The Stalin Military Order of Lenin Academy of Armoured and Mechanised Troops (later renamed the Malinovsky Military Armoured Forces Academy) was a prestigious military academy in the Soviet Union. The academy had been established in 1932 in Moscow to train commanders, staff officers, and engineers. In 1943, while still a student, Stechkin began lecturing at the Military Order of Lenin Academy. This was a demanding task since Stechkin, a young student, was lecturing to leading military men, many of whom had been honoured for their war service. Despite the difficulties, he achieved good results and was asked to continue even when senior scientists returned from the front to take up the teaching positions they had held at the Military Order of Lenin Academy before their active service.

In 1944 Stechkin began graduate studies aiming at obtaining a Candidate of Science degree (equivalent to a Ph.D.). He participated in the seminars of Andrey Nikolaevich Kolmogorov, Dmitrii Evgenevich Menshov, Nina Karlovna Bari and Sergi Natanovich Bernstein. The seminar participants were rather different due to the war. There were other students like Stechkin who had just graduated from the Faculty of Mechanics and Mathematics but there were older men who had been forced to disrupt their studies with military service and now returned to continue their studies after a break of several years. Stechkin undertook research advised by Menshov and Bernstein and, in 1947, was elected to the Moscow Mathematical Society, where he presented papers that formed his first publications.

Stechkin now undertook a variety of different jobs. In the autumn semester of the academic year 1947-48 he taught in the Physics and Technology Faculty of Moscow State University. Beginning on 27 October 1947 he undertook applied research at Research Institute-4 of the Academy of Artillery Sciences and, from the beginning of 1948, he was a part-time junior fellow at the V A Steklov Mathematical Institute of the USSR Academy of Sciences. Also in 1948 he submitted his thesis On the order of best approximations of continuous functions (Russian) for his Candidate of Science degree. It was examined by Aleksandr Osipovich Gelfond and Serge Mikhalovich Nikolskii. His first papers began to be published: A generalisation of some inequalities of S B Bernstein (Russian) (1948); On positive bilinear forms (Russian) (1949); and On the order of best approximations of continuous functions (Russian) (1949). This last mentioned paper was a short 3-page paper stating results from his thesis without proofs. The proofs were given in a 24-page paper with the same title in 1951. By 1951 Stechkin had nine papers in print.

In addition to this excellent work in pure mathematics, Stechkin was also producing important applied results and, over the course of two years, at the Research Institute 4 of the Academy of Artillery Sciences he analysed issues of external ballistics of anti-aircraft guided missiles. In April 1949 he completed reports on his work [5]:-
The "method equations" proposed by S B Stechkin turned out to be a fundamentally new method of modelling and resolving issues of the kinematics of a guided missile, i.e., along with the existing specific methods of calculation and control, a general approach to the entire class of kinematic problems was developed for the first time. The art of using this approach consists in selecting such a "method equation" in which the transformed system of kinematic equations turns out to be implemented as an aggregate, i.e. allows for an engineering control system.
Because of his impressive contributions Stechkin was nominated for the rank of engineer major in the Academy of Artillery Sciences. He continued to work both there and at the V A Steklov Mathematical Institute but in 1952 ended his work for the Academy of Artillery Sciences.

On 14 May 1949 Stechkin married Ekaterina Ivanovna Trifonova (1927-1987). She was a student in the Mechanics and Mathematics Department of Moscow State University at the time and was described as "tall, stately, brown-eyed, with a long braid." She played chess to a high standard and often enjoyed close matches with her husband. Sergei Borisovich and Ekaterina Ivanovna had a son Boris Sergeevich Stechkin who was born in 1950.

From 1952 Stechkin worked for the V A Steklov Mathematical Institute but in 1953 he taught the mathematical analysis course in the Faculty of Mechanics and Mathematics of Moscow State University. He took over teaching this course from Aleksandr Yakovlevich Khinchin who had taken ill. Teaching was for Stechkin the favourite aspect of his work and he had an outstanding reputation as a lecturer [6]:-
Stechkin gave distinctly original courses on mathematical analysis, as well as numerous and diverse special courses. His lectures were rigorous, clear and bright, and infallibly proved a success with the students. The undergraduate students who attended Stechkin's lectures often went on the candidate's degrees advised by Stechkin. Under the supervision of Sergei Borisovich about 30 Ph.D. theses were written altogether, and 16 of his students have become doctors of science. There were scientists from Hungary, China and Yugoslavia among Stechkin's students.
We have seen the title of some of his first papers above. The 70th birthday paper [22] gives more details of his early work:-
The first phase of Stechkin's writings was concerned with the approximation of functions by trigonometric polynomials. He generalised the direct and inverse theorems of the theory of approximations to moduli of continuity of arbitrary order, compared the precise orders of descent of best approximations of functions and their moduli of continuity, and investigated the connection between the best approximations of functions and their derivatives.

In 1936 one of Kolmogorov's essays was published, in which he introduced the concept of the width of a class of functions and found the widths of certain classes for approximations in the metric L2L_{2}. The next publication on width was the article by Stechkin which came out in 1954. In this article certain results known at the time were interpreted as theorems on widths and it was shown that the order of descent of the widths of classes of differential functions Wr,r=1,2,...W^{r}, r = 1, 2, ..., for approximations in the metric CC is reached by trigonometric polynomials (it was later shown that the subspace of trigonometric polynomials is extremal in this case).
Most of Stechkin's career was spent in Moscow working at the V A Steklov Mathematical Institute and lecturing at Moscow State University. He did spend one lengthy period away from Moscow and this came about in the following way. Stechkin's father rented a dacha in Abramtsevo, north of Moscow, from the spring of 1954. The whole Stechkin family would spend time at the dacha which was close to a dacha rented by Ivan Matveevich Vinogradov and his sister Nadezhda Matveyevna. The Stechkin and Vinogradov families spent time together, in particular they played vint together. Vint is a Russian card game similar to both bridge and whist and sometimes called Russian whist. These informal meetings between the families was an excellent opportunity to share ideas and Stechkin told Vinogradov that he thought the USSR Academy of Sciences should create a new institute where fundamental research could be carried out supported by the most powerful computers available. Vinogradov liked the idea and, always being an advocate for the development of mathematics in the provinces, he suggested Stechkin travel the country looking for a suitable site.

Stechkin's travels took him to Lake Baikal, Novosibirsk, Kazan, Kungur, Saratov, Kuibyshev and Sverdlovsk. He eventually chose Sverdlovsk, partly because it was an important industrial centre and partly because it had two universities, the Ural State University and the Ural Polytechnic Institute, both of which had strong mathematics departments. Vinogradov liked Stechkin's proposal and sought support from other members of the USSR Academy of Sciences. By 1956 the proposal to organise the Sverdlovsk branch of the Steklov Mathematical Institute was accepted and for the ten years, 1957-1967, Stechkin worked as deputy director of the Steklov Mathematical Institute for the Sverdlovsk branch. He was involved in the construction of the building, recruiting staff, obtaining the most powerful computers and building up the library.

The Steklov Mathematical Institute for the Sverdlovsk branch became the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. In 1964, Stechkin organised and became the head of the Department of the Theory of Approximation of Functions. Even after he left Sverdlovsk in 1967 and returned to Moscow he retained his role of head of the Department of the Theory of Approximation of Functions and made occasional visits to Sverdlovsk to support staff and students and to give lectures. He organised summer schools, the first in 1971 held near Sverdlovsk. In fact he organised twenty such summer schools, the last being in 1995, always in different locations but predominately in the Urals. Each lasted between ten and fourteen days and were attended by professors, graduate students and even final year undergraduates. These were friendly events, everyone had the opportunity to speak, and Stechkin set the tone of the meetings.

Back in Moscow in 1967 Stechkin launched a new journal Matematicheskie Zametki, also known as Mathematical Notes. Volume 1 appeared in 1967 with 83 papers in the volume, three of which were by Stechkin himself. These three papers were: Distribution of zeros of polynomials (Russian); Best approximation of linear operators (Russian); and Inequalities between upper bounds of the derivatives of an arbitrary function on the half-line (Russian). Volume 2 also appeared in 1967 with 80 papers and, each year between 1967 and 1991 two volumes each of six issues, were published. Stechkin was editor-in-chief for the first twenty years of publication. His aim was to publish short but interesting papers. He set himself a list of principles to which he rigidly adhered. Papers had to be original works with complete proofs. All employees and members of the editorial board had the responsibility of ensuring continuous publication. The level of acceptance for papers had to be at least up to "world" standard or better. Young mathematicians had to be be helped with their first publications, not by lowering standards, but by giving them assistance to reach the required standard. The language of the journal should be simple, clear, and distinct.

To see Stechkin's advice to young mathematicians on how to write a mathematics paper, see THIS LINK.

Let us quote from [5] to give a flavour of Stechkin's published research:-
Stechkin's scientific interests related to the problems of mathematical analysis, geometry of Banach spaces and number theory. Let us briefly note the issues that he studied.

Stechkin's works on mathematical analysis are devoted to the theory of approximation of functions, trigonometric and orthogonal series, and extremal properties of functions. He established the now classical direct and inverse theorems of approximation theory in terms of moduli of continuity of arbitrary order, obtained the first results on Kolmogorov widths in the uniform metric, and the most complete results on the asymptotics of approximations of classes of differentiable functions by Fourier sums. Stechkin proved a criterion for the absolute convergence of Fourier series of individual functions. Here, the main difficulty was in finding the terms in which this criterion is formulated.

Sergei Borisovich, his students, and followers constructed a theory of best approximations of unbounded operators by bounded ones, which has direct connections with the theory of ill-posed problems. Together with Nikolai Vladimirovich Efimov, Stechkin developed a geometric theory of approximations in Banach spaces. At the same time, a number of new approximative concepts were introduced, which turned out to be useful in other issues. He established a new logarithmic estimate for the zeros of the Riemann zeta function, obtained a strengthening of Ivan Matveevich Vinogradov's mean value theorem and unimprovable estimates for complete rational trigonometric sums.

Together with Yurii Nikolaevich Subbotin (1936-2021), Stechkin wrote the first monograph in Russian on the approximation of functions by splines, which contributed to the development of spline research in the USSR and their introduction into the practice of computational mathematics.
The book with Subbotin was Splines in numerical mathematics (Russian) (1976). Subbotin had been a student in Sverdlovsk who was recruited into the postgraduate programme by Stechkin. He had worked as an assistant at the Department of Function Theory of Ural State University from 1961 to 1964 [24]:-
The first monograph in Russian on spline theory was published in 1972. It was "The Theory of Splines and Their Applications" by J H Ahlberg, E N Nilson and J L Walsh. The translation from English was made by Subbotin and edited by Stechkin, and the monograph was supplemented with additional sections written by them. After the publication of this book, the term "spline" became firmly established in the Russian mathematical literature. Starting from the 1960s, splines gained popularity in computational practice as a means of an approximate representation of functions, curves, and surfaces as well as a tool for smoothing experimental data. The successful development of splines and their applications in various studies were promoted by the publication in 1976 of Stechkin and Subbotin's monograph "Splines in Computational Mathematics", which focused on the specific properties of splines important for their application in numerical analysis.
Carl R de Boor, reviewing this book writes [8]:-
The book is intended as a supplement and complement to the book by J H Ahlberg, E N Nilson and J L Walsh and stresses the contributions of Soviet mathematicians. Thus, much room is given to a detailed analysis of parabolic spline interpolation (also in several variables) with special emphasis on sharp error estimates, and the analysis of spline interpolation at the integers (cardinal splines) follows Subbotin's (rather than Schoenberg's) treatment. Splines of degree higher than cubic appear only with uniformly spaced knots and B-splines appear only with simple knots (and their recurrence relation appears not at all).
Stechkin's wife, Irina Nikolaevna Stechkina, made translations of French mathematical texts into Russian starting around 1964. From the early 1970s she worked at the "Soviet Encyclopaedia", and then at the publisher "Nauka" while continuing to translate French mathematical books into Russian. The couple divorced and, in 1978, Stechkin married the mathematician Tatyana Vasilievna Radoslavova who worked at Moscow State University. They had two daughters, Alexandra and Valeria [5]:-
The years of his second marriage were a time of special warmth and care with which Sergei Borisovich was surrounded. The Steklov Mathematical Institute gave him a new apartment, where the academic husband and loving father could live and work in peace. He loved to travel with his children. He always took his daughters to summer schools in the Urals, and in recent years he repeatedly went on business trips abroad with his son Sergei Borisovich Stechkin.
In 1993 Stechkin was awarded the Chebyshev Prize of the Russian Academy of Sciences for his work on the theory of approximations. In July 1995 he was diagnosed with cancer. After an operation and a course of radiotherapy he tried to return to his work and held a summer school in Moscow State University in August 1995. In September the Steklov Institute of Mathematics celebrated his 75th birthday. Although determined to carry on his mathematical work, his illness grew steadily worse and he was taken to hospital. He died on the morning of 22 November 1995.
Other Mathematicians born in Russia
A Poster of Sergei Stechkin

References (show)

  1. A Andreev, V I Berdyshev, B Bojanov, B S Kashin, S V Konyagin, S M Nikol'skii, K I Oskolkov, P Petrushev, Bl Sendov, S A Telyakovskii and V N Temlyakov, In memory of Sergei Borisovich Stechkin [1920-1995], East Journal on Approximations 2 (2) (1996), 131-133.
  2. V I Berdyshev, Stechkin's workshop - what is it?, East Journal on Approximations 2 (2) (1996), 135-140.
  3. V I Berdyshev, Chronology of S B Stechkin's Workshops 1971–2006, Proc. Internat. Stechkin Summer School on Function Theory (Izd. Tul'sk. Gos. Univ., Tula, 2007), 7-14.
  4. V I Berdyshev, V V Arestov and M Sh Shabozov, S B Stechkin's Workshop: Historical note, Proc. Internat. Summer Math. Stechkin School-Conference on Function Theory (Publishing House of "Ofset", Dushanbe, 2016), 6-10.
  5. V I Berdyshev, VF Kolchin, B S Stechkin, Yu N Subbotin, S A Telyakovsky, N I Chernykh, Sergei Borisovich Stechkin (1920-1995), N N Krasovsky Institute of Mathematics and Mechanics (2016).
    https://math.ru/history/tree/Stechkin
  6. O V Besov, V M Bukhshtaber, A G Vitushkin, A A Gonchar, S V Konyagin, L D Kudryavtsev, S M Nikol'skii, S P Novikov, Yu S Osipov, A Yu Popov, V A Sadovnichii, A F Sidorov, Yu N Subbotin, S A Telyakovskii, P L Ul'yanov and N I Chernykh, Sergei Borisovich Stechkin (obituary) (Russian), Uspekhi Matematicheskikh Nauk 51 (6)(312) (1996), 3-10.
  7. O V Besov, V M Bukhshtaber, A G Vitushkin, A A Gonchar, S V Konyagin, L D Kudryavtsev, S M Nikol'skii, S P Novikov, Yu S Osipov, A Yu Popov, V A Sadovnichii, A F Sidorov, Yu N Subbotin, S A Telyakovskii, P L Ul'yanov and N I Chernykh, Sergei Borisovich Stechkin, Russian Mathematical Surveys 51 (6) (1996), 1007-1014.
  8. C R de Boor, Review: Splines in numerical mathematics, by S B Stechkin and Yu N Subbotin, Mathematical Reviews MR0455278 (56 #13517).
  9. Editorial Board, Sergei Borisovich Stechkin (Russian), Matematicheskie Zametki 59 (2) (1996), 163.
  10. Editorial Board, Sergei Borisovich Stechkin, Mathematical Notes 59 (2) (1996), 115.
  11. S V Konyagin and S A Telyakovskii, In memory of Sergei Borisovich Stechkin (Russian), Fundamental'naya i Prikladnaya Matematika 3 (4) (1997), 955-957.
  12. I Yu Rebrova and V N Chubarikov, N M Korobov, V I Nechaev, S B Stechkin, N M Dobrovolsky and the revival of the Tula school of number theory (Russian), Chebyshevskii Sb. 21 (4) (2020), 196-217.
  13. Sergei Borisovich Stechkin (Russian), Matematicheskie Zametki 59 (2) (1996), 162.
  14. Sergei Borisovich Stechkin, Mathematical Notes 59 (1-2) (1996), 115.
  15. Sergei Borisovich Stechkin (on the occasion of his seventieth birthday) (Russian), Matematicheskie Zametki 48 (4) (1990), 5-6.
  16. Sergei Borisovich Stechkin (06.09.1920 - 22.11.1995), Moscow State University (1997).
    http://mech.math.msu.su/~tsar/sbs.html
  17. Sergei Borisovich Stechkin: List of publications, Math-Net.Ru (2005).
    https://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=8998
  18. Sergei Borisovich Stechkin, Chronicle of Moscow University (2025).
    http://letopis.msu.ru/peoples/2522
  19. V M Tikhomirov and G G Magaril-Il'yaev, On the life and work of S B Stechkin (1920-1995) (Russian), Vladikavkazskii Matematicheskii Zhurnal 23 (4) (2021), 119-128.
  20. P L Ul'yanov, Reminiscences about Sergei Borisovich Stechkin (Russian), Uspekhi Matematicheskikh Nauk 51 (6)(312) (1996), 11-20.
  21. P L Ul'yanov, Reminiscences about Sergei Borisovich Stechkin, Russian Mathematical Surveys 51 (6) (1996), 1015-1024.
  22. V A Vladimirov, A A Gonchar, L D Kudryavtsev, S M Nikol'skii, S A Telyakovskii and P L Ul'yanov, Sergei Borisovich Stechkin (on the occasion of his seventieth birthday) (Russian), Uspekhi Matematicheskikh Nauk 46 (3)(279) (1991), 219-221.
  23. V A Vladimirov, A A Gonchar, L D Kudryavtsev, S M Nikol'skii, S A Telyakovskii and P L Ul'yanov, Sergei Borisovich Stechkin (on the occasion of his seventieth birthday), Russian Mathematical Surveys 46 (3) (1991), 255-258.
  24. Yurii Nikolaevich Subbotin (A Tribute to His Memory), Proc. Steklov Inst. Math. 319 (Suppl 1) (2022), S1-S6.
    https://doi.org/10.1134/S0081543822060013

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Written by J J O'Connor and E F Robertson
Last Update June 2025