Vladimir Ivanovich Smirnov (on his 80th birthday)

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    (On H is 80th B i r thday)

    Yu .A . M i t ropo l ' sk i i , I .Z . Shtoka lo , E .Ya . Remez , A .N . Bogo lyubov , and V .N . Kosh lyakov

    The tenth of June, 1967, is the eightieth birthday of Hero of Socialistic Work Academician Vladimir Ivanovieh Smirnov, who has been Director of the Leningrad Mathematical School for the past ten years. He is often called the teacher of Soviet mathematicians (one might also say the teacher of Soviet physicists) because one of his achievements has been to write the unique f ive-volume work "A Course of Higher Mathe- matics" which is not only the most detailed encyclopedia of contemporary mathematics, but also a f irst c lass textbook. Thanks to this well-known work, the number of students of Vladimir Ivanovich has increased from a four-f igure number to a number at least two orders larger . His "Course" has been studied by mathe- maticians and physicists and has been used by pedagogues and engineers; a whole army of investigators working in a great variety of fields of science and engineering use this book in their research. However, the "Course" is only one of the important achievements of Vladimir Ivanovich.

    Vladimir Ivanovich Smirnov was born in St. Petersburg in 1887. In 1897 at the age of ten he entered an introductory gymnasium, and in 1904 he became a student at the Secondary St. Petersburg gymnasium from which he graduated in 1905 with a gold medal. In the autumn of the same year, Vladimir Ivanovich enrolled in the physico-mathematical faculty of St. Petersburg University. His scientific interests expanded during his stay at the university: In addition to courses in mathematics and physics he took courses in the history of philosophy, the history of law, political economy, the history of art, and other subjects. He was also seriously interested in music and in questions connected with its historical development and theory. His musical talent and his love of music has remained with him during his whole life.

    While Vladimir Ivanovich was a student at St. Petersburg University some of his professors were members of an outstanding group of mathematicians. He attended lectures by A. A. Markov, V. A. Steklov, D. K. Bobylev, I. L. Ptashitskii , and many other professors. In 1906 the mathematical staff was headed by V. A. Steklov; Vladimir Ivanovich followed a course in differential equations given by V. A. Steklov and soon became one of his favorite students.

    Vladimir Ivanovich obtained his degree for work on a subject suggested by I. L. Ptashitskii .

    In 1910 V. I. Smirnov graduated with a f irst class degree and began his pedagogical work as an instruc- tor in mathematics and physics in a gymnasium as one of a group of teachers led by Pr ivat-Dozent S. A. Stolbtsov. This gymnasium grew up during difficult years of reaction and was the type of school that allowed an ,unfaithful" student to obtain a certif icate of maturity. Hence at the very beginning of his pedagogical career Vladirnir Ivanovich was working with advanced pedagogical ideas. The improvement of teaching

    Translated from Ukrainskii Matematicheskii Zhurnal, Vo1.19, No. 5, pp. 119-122, September-October, 1967.


  • methods has continued to interest him all his life, as a student, as a pedagogue, and as an organizer and teacher of new mathematical ideas.

    In January 1912, on the advice of V. A. Steklov, Vladimir Ivanovich entered university to prepare for aprofessor ia l career. In the same year he began to teach a course in higher mathematics at the St. Petersburg Engineering Institute and three years later, in 1915, he started to give the same course at St. Petersburg University. V. I. Smirnov has thus been involved in pedagogical work for 57 years, during 55 of which he taught in higher educational institutes and during 52 of which he was a professor at Leningrad University.

    During the years of organization of the young Soviet Republic, Vladimir Ivanovich together with several Soviet mathematicians taught at Tavricheski i University (later Cr imea University) in the Cr imea under the direction of N. M. Krylov. Here he helped to raise the standard of physico-mathematicat teaching to its required level. During this period Vladimir Ivanovich continued to be interested in scientific research and did not lose contact with Leningrad University, to which he soon returned. We may thus assert that Vladimir Ivanovich has remained with his alma mater, Leningrad University, for 62 years of his life, f i rst as a stu- dent and finally as a world-famous professor.

    Vladimir Ivanovich's f irst research work was in differential-equation theory; his masters thesis was entitled "The Inversion of a Second Order Linear Differential Equation" and was defended in 1918. In this work Vladimir Ivanovich investigated the inversion problem and succeeded in solving it completely; he stud- ied the independent variable as a function of two part icular integrals. As one of the opponents during the defence of the thesis, V. A. Steklov rated it very highly and said that Vladimir Ivanovich had developed new approaches to problems in the analytic theory of differential equations.

    Vladimir Ivanovich continued his work in analytic differential equation theory from 1918 to 1921.

    In 1921 V. L Smirnov became interested in the improvement of the mathematical education of physi- cists. Starting at this time and continuing for almost half a century, he directed the teaching of mathema- tics f i rst in the physical division and later at the physics faculty. One of the main motives for writing his famous "Course" lay in his work in teaching physicists.

    Vladimir Ivanovich's creative work was not only in the direction of contributions to the solution of mathematical problems; from the beginning of his career he organized scientific teams and led them. He and G. M. Fikhtengol,ts were pioneers in the development in Leningrad of new regions of mathematics:l re- search. During the nineteen twenties they organized investigations into the theory of functions of a real variable.

    One period of Vladimir [vanovich,s creative activity was during the later nineteen twenties when he was studying the theory of functions of a complex variable. As in his previous investigations, he did not confine himself to personal study but also organized work in this direction. In 1926 a team for the study of functions of a complex variable was developed under his leadership at Leningrad University and also a series of special seminars. During the nineteen thirties G. M. Goluzin took over the leadership of this group.

    It is noteworthy that V. I. Smirnov's interests had no time limits: once he became interested in a mathematical problem he did not abandon it when other new ideas attracted him. This was always true of his scientific work.

    At the beginning of the nineteen thirties when the third period of his research began, connected with mathematical physics, he, together with N. E. Kochin, published the works of his prematurely deceased student I. A. Lappo-Danilevskii, who had continued and developed V. L Smirnov's work in differential-equa- tion theory.

    F rom 1929 to 1934 V. I. Smirnov directed the theoretical section of the Seismological Institute, Aca- demy of Sciences of the USSR. Here he collaborated with his student S. L. Sobolev in research in wave- propagation theory. His study of the wave equation led him to some elegant methods for the solution o~! related problems. One outcome of these investigations was the creation of a mathematical seismology divi- sion for the study of vibrations in stratif ied media.

    While working in the Seismological Institute, V. I. Smirnov also directed investigations carr ied out in the Scientific Research Institute for Mathematics and Mechanics at Leningrad University. In 1931 he became substitute director of the scientific section and in 1937 he was named director of the institute. In 1932 V. I. Smirnov was elected Corresponding Member of the Academy of Sciences of the USSR.


  • His investigations during the second half of the nineteen thirties were concerned with the development of the theory of the wave equation in connection with applications to problems of mechanics of elastic media. He also directed seminars on functional analysis and on approximate methods in mathematical analysis.

    After the outbreak of the Second World War, in 1942, Leningrad University was part ial ly evacuated to Saratov and part ly to Elabugu. V. I. Smirnov was in the group that moved to Elabugu. Here he worked on his five volume "Course of Higher Mathematics" which was published in 1947.

    In 1943 S. N. Bernshtein and A. N. Krylov sponsored V. I. Smirnov as a full member of the Academy of Sciences.

    Until the reopening of Leningrad University V. I. Smirnov continued to direct the mathematical group (later the mathematical-physics group) in the physics faculty. Beginning in 1947 he organized a seminar on mathematical physics and partial differential equations.

    One subject that should be mentioned in any summary of V. I. Smirnov's work is the history of Russian Mathematics. He remained interested in this subject for the whole of his teaching career.

    His f i rst historical work, written in collaboration with N. M. Krylov, was published in Transactions of the Mathematical Faculty of Cr imea University and dealt with the scientific works of 1% L. Chebyshev and A. A. Markov. During the nineteen twenties his work in the history of mathematics was devoted to a study of the publications of his teacher V. A. Steklov. In the next period he broadened his study to include the his- tory of Soviet mathematics during the nineteenth and twentieth centuries. He carr ied out a part icular ly thorough investigation of the works of those with whom he was associated in his activity in St. Petersburg (Leningrad).

    We mentioned above the important part taken by V. I. Smirnov in the publication of the works of his student I. A. Lappo-Danilevskii. Thepublication of works of Soviet mathematicians was one of the f irst tasks assumed by the Academy of Sciences after the Great October Revolution. As ear ly as May 21, 1918, Aca- demicians V. A. Steklov and A. N. Krylov brought to the attention of the general assembly of the Academy of Sciences the importance of publishing collections of articles written by the greatest mathematicians of this country. V. I. Smirnov played a very important part in this work. Immediately after the end of the Second World War in 1946 he published Volume 1 of the Collected Works of M. V. Ostrogradskii, which was printed by the Academy of Sciences Press under the very difficult conditions of the Leningrad blockade. Later, he published the collected works of A. M. Lyapunov and, with the collaboration of S. L. Sobolev, the book "Potential Theory" by N. M. Gyunter; he also studied the archives of the Academy of Sciences in con- nection with correspondence of L. Euler and A. M. Lyapunov; only recently, he has begun the difficult task of preparing for the publication of material f rom the archives on the work of A. N. Krylov.

    V. I. Smirnov has been very active during the past ten years (1957-1967). He has continued to direct mathematical physics teams, one in the physics faculty and one in the mechanics-mathematics faculty, he organizes scientific seminars, he is working on the perfection of his "Course of Higher Mathematics', (the twenty f i rst edition of Volume 1 appeared in 1965). He also continues his own scientific work. During the last few years he has published: a monograph on the theory of functions of a complex variable, a ser ies of art icles concerning problems in mathematical physics, differential equations, and the stability of motion, and a ser ies of notes on the history of mathematics in the Academy of Sciences of the USSR (several notes on the history of the pre-revoiut ionary period in the edition "History of the Academy of Sciences of the USSR", Vol. 2, 1964; also notes on the Soviet period in the press). V. I. Smirnov has helped and continues to help in prepar ing publications in the series "History of Soviet Mathematics" : he is taking part in the edit- ing of several sections of this series and he wrote part of the chapter "Part ial Differential Equations and Mathematical Physics."

    In spite of his age V. I. Smirnov is lively, energetic, and has many new ideas which he is always ready to share with his many students. He is aman of great charm, he is erudite and reflective, he is a painter with words and a remarkable teacher. His kindness and understanding are greatly appreciated by his stud- ents and fellow workers.

    The Soviet Government values highly the scientific and social-polit ical achievement of V. I. Smirnov. On the tenth of July, 1967, he was honored by being made a Hero of Socialist Work.

    We all wish him many more years of productive work as a leader among Soviet mathematicians.