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- Brief scientific biography
- Contributions to Education
- Relevant bibliography
- Publications on the teaching of mathematics

Sergei L'vovich Sobolev was born in St. Petersburg on October 6, 1908. He passed away in the same city on January 3, 1989. (St. Petersburg was renamed Petrograd in 1914, then Leningrad in 1924, and reverted finally to its original name in 1991.)

Sobolev was bereaved of his father at fourteen and was raised by his mother, a very educated woman who played an important role in his upbringing. She cultivated in the young Sobolev such qualities as adherence to principles, honesty and purposefulness, which characterized him as a scholar and a person throughout his life. Sobolev studied the course of secondary school largely on his own, already taking a great interest in mathematics. At fifteen he entered Leningrad School No. 190 and graduated with distinction a year later. After graduation he was still too young to be admitted to a university, so he took up studying piano at the First State Art School. In 1925 he entered the Faculty of Physics and Mathematics of Leningrad State University, meanwhile continuing his study at the First State Art School.

Sobolev was a truly worthy descendant of the St. Petersburg School, which is famous in the Russian history of mathematics through illustrious names such as Pafnuty Lvovich Chebyshev (1821-1894), Andrei Andreyevich Markov (1856-1922) and Aleksandr Mikhailovich Lyapunov (1857-1918). Indeed, at Leningrad State University and later at the Seismological Institute of the USSR Academy of Sciences (now the Russian Academy of Sciences) where he worked after graduation in 1929, Sobolev studied and did research work under the supervision of Nikolai Maksimovich Gyunter (1871-1941) and Vladimir Ivanovich Smirnov (1887-1974), who were themselves academic descendants of Chebyshev, Markov and Lyapunov.

Sobolev's first paper, which was published in 1929 in Dokl. Akad. Nauk SSSR, spoke for his talent in mathematics, which was apparent at an early age. During a lecture in the course on partial differential equations given by N. M. Gyunter, the second-year student Sobolev raised doubts about a theorem taught in class. Following the advice of Gyunter he read the original paper, discovered that the proof was incorrect, and constructed a counter-example for the theorem. Much impressed by this piece of work, Gyunter recommended that Sobolev write it up and submit it. From then on, Sobolev went on to make fundamental contributions to many branches of mathematics, both pure and applied. He created new theories and trends in mathematics, most notably the origin of the theory of generalized functions (distributions) and the concept which has come to be known as Sobolev space.

In 1933 he was elected a Corresponding Member in the Division of Physical-Natural Sciences of the USSR Academy of Sciences (now the Russian Academy of Sciences). In 1939, at the age of thirty-one, he was elected a Full Member in the same Division, and was for a long time the youngest Full Member ever elected to the Academy. His book Nekotorye primeneniya funktsional'nogo analiza v matematicheskoi fizike (Applications of Functional Analysis in Mathematical Physics) of 1950 played an extremely important role in the development of functional analysis and partial differential equations, and has educated several generations of mathematicians in these fields in Russia and abroad. (It was translated into English and published by the American Mathematical Society in 1963, with a third edition published in 1991, four decades after it first appeared.)

From 1939 to 1941 Sobolev was the Acting Director of the Steklov Institute of Mathematics, and was elected Director in 1941. Under difficult conditions during evacuation to the Caucasus in time of war, he did a lot for the organization of applied research at the Institute in support of the front line. In 1943 he moved to the Institute of Atomic Energy (originally known as Laboratory No. 2). For the main task of investigating complex systems to obtain nuclear fuel, he worked with physicists and was involved with a lot of numerical computation at a time when computer was not yet available as a calculating tool. Sobolev gave nearly all his time, strength and energy to this task, and made use of his unusual mathematical intuition and ingenuity to solve complex problems within the assigned time period. For the work he did at the Institute of Atomic Energy, Sobolev was twice awarded a First degree State Prize, and in 1951 he was awarded the title of a Hero of Socialist Labour for his exceptional services to his motherland. Sobolev later related that he developed a taste for computational mathematics through working at the Institute of Atomic Energy, so that he accepted an invitation to head the first Department of Computational Mathematics in Russia established at Moscow State University. Serving in that capacity from 1952 to 1959, he set the scientific and pedagogical direction of the department. He was one of the first Soviet mathematicians to use computers.

Since 1956 Sobolev had often met with his two friends, Mikhail Alexseevich Lavrent'ev (1900-1980) and Sergey Alekeyevich Khristianovich (1908-2000) to discuss various scientific and economic problems. One such question was the necessity of the development of science in Siberia, which had a rich store of natural resources but a total lack of scientific research. In 1958 the Central Committee of the Communist Party and the Soviet government approved of this plan and decreed its implementation, upon which the Praesidium of the USSR Academy of Sciences decided to form the Siberian Branch of the USSR Academy of Sciences. Sobolev was named the Director of the Institute of Mathematics of the Siberian Division set up at Novosibirsk Akademgorodok. When friends asked him why he left a strong department at Moscow State University in favour of Siberia, which was essentially virgin scientific soil, to take on the complex and troublesome project of building an institution from scratch, Sobolev answered:

"The natural desire of mankind is to live several lives and to begin something new."Above all, he took on the difficult task in Siberia because he considered this development to be one of the most important national problems. During the subsequent decade, under his leadership, the Institute of Mathematics (now the Sobolev Institute of Mathematics) became an internationally acclaimed center of mathematical sciences. Although he himself had never studied cybernetics or mathematical economics, he recognized their importance and did everything he could for their development at the Institute. He was also one of the organizers of Novosibirsk State University, founded in 1958 to nurture young scientists for the Siberian Branch of the USSR Academy of Sciences. A new journal, Siberian Mathematical Journal, was founded, with Sobolev as the Editor-in-Chief from 1968 till 1988.

In 1984 he went back to Moscow because of a deterioration in his health but continued to work at the Steklov Institute of Mathematics of the USSR Academy of Sciences. With his many doctoral students in the theory of partial differential equations, computational mathematics and mathematical physics, he was rightly one of the founders of the Soviet school in these areas. In 1981 he was awarded the Bolzano Gold Medal, and in 1989 the Lomonosov Gold Medal, and was decorated with honours by many foreign national academies.

Since his graduation from Leningrad State University Sobolev was continually involved in pedagogical work. The lectures he gave at Moscow State University for the course Equations of Mathematical Physics were turned into a popular textbook that was translated into many foreign languages.

He wrote many articles on the education of young people and was concerned about school education. In one article he wrote:

"What is the most important thing that a scholar must cultivate in himself? He must rid himself of unnecessary ambition. He must not think that only geniuses can be happy. He must train himself to value even small achievements, to be glad, and never overestimate himself. He must develop in himself a love of work. He must try to foster in himself the joy of knowledge, which is almost the same as the joy of life itself. Happiness is in the fact that something in one's life was needed by people."In 1967-1970 he was a Vice-President, then in 1971-1974 a Member-at-Large, of the ICMI. He once said:

"I live with the sensation that much was given to me earlier on credit: all my life I have strived to prove (although to myself) that all this was given to me for a purpose."

S.L. SOBOLEV 1968 (On his sixtieth birthday), Russian Math. Surveys, 23, 5, 131-140

S.L. SOBOLEV 1988 (On his eightieth birthday), Russian Math. Surveys, 43, 5, 1-18

Biography on S.L. SOBOLEV, Founder of the Sobolev Institute of Mathematics

S.L. SOBOLEV 1978, Teaching mathematics in the Soviet Union (in Russian), in Na putyakh obnovleniya shkol'nogo kursa matematiki (Ways of Renewing the School Mathematics Course), Moscow, 100-111

S.L. SOBOLEV, L.V. KANTOROVICH 1979, Mathematics in the modern school (in Russian), Mat. V. Shkole, 4, 6-10

Author

SIU, Man Keung

Department of Mathematics, University of Hong Kong

mathsiu@hkucc.hku.hk