# Biographies from a book about O A Zhautykov

We give two biographies below. The first is a biography of Sergey Lvovich Sobolev. Zhautykov wrote a biography of Sobolev in 1968. The second is a biography of Nikolai Nikolaevich Krasovskii. They are translations from biographies in the book G I Belgibaeva and L D Abenova (eds),

*Zhautykov Orymbek Akhmetbekovich: Academician of the Academy of Sciences of the Kazakh SSR*(Russian) (Almaty, 2014).**1. Sergei Lvovich Sobolev**

Sergey Lvovich Sobolev - (23 September (6 October) 1908 - 3 January 1989) - Soviet mathematician, one of the greatest mathematicians of the 20th century, who made a significant contribution to modern science, in his research.

Sergei Lvovich Sobolev was born on 23 September (6 October 1908 in the new style) in St Petersburg in the family of a juror of Lvia Alexandrovich Sobolev. Sergei was deprived of his father early, and the main concern for his upbringing was the mother - Natalia Georgievna, a well-educated woman, teacher and doctor. She made a huge effort to develop the extraordinary abilities of her son, manifested at an early age.

Shown by chance: Natalia Georgievna, (at that time - a medical student) rested for a year with her children on the shores of the Finnish Bay. So it turned out that the professor of the same Dogel Institute rested in those places. In the autumn at the examination on his subject (histology) Dogel gave her an excellent grade without a single question, saying: "If you manage with such a son, you, of course, coped with my subject very well." To such an extent Serezha Sobolev was self-sacrificing, determined and persistent in his desires.

In the years of the Civil War from 1918 to 1923 he lived with his mother in Kharkov, where he studied at the technical school. S L Sobolev mastered on his own the syllabus of secondary schools, being especially interested in mathematics. Moving from Kharkov to Petrograd in 1923, Sergei entered the last class of the 190th school. At the school where he studied, S L Sobolev was taught by the best teachers in St Petersburg. Sergei was interested in everything: mathematics, physics, medicine, literature. He was fascinated by verses and music. But the school the mathematics teacher saw in Sergei the future talented mathematician. She stubbornly insisted that he should enter the university's mathematics department.

In 1924 S L Sobolev graduated from high school with honours, and in 1924-1925 he studied at the 1st State Art Studio in the class of piano playing. In 1925 he entered the university.

At the university, Professor N M Gunther and V I Smirnov, noticing the curiosity and maturity of the young student, attracted him to scientific work. N M Gunther was the scientific advisor of S L Sobolev. S L Sobolev read the works of his second teacher V I Smirnov to his last days. S L Sobolev was totally committed to study the theory of differential equations. He listened to the lectures of famous mathematicians, V I Smirnov, G M Fichtengolz, and B N Delone. The university programme no longer satisfied him, so he studied specialised literature. One of the articles by S L Sobolev was published in "Reports of the Academy of Sciences".

As a mathematician Sergei Lvovich Sobolev began his career studying applications both at the university and after his graduation. For his student practice S L Sobolev went to the plant "Electrosila" in Leningrad, in the settlement bureau. The first task he solved for them, was the explanation of the appearance of new frequencies of the corresponding oscillations in the shafts with insufficient symmetry of the transverse section.

In 1929 he graduated from the Faculty of Physics and Mathematics of Leningrad University.

**Scientific activity**

After graduating from Leningrad University, S L Sobolev began studying geophysics at the Seismic Institute. Together with academician V I Smirnov he opened a new field in mathematical physics - functionally invariant solutions that allow one to solve a number of more complex problems associated with wave processes in seismology. They developed the Smirnov-Sobolev method which found a wide application in geophysics and mathematical physics.

Since 1934 S L Sobolev headed the department of differential equations at the V A Steklov Institute of Mathematics of the USSR Academy of Sciences. In the 30s S L Sobolev produced a number of important results on the analytical solutions of the system of differential equations in a single variable, integral-differential equations with many independent variables, and proposed new methods of solving the problems which arose. These results were published in the Reports of the Academy of Sciences of the USSR, in the Proceedings of the 2nd All-Union Mathematical Congress (1934), and in the collection "Mathematics and Natural Sciences in the USSR" (1938).

On 1 February 1933, at the age of 24, S L Sobolev was elected a corresponding member, and on 29 January 1939 (at the age of 30) he was an full member of the USSR Academy of Sciences in the Department of Mathematical and Natural Sciences (Mathematics). In the 1940s S L Sobolev developed the application of functional analysis and computational mathematics to solve the problems of mathematical physics. He wrote the monograph "Equations of Mathematical Physics". Its third edition was published in 1954.

From 1945 to 1948, S L Sobolev worked in the Laboratory No 2, later known as LIPAN and then as the Institute of Atomic Energy named after I V Kurchatov, dealing with the problems of the atomic bomb and nuclear energy. He soon became one of the deputies of Igor Vasilyevich Kurchatov and joined the group of Isaak Konstantinovich Kikoin, where the problem of uranium enrichment was studied with the help of cascades of diffusion machines for the separation of isotopes. S L Sobolev worked in a group on plutonium-239, and in the group on uranium-235, organised and directed the work of computers, developed questions of regulation of the process of industrial separation of isotopes and answered the question of the loss of labour.

For outstanding merits for his country in the creation of the atomic weapon S L Sobolev was awarded the title of Hero of Socialist Labour in 1951.

... Based on the methods of functional spaces proposed by Sobolev, there were known Sobolev inequalities which allowed one to study, in particular, the existence and regularity of solutions of differential equations. The history of generalized functions and Sobolev spaces includes research by V A Steklov, K O Friedrichs (Kurt O Friedrichs), G Levy, S Bochner (Salomon Bochner) and others. S L Sobolev proposed his theory of generalised functions in 1935. Ten years later these ideas were independently studied by L Schwartz, who connected all the previous approaches, proposed a convenient formalism based on the theory of topological vector spaces and built a theory of transformation of generalised Fourier functions, which S L Soboleva had not done and who highly appreciated this contribution of . Schwartz. However, in confirmation of the special contribution of S L Sobolev, as the pioneer of the new subject, the outstanding French mathematician Jean Leray, who in his time visited L Schwartz, pointed out - "distributions (generalised functions), were invented by my friend Sobolev."

In 1952 S L Sobolev headed the department of computational mathematics of the Faculty of Mechanics and Mathematics of the Moscow State University. This department was set up in 1949. To this chair, in 1952 S L Sobolev invited Professor A A Lyapunov for deliver the course "Programming".

During the years of its existence (1949-1969) the department has prepared more than a thousand specialists who have made significant contributions to the development and application of computational mathematics, and created their own scientific schools. In 1955 S L Sobolev was the initiator of the creation of the Computing Centre of the Moscow State University, which for a short time was one of the most powerful in the country.

Together with M Lavrentev and S A Christianovich, S L Sobolev became the initiator of the founding and the organiser of the Siberian branch of the Academy of Sciences of the USSR, which began with the construction of the Novosibirsk Academy of Sciences. From 1957 to 1983, S L Sobolev headed the Institute of Mathematics of the Siberian Branch of the Academy of Sciences of the USSR (Novosibirsk), where there were large mathematical schools in the field of functional analysis, differential equations, mathematical economics, algebra and logic. He contributed to the establishment of the Novosibirsk School of Computational Mathematics and Programming. Now the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences bears his name. In his Siberian years, S L Sobolev created the theory of cubic formulas, proposing a fundamentally new approach to numerical integration with the help of methods of generalised theories of functions.

S L Sobolev was distinguished not only by his broad erudition as a scholar, but also by his brilliant talent for mathematics, but also by the activities in his life. In the 1950s, when cybernetics and genetics were considered in the USSR to be 'pseudoscience', S L Sobolev actively stood up for their protection. In 1955 he signed the "Letter of three-hundred". The article by S L Sobolev, A I Kitov and Lyapunov "The Main Features of Cybernetics", published in the journal "Questions of Philosophy" (1955, No 4), played a decisive role in changing attitudes to cybernetics.

In the early 1960s S L Sobolev supported the work of L V Kantorovich on the application of mathematical methods in economics, which at that time were considered in the USSR as a departure from "pure pedigree" Marxism-Leninism and the apology of capitalism. Resolution of the methodological seminar of the Institute of Mathematics of the Academy of Sciences of the USSR, containing the assessment of the work of L V Kantorovich, was signed by academician S L Sobolev and A V Bitsadze, a corresponding member of the Academy of Sciences of the USSR, and published in response to an article by L Gatovsky in the journal "Communist" (1960, 15).

**Interesting cases**

During the Great Patriotic War, warm clothes were not enough. S L Sobolev learned to knit and made himself a sweater, and then taught this craft to children.

**2. Nikolai Nikolaevich Krasovskii**

Academician Nikolai Krasovsky is one of the greatest mathematicians in Russia.

The founder of the Ural school on the theory of stability of motion and mathematical control theory, Academician of the Russian Academy of Sciences, Nikolai Nikolaevich Krasovsky was born on 7 September 1924 in Yekaterinburg in the family of a well-known doctor in the city. In 1949 he graduated from the metallurgical faculty of the Ural Polytechnic Institute (UPI). For 10 years he worked at the Department of Higher Mathematics of the UPI, and in 1959-1970 at the Ural State University. From 1970 to 1977 he headed the Institute of Mathematics and Mechanics (IMM) of the Ural Scientific Centre of the USSR Academy of Sciences. In recent years, he was the chief researcher of the Department of Dynamic Systems of the Institute of Mathematics and Mechanics of the Ural Branch of the USSR Academy of Sciences. Since 1964 he has been a corresponding member, and since 1968 he has been a full member, of the USSR Academy of Sciences (now the Russian Academy of Sciences). He is an advisor to the Russian Academy of Sciences, an honorary doctor of the Ural Federal University, and a foreign member of the Hungarian Academy of Sciences. He is the author of six monographs, 280 scientific publications.

Nikolai Krasovsky is one of the founders of the theory of optimal control. Using the methods of functional analysis, he developed a remarkable theory of optimal control, which makes it possible to formulate effective conditions for the existence of optimal solutions, and necessary and sufficient conditions for optimality. A great contribution to world science was made by Krasovsky's fundamental works on key problems of the theory of stability and the stabilisation of motion.

Krasovsky is the founder of a large scientific school, which has dozens of students who have achieved world-class scientific results. Among them are RAS President Academician Yuri Osipov, Academicians Alexander Kurzhansky, Andrey Subbotin, RAS Corresponding Members Alexander Chentsov, Vladimir Tretyakov, Vladimir Ushakov, Nina Subbotina, Doctors and Candidates of Sciences, engineers and teachers.

Among Krasovsky's awards is: the Star of the Hero of Socialist Labour; the title of Laureate of Lenin, State; and scientific Demidov Prizes. He was awarded the orders of Lenin, the October Revolution, the Red Banner of Labour, "For Merit to the Fatherland" III and II degrees. He was honoured with the Grand Gold Medal of the Russian Academy of Sciences named after M V Lomonosov, the Gold Medal of the Russian Academy of Sciences named after A M Lyapunov, Gold Medal named after Academician S V Vonsovsky Ural Branch of the Russian Academy of Sciences, as well as the award of the International Society of Electrical and Electronics Engineers (IEEE). Winner of the Triumph Prize of the Presidium of the Russian Academy of Sciences in 2001, which is awarded to Russian scientists who have made a significant contribution to the development of domestic and world science.

Last Updated March 2022