# Mikhail Alekseevich Lavrentev

### Born: 19 November 1900 in Kazan, Russia

Died: 15 October 1980 in Moscow, Russia

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**Mikhail Alekseevich Lavrent'ev**'s name. These are most commonly Lavrent'ev, Lavrentev, Lavrentieff, Lavrentiev, Lavrentyev or Lavrentjev. His father, Aleksii Mikhailovich Lavrent'ev, taught mathematics at a technical college in Kazan and later was a professor of mathematics at Kazan University. His mother was Anisa Mikhailovna. When Mikhail Alekseevich was nearly ten years old, his father went to Germany to study at Göttingen and took his family with him. During the year 1910-11 that Aleksii Mikhailovich studied mathematics at Göttingen, his son Mikhail Alekseevich attended school in the city. It was during this trip to Göttingen that Aleksii Mikhailovich met another Russian, Nikolai Nikolaevich Luzin, who was studying there with Edmund Landau. Aleksii Mikhailovich and Nikolai Nikolaevich became good friends and, after returning to Russia, Luzin often visited the Lavrent'ev home in Kazan. Luzin had a very strong influence on Aleksii Mikhailovich's young son. After this year in Germany, the Lavrent'ev family returned to Kazan and Mikhail Alekseevich continued his education at a six-year commercial college. At this stage in his studies, it was chemistry that interested Lavrent'ev most. However, there is a story told that one day when his parents were out visiting, he took the opportunity to carry out some chemical experiments on the table in his home. The chemicals reacted strongly, damaging the table and giving off clouds of black smoke. When his parents returned and saw the damage to their home they told Lavrent'ev that he had to give up chemistry. After this he turned to mathematics.

In 1918, he entered the Faculty of Physics and Mathematics of Kazan State University after graduating from the commercial college and he studied there for three years. At this time he was particularly influenced by two of his lecturers, Evgenii Aleksandrovich Bolotov (1870-1922) and Dmitrii Nikolayevich Zeyliger. However, in 1921 Lavrent'ev's father was appointed as a professor of mathematics at Moscow State University and the family moved to Moscow. Lavrent'ev moved with his family and continued his studies at Moscow State University, graduating in 1922. After arriving in Moscow, in addition to his studies, Lavrent'ev taught mathematics at Moscow Higher Technical School. He would continue to keep this post until 1929.

At Moscow University, Lavrent'ev had been taught by his father's friend Nikolai Nikolaevich Luzin among others and, after graduating, he continued to undertake research on set theory and topology advised by Luzin. He studied under Luzin from 1922 to 1926, then in 1927, after successfully defending his candidate's thesis on set theory, he was sent to France to study in Paris for six months. This was an important time for the young mathematician who was advised by Paul Montel, attended lectures by Émile Borel, Gaston Julia and Henri Lebesgue, and participated in Jacques Hadamard's seminar. At this stage in his career, Lavrent'ev stopped his research in set theory and topology, moving towards the theory of complex variables. This was due to the Paris school where variational methods in the theory of conformal mappings were being developed. Returning to Moscow near the end of 1927, he was appointed as an assistant professor at Moscow State University and delivered a course on conformal mappings. Also at this time he became a member of the Moscow Mathematical Society. The year 1929 was one of great importance for Lavrent'ev. He was appointed as a professor and head of the department of mathematics at the Moscow Institute of Chemical Technology. Also in 1929 he was invited by Sergei Alekseevich Chaplygin to accept the post of senior engineer at the Zhukovsky Central Institute of Fluid Dynamics. This Institute, set up by Nikolai Egorovich Zhukovsky and Sergei Alekseevich Chaplygin in 1918, provided a remarkable research environment. It was, at this time, directed by Chaplygin (Zhukovsky had died several years before) and Lavrent'ev became one of the leading scientists at the Institute. At the Institute [31]:-

Mstislav Vsevolodovich Keldysh had been a student of Lavrent'ev's at Moscow State University and, after he graduated in 1931, Lavrent'ev recommended that he be appointed to the Zhukovsky Central Institute of Fluid Dynamics. Keldysh and Lavrent'ev produced several important joint papers as indicated in the quotation above. Lavrent'ev was appointed as a professor at Moscow State University in 1931 and from 1933 he held the chair of the Theory of Functions of a Complex Variable at the Steklov Institute of Mathematics of the USSR Academy of Sciences. The Steklov Mathematical Institute, together with some other institutions of the USSR Academy of Sciences, had been moved from Leningrad to Moscow in 1933. He was awarded his doctorate in engineering (equivalent to a D.Sc.) by Moscow State University in 1934 and, in the following year, his doctorate in mathematical sciences without having to defend a thesis. Over the years 1927-1938 he published a number of fundamental results in the theory of functions of complex variable and laid the foundations of a new mathematical theory, namely the theory of quasiconformal mappings.... he obtained many classical results in fluid dynamics. To a considerable extent, they are related to the problems of aerodynamics and strength of airplanes. Lavrent'ev gave excellent examples of practical application of theoretical solutions. For example, he applied variational properties of conformal mappings and reduced the important problem of flow around a wing to the solution of a singular integral equation of the first kind. In his works written together with Mstislav Vsevolodovich Keldysh, important results obtained in the theory of conformal mappings were used for the solution of numerous applied problems. For example, the problem of rigid impact against water was solved and the motion of a wing under the surface of a heavy liquid was investigated; the latter result became the theoretical foundation for a rapidly developing branch of contemporary hydrodynamics(the theory of hydrofoils).

In 1932 Lavrent'ev's son, Mikhail Mikhailovich Lavrent'ev, was born in Moscow. He studied at Moscow State University, graduating in 1954. His thesis advisor was Sergei L'vovich Sobolev. He worked at the Siberian Division of the USSR Academy of Sciences from 1957, specialising in ill-posed problems in mathematical physics. Mikhail Mikhailovich's son, Mikhail Mikhailovich Jr, was born in 1956. He is also a mathematician who, after studying at Novosibirsk State University, was awarded a Ph.D. for his work on differential equations in 1982.

From 1939 to 1941 and then again from 1944 to 1949, Mikhail Alekseevich Lavrent'ev was the Director of the Institute of Mathematics of the Ukrainian Academy of Sciences in Kiev. He was appointed to this role following the death of the previous director, Dmitry Aleksandrovich Grave, in December 1939. In 1945 Lavrent'ev was also appointed vice-president of the Ukrainian Academy of Sciences. During 1945-1948 he was a professor in the Physics and Mathematics Faculty of the Kiev State University. Yurii Alekseevich Mitropolskii writes [31]:-

Lavrent'ev's Kiev period has a break from 1941 to 1944 which, of course, coincides with the period in which the Soviet Union was at war with Germany. The Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union meant that the initial years of the war had little effect on life in Kiev and Lavrent'ev continued his work there. However, things changed dramatically on 22 June 1941 when Germany broke the non-aggression pact and invaded the Soviet Union. Kiev was soon threatened by the advancing German armies (they entered the city on 19 September 1941) and the Ukrainian Academy of Sciences was relocated to the city of Ufa. Lavrent'ev, along with several other leading scientists, approached the government with a proposal to undertake scientific research directly related to the development of military equipment. One of the projects Lavrent'ev worked on was the creation of a silencer for a gun. He also worked on the use of explosions in the construction industry, in particular in the construction of dams. By the end of 1943 Soviet troops had liberated Kiev and in the following year Lavrent'ev returned to the city when the Ukrainian Academy of Sciences returned. He was awarded the Order of the Patriotic War (Second Class) in 1944 for his contributions to the war effort.In the Kiev period of his scientific work ..., Lavrent'ev extensively developed his main results in mathematics and mechanics and obtained new important(theoretical and applied)results. ... First, in this period, his role as a remarkable Soviet scientist, prominent organizer of science, and outstanding public figure was finally formed. Second, the scientific activity of Lavrent'ev had a considerable influence on the development of mathematics and mechanics in the Ukraine. Here he carried out a large amount of work devoted to the development of physical and mathematical sciences and created a ramified school in the theory of functions of complex variables and its applications to the mechanics of continua. The scientific work carried out at the Institute of Mathematics of the Ukrainian Academy of Sciences under the guidance of Lavrent'ev was aimed at the solution of not only fundamental theoretical problems but also numerous important applied problems. A great merit of Lavrent'ev lies in the fact that he resolutely directed the theoretical investigations at the Institute of Mathematics of the Ukrainian Academy of Sciences towards the solution of the urgent problems of national economy.

Then, in 1950, he became director of the Institute of Mechanics and Computational Technology of the Ukraine. He was appointed as Academic Secretary of the Department of Physics and Mathematical Sciences of the USSR Academy of Sciences in 1951 and, in the same year, became a professor at Moscow State University. In 1955 he was appointed as head of the Department of Physics of Fast Processes of the Moscow Physical-Technical Institute.

Lavrent'ev moved to Novosibirsk when he was vice-president of the USSR Academy of Sciences between 1957 and 1975. During this time he was Head of the Siberian Division of the Academy of Sciences of the USSR. One of his achievements was the foundation of Akademgorodok, or 'Academic Town', situated just outside Novosibirsk (today it is a district of Novosibirsk). The idea was to attract leading scientists from the west of the Soviet Union to Siberia and this was achieved by building the necessary homes, schools and institutions to provide an attractive environment for scientists. The residents often called Lavrent'ev the 'grandfather' of Akademgorodok. From 1959 to 1966 he was a professor at Novosibirsk State University and he gained high international recognition, being vice-president of the International Mathematical Union from 1966 to 1970. Then, in 1975, Lavrent'ev returned to Moscow where he worked at the Institute of Physics and Technology until his death. However, during this period he was Honorary Chairman of the Siberian Branch of the USSR Academy of Sciences and made visits to Novosibirsk.

We have already indicated some of the areas on which Lavrent'ev worked but we now summarise his contributions. Yurii Alekseevich Mitropolskii writes [31]:-

He is remembered for an outstanding book on conformal mappingsThe scope of scientific investigations of Lavrent'ev, a world-known scientist who made a large contribution to the world science, was extremely wide. His outstanding scientific results in mathematics and its applications substantially affected the development of the theory of functions of complex variables, theory of differential equations, hydrodynamics, theory of motion of underground water, theory of long waves, dynamic stability, theory of cumulation, and many other fields of science and engineering.

*Conformal Mappings and Their Applications to Certain Problems of Mechanics*(1946) and he made many important contributions to that topic. In the 1940s he developed the theory of quasi-conformal mappings which gave a new geometrical approach to partial differential equations. One of the major areas to which he applied this work was to hydrodynamics. The 1940s was a period of industrialisation and construction and, after 1945, Lavrent'ev founded new areas of research in mechanics and applied physics which were aimed at laying the theoretical foundation necessary for the large construction projects of building dams, canals and bridges on the Volga, Dnieper and Don rivers. He also applied the theory of complex variables to other topics, in particular to non-linear waves in important papers such as

*On the theory of long waves*(1943). Other topics where he made substantial contributions were the theory of sets, the general theory of functions, and the theory of differential equations.

Many international honours were given to Lavrent'ev in addition to those mentioned above. He was elected to the Czechoslovak Academy of Sciences (1957), the Bulgarian Academy of Sciences (1966), the International Academy of Astronautics (corresponding member 1966, full member 1970), the Berlin Academy of Science (1969), the Finnish Academy of Science and Letters (1969), the Paris Academy of Sciences (1971), the German Academy of Scientists Leopoldina (1971), and the Polish Academy of Sciences (1971). He was awarded the M V Lomonosov Gold Medal (1977):-

He has received many other honours. For example, the Institute of Hydrodynamics of the Siberian Division of the USSR Academy of Sciences which Lavrent'ev founded was named after him in 1980. Several towns have streets named after him, a specialist mathematical school has been named after him, as has a research vessel. Other honours he received from his own country include being awarded the Order of the Red Banner of Labour four times (1945, 1948, 1953, 1954) and the Order of Lenin five times (1953, 1956, 1960, 1967, 1975). He also received the Order of the October Revolution (1970) from his own country and he was made Commander of the Légion d'honneur by France in 1971.... for outstanding achievements in mathematics and mechanics.

Although he died in Moscow, Lavrent'ev was buried in the Cherbuzinskom cemetry in Novosibirsk. We end this biography by quoting Vladimir Mikhailovich Titov (1933-), one of Lavrent'ev's postgraduate students who became one of his closest collaborators at the Siberian Division of the USSR Academy of Sciences:-

Up to the end of his life, Lavrent'ev, as a scientist, did not get tired of wondering at mysteries of the nature and trying to solve them. In fact, he was a prominent naturalist in the widest sense of this word, which becomes obsolete in our time of high specialization. His extraordinary intuition and capability of applying methods developed in one field of science to a different field and constructing models of phenomena paradoxical at the first sight astonished those who knew him and worked by his side.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (44 books/articles)

**A Poster of Mikhail Alekseevich Lavrent'ev**

**Mathematicians born in the same country**

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