Russian astronomers. General issues of cybernetics

Was born October 8, 1911 in Moscow .

Alexey Andreevich Lyapunov brought up V family rich in their
historical And cultural traditions .
Lyapunovs - old family , from whose ranks many scientists emerged ,
including mathematicians.
By family legends the Lyapunov family originates from Prince Constantine Galitsky - brother Alexander Nevsky.
Vasily Alexandrovich Lyapunov - one from ancestors , since 1820 held various administrative positions V Kazan University.
His children - Michael, Victor, Natalia And Catherine - became the founders
four branches ,V each from whose names appear With world famous. Mikhail Vasilievichwas Director of the Observatory at Kazan University;
his son is a famous mathematician And mechanic, creator of stability theory
Alexander Mikhailovich Lyapunov, Victor Vasilievichwas a prominent physician ;
among his grandchildren - Alexey Nikolaevich Krylov - famous mathematician, mechanic
And shipbuilder,AndAndrey Nikolaevich Lyapunov - railway engineer ,
father Alexey Andreevich .
From representatives of other sciences,related WithLyapunovs,
it is worth mentioning the physiologist THEM. Sechenov, organic chemist A. M. Zaitseva,
philologist B.M. Lyapunova, ophthalmologist V.P. Filatova, physics
And Nobel laureate Pyotr Leonidovich Kapitsa.

After my father's death, scientist's mother Elena Vasilievna Lyapunova became a wife
Sergei Semenovich Nametkin (1876 - 1950 ) - Outstanding organic chemist, Full member of the USSR Academy of Sciences, Director of the Institute of Petroleum of the USSR Academy of Sciences,
which before buried his wife - sister's husband A Elena Vasilievna-
Lidia Nikolaevna Lyapunova .
Father of two children from first marriage Sergey Semyonovichadopted children
Elena Vasilievna.

Alexey Lyapunov received his primary education V the walls of your house,
then in 1924 he was enlisted V 5th grade Moscow
schools (nine-year-olds) No. 42 , which he graduated from in 1928.

From 1926 to 1930 year was Member om Moscow Society of Astronomy Amateurs. His observations were published in 1926 year V "Bulletin of KN MOLA"
in the article by A.P. Moiseev ( № 7 , With. 43) .

In 1928 yearA.A. Lyapunov entered Faculty of Physics and Mathematics
Moscow State university, however, due to his noble origin, he was forced to leave Moscow State University after a year and a half.

From 1930 to 1932 Alexey Andreevich worked as a laboratory assistant ,then - Junior Researcher V State Geophysical Institute, led by Academician A P.P. Lazarev ,where he was involved in modeling lunar craters, ocean currents And other tasks.

In 1932 formation beginsAlexey Andreevich Lyapunov like mathematics.
He p stepped upTo studying mathematics under guidance of their Scientific Supervisors
And academicians Nikolai Nikolaevich Luzina And Peter Sergeevich Novikov.

In 1932-1934 A.A. Lyapunov worked in the position Junior his researcher at the seismic laboratory of the Oil Geological Exploration Institute.

In 1934 year in the collection of Reports of the USSR Academy of Sciences published the first scientific publicationAlexey Andreevich “On the separability of analytic sets” .

In 1934-1936 A.A. Lyapunov have worked Junior Researcher, Department of Biophysics, All-Union Institute of Experimental Medicine(VIEM).

In 1934-1937 was a junior researcher at the theory department
functions of a real variable Moscow Institute of Mathematics
named after V.A. Steklov.

In 1935 Alexey Andreevich Lyapunov was elected Full Member of the Moscow Mathematical Society , and in 1954-1962 was a Member
Board of the Society.
From 1936 to 1941 he worked for Department of Mathematical Analysis, Moscow State University, first as an assistant, and since 1937 - performing m responsibilities of the department assistant professor.

In 1937-1938 he p prepared And passed exams as an external student By university courses And candidate minimum By mathematics.

At the same time A.A. Lyapunov n reproducing V Kalinin Teachers' Institute.

From 1937 to 1941 he led a special seminar By set theory
for graduate students and senior students at the Research Institute of Mathematics of Moscow State University.

In 1939 Alexey Andreevich was approved in academic degree
Candidate of Physical and Mathematical Sciences behind dissertation
“On the uniformization of analytical additions”.

In 1939 - 1941 he is an Associate Professor at the Department of Mathematical Analysis
Moscow City Pedagogical Institute named after Karl Liebknecht.

From 1939 to 1942- Senior Researcher at the Institute of Mathematics
named after V.A. Steklov Academy of Sciences of the USSR.

After the outbreak of war, in September 1941, without interruption from scientific work,
A.A. Lyapunov was on labor front under Moscow And participated V fire protection
And air defense By place of residence and in building of the Institute of Mathematics named after V.A. Steklov Academy of Sciences of the USSR.
IN October was evacuated V Kazan With Academy of Sciences of the USSR.

It was the second year of the Great Patriotic War.
Andrey Alekseevich Lyapunov as a scientist, and also a Candidate of Sciences,
could use the "reservation", But as a patriot of your country, he refused
from her And left voluntarily to Army , after completing six months of training
in Vladimir Infantry School.
Until October 1943 was in Moscow Command Reserve
military district (Stalingrad Front), as well as being treated in hospitals :
In July-September 1943 was a cadet, then Teacher of the officer training battery.

From October 1943 to April 1945 served V Active Army.
Guard senior lieutenant Andrey Alekseevich Lyapunov took part in battles
on the 4th Ukrainian, 3rd Belorussian, 1st Baltic Front behind liberation Crimea A , Baltic And, Ukraine and East Prussia V as the Commander of the top computing platoon of the 22nd Krasnogvardeysky Evpatoria
artillery regiment, 3rd Guards Red Banner Rifle Division,
2nd Guards Army.

Even V difficult military conditions, he sought to make the most of
your mathematical knowledge.
Later, a number of V those years of results on shooting theory,
By ways to improve the accuracy of topographic work ( in particular,
target accuracy ) was published V "Artillery Magazine"
And "Izvestia of the Artillery Academy".

In January-February 1945 was V vacation V Moscow With scientific purpose.

In April 1945 A.A. Lyapunov departed V Artillery Order of Lenin
And Order of Suvorov, 1st degree, Academy named after F.E. Dzerzhinsky,
Where have worked to January 1946 Laboratory assistant, and then - Head of department
topographic reconnaissance.

In January 1946 Alexey Andreevich was demobilized And appointed
on position of Senior Lecturer, and in 1950 - Professors
Departments of Mathematics, Faculty No. 6 Jet Weapons
Artillery Academy named after F.E. Dzerzhinsky .

Almost simultaneously in 1946-1949 A.A. Lyapunov studies
V Ddoctoral studies at the V.A. Mathematical Institute Steklova
Academy of Sciences of the USSR.

In 1950 Andrey Alekseevich Lyapunov P awarded an academic degree
Doctor of Physical and Mathematical Sciences behind dissertation
“On operations leading to measurable sets”.

In 1949-1951 is a Senior Research Fellow at the Institute
geophysics of the USSR Academy of Sciences, and in the summer of 1950 participates
V North Tien Shan expedition V Expedition Leader positions.
He supervises the work By interpretation of gravitational
observations And deep seismic sounding.

In 1949-1955 was a People's Assessor of the People's Court
Leninsky district of Moscow.

From 1951 to June 1953he worked as a Senior Researcher
Moscow Mathematical Institute named after V.A. Steklova
Academy of Sciences of the USSR.

In 1952-1961 A.A. Lyapunov - Professor of the Department of Computational Mathematics
Faculty of Mechanics and Mathematics of Moscow State
University named after M.V. Lomonosov .

In 1953 Alexey Andreevich Lyapunovwas invited Academician
Mstislav Vsevolodovich KeldyshV created on the basis of the Mathematical Institute named after V.A. Steklov Department of Applied Mathematics
(now - Institute of Applied Mathematics named after M.V. Keldysh ) , where he works
until 1954 in positions Acting Manager,
Head of department.

Since 1954 he - Senior Researcher, Programming Department,
from 1958 to 1961 - Senior Researcher, Department of Cybernetics,
Chairman of the Branch Library Council.

Scientific activity Alexey Andreevich Lyapunov was inextricably
tied With VTs-1 - Computer center created By Order
Minister of Defense of the USSR dated May 1, 1954.
One of areas of work of VTs-1 were carrying out calculations,
which made it possible to launch artificial Earth satellites,
space station flights To planets of the solar system,
human flight into the space .
This Center was led by a Disciple A.A. Lyapunova, Outstanding scientist,
one of the pioneers of Russian cybernetics, Professor, Colonel
Anatoly Ivanovich Kitov.
WITH among those who worked in VTs-1 side by side with A.A. Lyapunov worth mentioning
such luminaries of mathematics And Computing as
Lazar Aronovich Lyusternik,Nikolai Panteleimonovich Buslenko
(also a student of A.A. Lyapunov) , Mikhail Romanovich Shura-Bura,
Igor Andreevich PoletaevAnd a lot others.
In 1955, together with S.L. Sobolev and A.I. Kitov A.A. Lyapunov
publishes an article V journal "Questions of Philosophy" -
“The main features of cybernetics. The beginning of the struggle for cybernetics".

In 1955-1964 Alexey Andreevich Lyapunov Rled the all-Moscow seminar he created By cybernetics, V in which mathematicians took part, biologists, economists, engineers, military, linguists,philosophers.

In 1956 he was elected Full Member of the Moscow Society of Natural Scientists And took part in work of the III All-Union Mathematical Congress(held in Moscow), performed with three reports.
From 1956 to 1973 was the Editor of the series of collections "Problems of Cybernetics" organized by him.

From 1957 to 1964 was a Member of the Technical and Economic Council
at Council of the National Economy of the Moscow Regional Economic
region of the RSFSR.
In 1959 as Head of the Cybernetics Section And mathematical logic took part V work of the All-Union Conference By computational mathematics
And computer technology V Moscow.

Since 1959 was Deputy Chairman of the Scientific Council for Integrated
problem "Cybernetics" at the Presidium of the USSR Academy of Sciences.

Since 1961 and before passing away Alexey Andreevich Lyapunov
lived V Novosibirsk And have worked V Siberian Branch of the USSR Academy of Sciences.
Before 1964 he was a Member of the United Academic Council
By historical and philological And Philosophical Sciences of the Siberian Branch
Academy of Sciences of the USSR.

From 1961 to 1970 he - Head of the Department of Mathematical Logic
And Cybernetics Institute of Mathematics Siberian Branch of the USSR Academy of Sciences (city ​​Novosibirsk) .

In 1962, 1963 and 1964 was Deputy Chairman
Organizing Committee of the I, II and III All-Siberian Physics and Mathematics Olympiads
schoolchildren V Novosibirsk.
I took part V work of the IV All-Union Conference By general algebra V Kyiv,
on spoke at the plenary session With report.

From 1962 until the end of his life Acted as Head of the Department of Higher Mathematics, headed the Department of Mathematical Analysis, worked as Professor of the Department of Algebra And mathematical logic of Novosibirsk State University.

Alexey Andreevich Lyapunov was Member of the United Academic Council
By physical and mathematical And technical sciences Siberian Branch of the USSR Academy of Sciences;
Member of the Joint Section of Mathematics, mechanics And astronomy
Scientific and technical councils of the Ministry of Higher And secondary specialized education of the USSR And Ministry of Higher And secondary specialized education of the RSFSR; Member of the Academic Council of Novosibirsk State University.

In 1963-1971 - Chairman of the Academic Council of Novosibirsk
Physics and mathematics boarding school at Siberian Branch of the USSR Academy of Sciences.

Since 1963 he has been Scientific director of the Council of Young Scientists of the Siberian Branch of the USSR Academy of Sciences.

June 26, 1964 Alexey Andreevich Lyapunov was elected
Corresponding Member of the USSR Academy of Sciences By Department of Mathematics.

In 1964-1971 was Deputy Chairman of the Committee By holding olympiads And Deputy Chairman of the Scientific Council By problems
education of the Siberian Branch of the USSR Academy of Sciences.

Since 1967 and until the end of his life he was a Member of the United Academic Council
By biological sciences Siberian Branch of the USSR Academy of Sciences, and since 1968 - Member of the Academic Council
Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR.
In 1969 and 1970 he took part at work I and II All-Union Conferences
By problems of theoretical cybernetics in Novosibirsk, on plenary sessions of which he spoke with reports.

Since 1970 Head of the Laboratory of Theoretical Cybernetics
Institute of Hydrodynamics, Siberian Branch of the USSR Academy of Sciences.

In 1972 was a member of the organizing committee of the 1st All-Union Conference
By operations research in Minsk, and in 1973 - Member of the working
UNESCO group "Man and the Biosphere" at the Scientific Council for problem
"Study of the human environment And rational use
biosphere resources" of the State Committee in science and technology
under the Council of Ministers of the USSR And Presidium of the USSR Academy of Sciences.
Awards :
Alexey Andreevich Lyapunov was awarded the Order of Lenin
(1971 , "For great services in the development of mathematical science and in connection with the sixtieth anniversary of his birth"); Red Star (1944) ;
"Badge of Honor" (1953) ; two Orders of the Red Banner of Labor
(1956 , " For scientific and pedagogical activities" ;
1967 , "For the creation of the Novosibirsk Scientific Center of the Siberian
branches of the USSR Academy of Sciences and achievements
in the development of science" ).

Alexey Andreevich was also awarded medals:
“For victory over Germany in the Great Patriotic War
1941-1945" (1945 ); “In memory of the 800th anniversary of Moscow” (1949 ); "Twenty years of victory in the Great Patriotic War of 1941-1945"
(1965 ); "50 years of the USSR Armed Forces" (1967 );
"For valiant work. In commemoration of the 100th anniversary
since the birth of Vladimir Ilyich Lenin" (1970 ). During the Great Patriotic War A.A. Lyapunov received four commendations from the Supreme Commander-in-Chief I.V. Stalin.

In 1996 Alexey Andreevich the medal was awarded posthumously
"Pioneer computer equipment" ("Computer Pioneer")
On the reverse side of the medal is the inscription: "The Computer Society has recognized
Alexey Andreevich Lyapunov the founder of Soviet cybernetics
and programming".

During the period of the late 40s - early 50s. In the 20th century, the urgent needs of science and technology began to stimulate the development of both a number of traditional and fundamentally new areas of mathematics. At this time, the foundations of the general theory of communications, information theory, optimal control, and cybernetics were laid. The first computers appeared, the improvement of which required the development of an appropriate mathematical apparatus. It was at this time that technology came close to creating systems capable of simulating individual functions unique to humans, and performing some of them faster and more efficiently. Such a situation required deep philosophical understanding and a precise, adequate description, which led to an expansion of the range of problems that arose that required solutions. Moreover, they turned out to be closely related to each other not only because methods of mathematical statistics were used to solve them, but also because they were based on the concept of “information”, the principles of its optimal processing, its use in management and in the functioning of self-organizing systems.

To develop the principles and methodology for studying the noted problems and their interrelationships, outstanding scientists with a broad scientific worldview and mastery of the mathematical apparatus were needed. Such scientific potential was possessed by the American mathematician who formulated the foundations of cybernetics, Norbert Wiener (1894 - 1964) and our domestic scientist Alexei Andreevich Lyapunov (1911 - 1973). These two scientists were distinguished by high scientific erudition, extraordinary mathematical abilities and a number of common stages in their creative path. Both were engaged in set theory: N. Wiener - Banach spaces, A.A. Lyapunov - descriptive set theory; both worked on applying the methods of mathematical statistics to biological systems, and during the war - by solving very similar problems related to defense issues; both were interested in optimal methods of information processing: N. Wiener - optimal filtering, A.A. Lyapunov - the theory of statistical solutions; and, finally, both made great contributions to the mathematical and philosophical understanding of the foundations of cybernetics.

The publication of Norbert Wiener's book "Cybernetics" in 1948 and the publication of fundamental works on information theory by Claude Shannon (1916 - 2001) marked the beginning of a period of rapid development and implementation of computers. However, although N. Wiener was proclaimed the father of cybernetics, his book “Cybernetics” did not contain either a consistent course of the new science, or a description of its theoretical apparatus, or a statement of its methods. More specifically, the essence of the principles and methods of studying complexly organized systems was shown 35 years before Wiener by Kharkov University graduate A.A. Bogdanov (1873 - 1928) in science, which he called technology; but in the USSR it was subject to a severe ban.

In the Soviet Union, cybernetics met with misunderstanding and was declared a “pseudoscience of obscurantists,” but the needs of the development of science, industry, and the national economy as a whole led to the fact that the most active apologists of the existing system, the doctrine of which did not correspond to some provisions of the new science, were forced to agree with the need acceptance of the ideas of cybernetics. Scientific community Soviet Union began the fight for official recognition of cybernetics.

An article published in 1955 by S.L. Soboleva, A.I. Kitova, A.A. Lyapunov's "Basic Features of Cybernetics" marked the beginning of this process. Other prominent scientists also joined him, including Academician A.N. Kolmogorov. As a result of their efforts, an article by A.N. appeared in the Great Soviet Encyclopedia. Kolmogorov's "Cybernetics", revealing the true essence of this science, and the Council on Cybernetics was established under the Presidium of the USSR Academy of Sciences, headed by Academician A.I. Berg: It's difficult to specify. the exact date the “first” work in the USSR, which would be directly related to those issues for which the term “cybernetics” began to be used. There are certain reasons to start with theory relay circuits- their design is closely related to the use of logical algebra. Perhaps the world's first work in the field of the theory of relay devices was the work of V. Shestakov, “Some mathematical methods for constructing and simplifying two-terminal circuits,” completed in 1935 at the Faculty of Physics of Moscow State University. In 1938, K. Shannon published a paper on the same topic (“Symbolic Analysis of Relay and Switching Circuits”). As happens very often, the relevance of the topic caused the emergence of similar solutions where serious work was being carried out - the Japanese Nakashima also proposed a similar solution independently. The further development of this direction is associated with the name of Mikhail Aleksandrovich Gavrilov (1903 - 1979). He defended his doctoral dissertation on this topic in 1946. The world's first monograph on methods for constructing relay circuits - "The Theory of Relay Circuits" by Gavrilov - was published in 1950 by the publishing house of the USSR Academy of Sciences. In the mid-40s. In the 20th century, the name of another outstanding scientist in the field of computer technology and control systems - Sergei Alekseevich Lebedev (1902 - 1974) - became known. In 1945, under his leadership, an analog computer was created for solving systems of ordinary differential equations.

The date “1948” stands out separately - this year the Institute of Precision Mechanics and Computer Science of the USSR Academy of Sciences was created in Moscow, which since 1975 has been named after S.A. Lebedev, and the Special Design Bureau at the Calculating and Analytical Machines (CAM) plant in Moscow. Thus, by 1948, two powerful competing organizations had taken shape - ITMiVT of the USSR Academy of Sciences and a united scientific and production association, which included the Research Institute of Computing Machinery (Research Institute SchetMash, SKB-245 and the SAM plant). In the same year, Isaac Semenovich Brook (1902 - 1974) together with Bashir Iskandarovich Rameev (1918 - 1944) received the first domestic copyright certificate for the invention of a computer

One of the tasks facing the founders of cybernetics was to unite various specialists into a single informal team to coordinate research and develop common approaches, the second was to explain the theoretical and applied significance of cybernetics. In solving these problems, the leading role of A.A. is undoubted. Lyapunova. In the 1954 - 1955 academic year in Moscow state university he, with the support of S.L. Soboleva organizes a scientific seminar for undergraduate and graduate students, which worked for ten years and made a decisive contribution to the development of information and cybernetic research in our country. The following took part in the seminar: A.I. Kitov, a student of Lyapunov, who back in 1953 compiled a report on the essence of cybernetics for a speech at a seminar at one of the research institutes; I.A. Poletaev, whose speeches at this seminar formed the basis of his book "Signal"; A.P. Ershov, an active participant in the seminar, later an academician, one of the founders of theoretical and system programming, founder of the Siberian School of Informatics, N.E. Kobrinsky, N.P. Buslenko, S.V. Yablonsky, academician O.B. Magnifier new and others.

Life and art. Corresponding Member of the USSR Academy of Sciences, Doctor of Physical and Mathematical Sciences, Professor Alexey Andreevich Lyapunov is an outstanding mathematician with broad scientific interests: descriptive set theory, probability theory, mathematical statistics, convex analysis; problems of applied and computational mathematics: computer programming, programming automation and input languages, applications of mathematics to the natural and human sciences: mathematical linguistics, machine translation of texts with foreign languages, geology, systematics, genetics, endocrinology, biogeocenology, operations research, etc., up to philosophical issues of natural science.

Alexey Andreevich was born on October 8, 1911 in Moscow into a noble family rich in cultural and scientific traditions. His father, Andrei Nikolaevich Lyapunov, received a physics and mathematics education at Moscow and Heidelberg universities, and until 1917 he served in the Railway Department, engaged in road construction. After the revolution, Andrei Nikolaevich worked at the Institute of Biophysics and at the Commission for the Study of the Kursk Magnetic Anomaly, where he collaborated with Academician P.P. Lazarev. Alexey Andreevich’s mother, Elena Vasilievna, received a good musical education and tried in every possible way to introduce her children to musical and theatrical culture. Under the influence of his parents, and from the age of twelve, his stepfather, the famous chemist Academician S.S. Nametkin, schoolboy Alyosha Lyapunov developed an interest in mathematics, astronomy, geology, biology, various areas of culture, Russian history, architecture, painting, music, etc.

Alexey Andreevich received his primary education at home, and in 1924 he entered the 5th grade of experimental nine-year school No. 42 of the Baumansky district of Moscow, where he received solid training not only in languages ​​and literature, but also in mathematics, physics, astronomy and other natural science disciplines. He spoke German and French fluently. In 1928 after graduating from high school. A.A. Lyapunov entered the Faculty of Physics and Mathematics of Moscow University. Without graduating, in 1930 he began working as a laboratory assistant, then as a junior researcher at the State Geophysical Institute (GGFI), the Oil Geological Prospecting Institute, and the All-Union Institute of Experimental Medicine.

In 1932 A.A. Lyapunov became a student of academician Nikolai Nikolaevich Luzin (1883 - 1950), under whose guidance and program he received a full-fledged mathematical education and began work in the field of set theory. In 1934, under the leadership of N.N. Luzina performs her first scientific work on set theory and becomes a junior researcher at the V.A. Mathematical Institute. Steklova. In this leading mathematical institution of the country, as well as in the Institute of Applied Mathematics, which spun off from it, Alexey Andreevich’s scientific activity took place until he transferred to the Siberian Branch of the USSR Academy of Sciences in 1961. The famous mathematical school of Luzin produced such luminaries of mathematics as A.N. Kolmogorov, P.S. Novikov, M.A. Lavrentiev, L.V. Keldysh, N.K. Bari, L.K. Lyusternik, D.E. Menshov et al. At the Mathematical Institute. V.A. Steklov Academy of Sciences of the USSR Lyapunov worked from 1934 to March 1942. At the same time, from 1936 to 1941, he worked at the Faculty of Mechanics and Mathematics of Moscow University, first as an assistant in the department of analysis, then as an associate professor in the correspondence sector and as the head of a special seminar on the theory of functions of a real variable. In 1937 - 1938 Alexey Andreevich prepared and passed external exams in university courses and the candidate minimum in mathematics at the Research Institute of Mathematics of Moscow University and defended his dissertation for the degree of candidate of physical and mathematical sciences on the topic “On the uniformization of analytical additions.” From the autumn of 1939 to August 1941, A.A. Lyapunov - Associate Professor at the Pedagogical Institute. K. Liebknecht.

In 1941, during the war, Alexey Andreevich was on the labor front near Moscow (September) and participated in fire and air defense at his place of residence and in the building of the Institute of Mathematics of the USSR Academy of Sciences. In October, together with the USSR Academy of Sciences, he was evacuated to Kazan. During the Great Patriotic War, A.A. Lyapunov voluntarily went to the front and participated in battles with the fascist invaders in the Crimea, Ukraine, the Baltic states and East Prussia. He was the commander of a top computing platoon in artillery, where he used his mathematical knowledge in difficult military conditions. The most interesting information about Lyapunov’s military path is contained in “Letter to D.S. Nalivaiko.” Later, a number of results he obtained in those years on the theory of shooting and on methods for increasing the accuracy of topographic work were published in the Artillery Journal and Izvestia of the Artillery Academy. In 1945 A.A. Lyapunov began teaching at the Artillery Academy named after. F.E. Dzerzhinsky, where he worked until 1951. At the Art Academy, Alexey Andreevich led seminars on various sections of mathematics that were not included in the compulsory programs, but were necessary for human mathematical and general scientific culture. Young listeners were impressed by the simplicity and clarity of the presentation of the material, as well as the scientist’s erudition in various fields of science. Lyapunov’s seminars often continued in his apartment in Khavsko-Shabolovsky Lane. At these seminars, various issues were discussed, including those related to persecuted genetics and cybernetics, and interesting people took part in them: I.A. Poletaev, N.P. Buslenko, A.I. Kitov, S.V. Yablonsky et al.

From January 1946 to April 1949, being a doctoral student at the Institute of Mathematics. V.A. Steklov Academy of Sciences of the USSR, Alexey Andreevich received a scholarship named after Academician Krylov. In April 1949, he presented and in December defended his dissertation for the degree of Doctor of Physical and Mathematical Sciences on the topic “On operations leading to measurable sets.” From May 1949 to 1951, Lyapunov was a part-time senior researcher at the Institute of Geophysics of the USSR Academy of Sciences. He achieved a number of significant scientific results in research on the problems of separability, uniformization and measurability of sets, properties of R-operations and R-sets, etc. The scientist carried his interest in descriptive set theory throughout his life. He published over 60 works in this area, the last publication dates back to 1973. The main works in this area were included in the collection of works by A.A. Lyapunov "Questions of set theory and function theory." (M.: Nauka, 1979).

The advent of electronic computers in the 50s of the 20th century led not only to the possibility of speeding up and facilitating computational tasks, but also to the use of mathematical methods in processing information in various fields of science: biology, economics, linguistics, etc. At the end of 1952, Aleksey Andreevich got acquainted in Feofania (near Kiev) with the work of MESM - the first of the domestic computers, created under the leadership of S.A. Lebedev, and begins to develop a description of the process of solving the problem, which precedes the preparation of the program. In the same year, Academician S.L. Sobolev invited Lyapunov to teach at the Department of Computational Mathematics, created at the Faculty of Mechanics and Mathematics of Moscow State University. Here, in the 1952-1953 academic year, he taught the country's first special course on programming. This special course, which consisted of eight lectures entitled “Principles of Programming,” outlined the basics of an approach called the “operator method of programming.” A.A. Lyapunov showed how one can describe the process of solving a certain problem on a computer using the operator logic circuits he proposed. For the first time, programming was defined as an independent scientific direction, the task of which is to develop rational ways of composing programs for solving various problems on automatic high-speed computers.

A new approach to the description of algorithms, which was based on the idea of ​​a “large-block” description of an algorithm, implemented in the operator method, opened the way to new formalizations of the concept of “algorithm”. This was a significant contribution of Alexey Andreevich Lyapunov to the theory of algorithms. Operator schemes were a sequence of operators different types(arithmetic operators, control operators) and logical conditions that determine the order of execution of the operators. The use of logical operator circuits made it possible not only by means of equivalent transformations to optimize the process of solving a problem using a mathematical apparatus even at the preliminary stages, before writing a program, but also made it possible to automate the transition from representation in the language of operator circuits to a program written in machine language, using an implementing this transition of the "programming program". The problem posed by Lyapunov of constructing an algorithm for establishing the equivalence of circuits and finding a complete system of equivalent transformations was solved by his graduate student Yu.I. Yanov, work on equivalent transformations of operator circuits of programs was continued by his other students - A.P. Ershov, R.I. Podlovchenko and others. Students of the first Lyapunov programming course: A.P. Ershov, I.B. Zadykhailo, E.Z. Lyubimsky, B.C. Shtarkman participated in the development of the country's first programming programs. Problems of program optimization and translation problems from languages high level in the language of machines are today central problems system programming. The ideas of Alexei Andreevich Lyapunov laid the foundation for the Soviet school of theoretical programming.

The emergence of a new scientific direction about control systems and control processes, called by N. Wiener “cybernetics or control and communication in animals and machines,” attracted the attention of progressive scientists in our country, including A.A. Lyapunova. Alexey Andreevich began to study cybernetics directly in the early 50s. XX century He became an active organizer of cybernetic research, overcoming misunderstanding and mistrust of cybernetics in our country in its first steps. You can read more about the development of cybernetics in our country in. The scientist did a great job of defining the subject of cybernetics research, classifying tasks and methods, developing a unified terminology, attracting interest in the new science among scientists of different specialties, and training personnel. A.A. Lyapunov noted the deep kinship between the axiomatic approach to the study of sets and the systematic approach to the study of large systems: this is a hierarchical design, with the help of which the entire system of objects to be studied is formed from some initial elements and freedom in choosing a system for describing the set of objects being studied. These considerations formed the basis scientific concepts, introduced by Aleksei Andreevich into cybernetics, their verification required an experiment, the possibility of which appeared only with the creation of high-speed computers.

The first publication on theoretical cybernetics in our country was the article “Basic Features of Cybernetics,” written by A.A. Lyapunov in collaboration with S.L. Sobolev and A.I. Kitov and published in 1955 in the journal "Questions of Philosophy". In 1956, at the third All-Union Mathematical Congress A.A. Lyapunov together with A.I. Kitov, I.A. Poletaev and S.V. Yablonsky presented a report “On Cybernetics”. This text under the same title and in the same year was published in the journal “Uspekhi Matematicheskikh Nauk”. In 1957, a report by A.A. was published in the materials for the All-Union Conference on Philosophical Issues of Natural Sciences. Lyapunova and S.L. Sobolev "Cybernetics and natural science". Alexey Andreevich created the Great Cybernetic Seminar at Moscow University, which played a significant role in the development of cybernetics in our country. The seminar began work in the 1954 - 1955 academic year as a cybernetic seminar for undergraduate and graduate students. It was led by A.A. Lyapunov and S.V. Yablonsky. The scientist attracted specialists from various fields to participate in the seminar - mathematicians, biologists, doctors, linguists, economists, transport workers, military specialists, etc. gave their reports. The large cybernetic seminar lasted for ten years.

In 1958, it was possible to achieve a translation into Russian of N. Wiener’s book “Cybernetics”. At the same time, the first issue of the famous series of collections “Problems of Cybernetics”, the leading cybernetic journal in the USSR, founded by Alexei Andreevich, was published. It contained two fundamental works by A.A. Lyapunova: “On some general issues of cybernetics” and “On logical circuits of programs.” Under the editorship of the scientist, 29 volumes of “Problems of Cybernetics” were published, “Cybernetic collections”, “Mathematical education” began to appear. In the report of A.A. Lyapunov and S.V. Yablonsky’s “Theoretical Problems of Cybernetics”, made in 1961 at the “United Theoretical Conference of Philosophical Methodological Seminars”, he defined the subject of cybernetics as follows: “Cybernetics is the science of the general laws of the structure of control systems and the flow of control processes.” The main provisions of the report were published in the collection "Problems of Cybernetics", vol. 9. Created in 1959 under the Presidium of the USSR Academy of Sciences, the Scientific Council on the complex problem of “Cybernetics”, chaired by Admiral Academician A.I. Berg, and the deputy chairman of the Scientific Council is A.A. Lyapunov, played a big role in the development of cybernetics. Alexey Andreevich carried out not only scientific and organizational work, but also took part in specific research works on individual problems of cybernetics. In 1962, the Scientific Council on the complex problem of "Cybernetics" acquired the status of an independent scientific institution with the rights of an institute.

In 1962, Alexey Andreevich moved from Moscow to the Novosibirsk Academgorodok, where he continued to work in the field of pure mathematics and in the field of cybernetics. In 1964 A.A. Lyapunov is elected corresponding member of the USSR Academy of Sciences. In Akademgorodok, the scientist devoted a lot of time to teaching. At Novosibirsk University, he lectured both on the problems of cybernetics and on classical branches of mathematics, and developed new course programs. On the initiative of A.A. Lyapunova and M.A. Lavrentyev, a physics and mathematics boarding school was created in the Novosibirsk Academgorodok, Lyapunov became the first chairman of its Council. To select talented schoolchildren for this school, a large-scale system of Olympiads was organized, which were held in three rounds. At the physics and mathematics school, Alexey Andreevich taught various subjects: mathematics, mineralogy, astronomy, geoscience (a course developed by him). The Physics and Mathematics School still exists; its graduates teach both at the Physics and Mathematics School and at the university, and work successfully in both science and business.

At the IV All-Union Mathematical Congress (1966) A.A. Lyapunov sums up the period of struggle for cybernetics:

“In a short period of time, the attitude towards cybernetics went through the following phases:

2) statement of existence;

3) recognition of usefulness, lack of tasks for mathematicians;

4) recognition of some mathematical problems;

5) full recognition of the mathematical problems of cybernetics."

At Novosibirsk University, along with teaching courses on theoretical cybernetics, computer programming and theory, set theory, mathematical analysis, machine translation, Lyapunov participates in the organization of a new discipline - mathematical linguistics, pays great attention to the use of modeling methods in the study of production processes and in machine translation . Lyapunov’s student N.P. worked in the first direction. Buslenko, in the second - Alexey Andreevich himself together with his students and, first of all, with O.S. Kulagina. The results obtained in solving a complex cybernetic problem, such as machine translation, have found application in other areas of cybernetics. O.S. Kulagina published a review of Alexey Andreevich’s works on machine translation and mathematical linguistics in the collection “Problems of Cybernetics”, no. 32. It should be noted that, even after moving away from direct participation in work in this area, Alexey Andreevich continued to have a great influence on the direction as a whole. On the initiative of A.A. Lyapunov, the First All-Union Conference on Theoretical Cybernetics was convened (Novosibirsk, 1969). Over time, holding such conferences became a tradition; they were held both in Novosibirsk and in other cities; the next XIII conference was held in Kazan in 2002.

All his life, Alexey Andreevich was interested in mineralogy and collected a rich collection of minerals and rocks. He showed great interest in astronomy - his observations during his school years were twice published in the Bulletin of the Moscow Society of Astronomy Amateurs, and later he organized an observatory for schoolchildren in Novosibirsk. But of all the natural sciences, Alexei Andreevich was most deeply interested in biology. In the sixties, he paid much attention to the theoretical analysis of general and particular problems of biology, the application of mathematics and cybernetics in biology, and mathematical modeling of biological phenomena, processes and objects. In the last years of A.A.’s creativity. Lyapunov dealt with general problems in the study of complex systems, including methodological aspects of the use of set-theoretic apparatus, fundamental concepts of the theory of probabilistic processes and methods of computational mathematics for understanding and analyzing a wide variety of natural and man-made systems.

Long-term diabetes mellitus, heart disease - all this could not force the scientist to reduce the volume of his workload and not affect his health. On June 23, 1973, during a business trip to Moscow, Alexey Andreevich Lyapunov died suddenly. He is buried at the Vvedensky cemetery, where the ashes of his teacher N.N. rest. Luzina.

On October 1, 1997 in Moscow, at a ceremony held in the building of the Presidium of the Russian Academy of Sciences, the works of our outstanding compatriots - S.A. Lebedev and A.A. Lyapunova. Their achievements in creating the foundations of computer technology and programming are officially recognized by the world's largest and one of the most authoritative professional organizations in the field of high technology - IEEE Computer Society (The Institute of Electrical and Electronics Engineers). On the Lyapunov medal there is an inscription: “The Computer Society recognized Alexei Andreevich Lyapunov as the founder of Soviet cybernetics and programming.” IEEE as an international community has existed for over 100 years. In 1946, a structural division was founded - the Computer Society (CS), which unites hundreds of thousands of professionals working in the field of computer science and industry: computer science, programming, computer equipment production and computer business.

Each year, the IEEE Computer Society presents awards and diplomas in 16 categories, recognizing the world's best achievements in fundamental research and practical applications, as well as achievements in organizational activities and education. The Computer Society's most prestigious award, the Computer Pioneer Medal, was established in 1981 to recognize the contributions of outstanding individuals in the field of computer technology whose major contributions have been time-tested for at least 15 years. Among the 55 laureates of this honorary award one can name such legendary names as J. Atanasoff (John Vincent Atanasoff) - for the creation of one of the first electronic computers, N. Wirth (Nicklaus E Wirth) - for the development of the Pascal language, J. McCarthy ( John McCarthy) and M. Minsky (Marvin Minsky) - for work in the field of artificial intelligence, E. Codd (Edgar Frank Codd) - for creating a relational data model, etc.

In 1998, a scientific conference was held at the Polytechnic Museum in connection with the 50th anniversary of the publication of N. Wiener’s book “Cybernetics”; an exhibition dedicated to this date was opened in the museum, where models of A.A. medals were displayed. Lyapunova and S.A. Lebedeva. In Novosibirsk named after A.A. Lyapunov is the name of the street on which the famous physics and mathematics boarding school, created on his initiative, is located. The Physics and Mathematics School of the St. Alexis Hermitage in the Yaroslavl Region bears his name.

Alexey Andreevich Lyapunov left works in the field of pure and applied mathematics, biology, geophysics, logic and methodology of science, and theory of pedagogy. He was a born teacher, an organizer of science; his name is associated with the formation of cybernetics and programming theory, the theory of machine translation, the development of mathematical biology, the organization of many publications, scientific councils, laboratories and departments. An intellectual in spirit, democratic in his interactions with hundreds of people, the scientist was consistent and firm in the struggle for scientific truth. Theoretical works by A.A. Lyapunov, which formed the basis for the development of cybernetics, together with his organizational and propaganda activities, give reason to consider him the founder of cybernetics in our country. Number of followers of A.A. Lyapunov and his students number many hundreds. His contribution to science is highly appreciated not only in our country, but also in the world.

Prepared by:

Lebedeva, S.N. A.A. Lyapunov - the founder of Soviet cybernetics and programming // Problems of cultural heritage in the field of engineering: collection of articles. – Issue 5. – M., 2007. – P.193 - 234. – Bibliography: p.2232−234.

Abroad, Bogdanov’s theggalological ideas were repeated by L. Bergalanffy /Austria, 193?/; The works of W. R. Ashby /England, 1956/, who discovered the law of differentiable diversity, Art. Beer /England, 1958/, who put forward the principle of external addition, and the subsequent works of domestic scientists, reflecting a new broad interpretation of cybernetics. But the name of this science was given by N. Wiener's book.

In the report of the professor of the Department of Cybernetics at MEPhI G.N. Povarov (editor of the second edition of N. Wiener’s book “Cybernetics”), made in 2001 at the annual meeting of MIAB (International Institute of Alexander Bogdanov), spoke about the difference in approaches to cybernetics in different countries. If in the USSR and the Russian Federation cybernetics is interpreted as a predecessor and component of computer science, then in France, where the term computer science appeared (Louis Couffignal, 1963), computer science and cybernetics are different disciplines. A similar approach prevails in the USA, where the Cybernetics Society (Systems, Man, and Cybernetics (SMC) Society) deals only with issues of artificial intelligence, systems theories, human-machine interaction and other things, that is, very close to what was understood by cybernetics Wiener himself.

An important distinctive feature of cybernetics is that it introduced fundamentally new method studying objects and phenomena - a so-called mathematical experiment, or machine modeling, which allows one to study an object according to its description (mathematical model), without resorting to constructing and studying a real physical model of this object.

Childhood

Alexander Mikhailovich was born on May 25 (June 6), 1857 (18570606) in Yaroslavl in the family of the famous astronomer, director of the Demidov Lyceum Mikhail Vasilyevich Lyapunov. Alexander Lyapunov and his younger brothers Sergei and Boris received their initial education under the guidance of their mother, Sofia Alexandrovna. However, from the age of seven his sons were systematically taught by their father, a man of broad interests (astronomy, history, philosophy, geography, etc.). Alexander was 11 years old when his father died. The question arose about further education. The studies were continued in the family of Rafail Mikhailovich Sechenov, whose wife was Alexander’s paternal aunt. R.F. himself Sechenov was I.M.’s brother. Sechenov.

In 1870, Alexander with his mother and brothers moved to Nizhny Novgorod. This move was caused by the need to continue studying at the secondary level. educational institution. For Sofia Alexandrovna, the extraordinary abilities of her sons were undeniable, and she sought to provide conditions for the possibility of further education of Alexander and Boris at the university, and Sergei at the conservatory.

Little information has been preserved about A. M. Lyapunov’s studies at the gymnasium. Mathematics and physics were taught to him by A.P. Gruzintsev, a talented teacher and scientist. Another teacher who taught mathematics to Lyapunov was D.K. Gik. In the fall of 1876, A. M. Lyapunov graduated from high school with a gold medal.

Student years

In 1876, Lyapunov entered the department of natural sciences of the Faculty of Physics and Mathematics of St. Petersburg University. Feeling, however, an inclination towards mathematical sciences, he transferred to the mathematics department within a month. At St. Petersburg University, during the period of Lyapunov’s studies there or shortly before, the brilliant P. L. Chebyshev, D. I. Mendeleev and I. M. Sechenov, the famous professors of mathematics and mechanics A. N. Korkin, O. I. Somov, worked there. D. K. Bobylev, K. A. Posse, E. I. Zolotarev.

From the first days of his studies at the university, A. M. Lyapunov diligently studied chemistry and enthusiastically listened to the lectures of D. I. Mendeleev. And even after moving to the mathematics department, he continued to study chemistry. And Chebyshev’s lectures and consultations largely determined the nature of all subsequent scientific and teaching activities of Lyapunov.

Remarkable natural abilities and hard work allowed Lyapunov to receive excellent preparation for future scientific work. A. M. Lyapunov was given great attention at this time by Professor D. K. Bobylev, on whose recommendation Lyapunov was retained at the university to prepare for a professorship in the department of mechanics.

Immediately after passing his master's exams in 1882, A. M. Lyapunov began searching for a topic for his master's thesis. He talked about this topic with P. L. Chebyshev. Chebyshev's task was as follows. It was known that a liquid homogeneous mass rotating uniformly around a certain axis, the particles of which are attracted to each other according to Newton’s law, can maintain the shape of an ellipsoid until the angular velocity of rotation exceeds a certain limit. If the angular velocity exceeds this limit, ellipsoidal equilibrium figures become impossible. If - some value angular velocity, to which the equilibrium ellipsoid corresponds, and a sufficiently small increment of angular velocity is given, then the question posed is the following: are there other equilibrium figures for angular velocity, different from ellipsoidal ones, and continuously changing with the same change, and coinciding with the ellipsoid? Subsequently, when Lyapunov made progress in solving and shared information with the teacher about new and emerging difficulties, Chebyshev himself was surprised at the difficulty of the problem he proposed.

Intense work on the problem posed by Chebyshev lasted two years. At the same time, Lyapunov managed to successfully use the method of successive approximations and analyze the first approximation in detail. However, since this approximation turned out to be insufficient, the young Lyapunov was not then able to give a complete solution to the problem. After several unsuccessful attempts, he postponed the decision on this issue. But this question led him to another one - about ellipsoidal forms of equilibrium, which was the subject of his master's thesis. The problem posed and solved by Lyapunov even before him attracted the attention of a number of first-class scientists - Liouville, Riemann, Thomson, Tate, etc. However, research in this area did not have the necessary rigor.

Scientific career

The defense of his master's thesis gave A. M. Lyapunov the right to teach. In the spring of 1885, Lyapunov was confirmed with the rank of private assistant professor at St. Petersburg University. But Lyapunov received an offer to occupy the vacant department of mechanics at Kharkov University. In 1885, Lyapunov moved to Kharkov and, with the same rank of private assistant professor, began lecturing on all courses of the department. A. M. Lyapunov did not consider the preparation of courses to be a completely creative matter and, speaking about the first years of his work at Kharkov University, he characterized them as a break in scientific activity. “Meanwhile, the courses compiled by him in all departments of mechanics contain such valuable and sometimes new materials that could not be found in any of the manuals available at that time...” wrote V. A. Steklov.

Alexander Mikhailovich timed his short trip to St. Petersburg, during which on January 17, 1886 the wedding of A. M. Lyapunov with Natalia Rafailovna Sechenova (his cousin) took place, to coincide with the winter holidays, not allowing himself to suspend his teaching activities even for a short time.

But the period of temporary decline in Lyapunov’s scientific activity was soon left behind. If you look at the pages of the “Communications of the Kharkov Mathematical Society” for the years 1887-1891, where Lyapunov’s works were published, you can see how purposefully he approached a comprehensive solution to the problem he set for himself.

According to mechanics and mathematicians - contemporaries of A. M. Lyapunov, already his master's thesis in its own way scientific level and the significance of the results obtained significantly exceeded many doctoral dissertations. There was a real opportunity to present as a doctoral dissertation a generalization of the master's thesis and research conducted at Kharkov University. However, Lyapunov, with his inherent demands on himself and his work, did not want to do this.

All these years, A. M. Lyapunov worked hard on his doctoral dissertation “The General Problem of Stability of Movement.” In this fundamental work, Lyapunov comprehensively considered the problem of stability of motion of systems with a finite number of degrees of freedom. The defense of the dissertation took place on September 30, 1892 at Moscow University. The opponents were Professor N. E. Zhukovsky and the prominent mathematician Professor B. K. Mlodzeevsky. The defense went brilliantly, and soon, in January 1893, the thirty-five-year-old scientist received the title of ordinary professor at Kharkov University. He continued teaching at this university until the spring of 1902.

Petersburg period

The official recognition of A. M. Lyapunov’s merits was his election as a corresponding member of the Academy of Sciences in the section of mathematical sciences, which took place in December 1900. Less than a year later, forty-four-year-old Lyapunov was elected an ordinary academician in the department of applied mathematics. Under the conditions of that time, election to academicianship required a mandatory move to St. Petersburg. In the spring of 1902, Alexander Mikhailovich moved to St. Petersburg.

The position of an academician allowed A. M. Lyapunov to concentrate all his efforts on scientific studies. He returns to the problem of equilibrium figures, proposed to him by Chebyshev 20 years ago. In 1905, his work “On one problem of Chebyshev” appeared on the pages of “Notes of the Academy of Sciences”. In subsequent years (1906-1914), a large work by A. M. Lyapunov was published in French in four parts, “On equilibrium figures of a homogeneous rotating fluid, not much different from ellipsoidal ones.”

In the first part of his fundamental work, Lyapunov derived the basic equations and indicated a method that makes it possible to prove in a completely rigorous manner the existence of new equilibrium figures and to determine these figures with any degree of accuracy. The second part of this work is devoted to calculations by successive approximations of new equilibrium figures close to Maclaurin ellipsoids. For new figures, studies of the angular velocity of rotation and angular momentum were also carried out. In the third part of Lyapunov’s work, these same questions are solved for new equilibrium figures close to Jacobi ellipsoids. Finally, the fourth part is devoted to a new method for finding equilibrium figures and establishing a connection between the results obtained with its help and the formulas used in the first part of this work.

• 1902-1915 - Sredny Avenue, 48.

Last days

The most intense and dramatic was the life of A. M. Lyapunov in Odessa, where he and his wife went in June 1917 at the insistence of doctors, in the hope of the beneficial effect of the southern climate on Natalya Rafailovna’s seriously deteriorated condition (pulmonary tuberculosis). In the early autumn of 1918, A. M. Lyapunov began giving lectures at Novorossiysk University. It was a course “On the shape of celestial bodies.” The course of lectures by A. M. Lyapunov ended after the seventh lecture. Lyapunov gave his last lecture on the last Monday of his life, October 28, 1918.

On Thursday, October 31, Natalia Rafailovna died. For Alexander Mikhailovich the blow was too strong, although he had, of course, long ago understood the inevitability of such an outcome. On the day of Natalia Rafailovna’s death, Lyapunov shot himself and was unconscious for three days. On November 3, 1918, Alexander Mikhailovich, without regaining consciousness, died in the university surgical clinic.

Achievements

• A. M. Lyapunov created the theory of stability of equilibrium and motion of mechanical systems with a finite number of parameters.
• Works in the field of: differential equations, hydrodynamics, probability theory.

The creator of the theory of stability of motion, the doctrine of equilibrium figures of a rotating fluid, methods of the qualitative theory of differential equations, the author of the central limit theorem of probability theory and other in-depth studies in the field of mechanics and mathematical statistics.

The inscription on the gravestone of A.M. Lyapunova

Alexander Mikhailovich Lyapunov (May 25, 1857 - November 3, 1918) - an outstanding Russian mathematician and mechanic, academician of the St. Petersburg Academy of Sciences.

Lyapunov was born in Yaroslavl. His father Mikhail Vasilyevich Lyapunov had shortly before left his post as head of the Kazan University Observatory and was appointed to Yaroslavl as director of the Demidov Lyceum. In 1863 M.V. Lyapunov retired and settled with his family in the Simbirsk province on his wife’s estate, devoting himself entirely to teaching his three sons, of whom Alexander Mikhailovich was the eldest. The middle son, Sergei Mikhailovich, later became a famous composer, and the youngest, Boris Mikhailovich, became a major specialist in Slavic philology, an academician of the USSR Academy of Sciences. The Lyapunovs' house had a huge library of books in Russian, German and French on mathematics, astronomy, natural sciences, philosophy, history, ethnography and political economy. Mikhail Vasilievich, having the ability to quick counting, taught this to children. They spent long winter evenings drawing geographical maps and playing games that consisted of traveling around the world.

After the sudden death of his father in 1868, Alexander Mikhailovich's training continued in the family of his uncle, Rafail Mikhailovich Sechenov, brother of the famous physiologist Ivan Mikhailovich Sechenov. Alexander and his cousin (future wife Natalya Rafailovna) studied in the gymnasium program. In 1870 A.M. Lyapunov, along with his mother and brothers, moved to Nizhny Novgorod, where he was immediately admitted to the third grade of the Nizhny Novgorod gymnasium. In 1876, Alexander Mikhailovich graduated from high school with a gold medal and in the fall of the same year he entered the natural sciences department of the Faculty of Physics and Mathematics of St. Petersburg University. There he listened to lectures by Professor D.I. Mendeleev and enthusiastically studied chemistry, but after a month he transferred to the mathematical department of the university, because he realized that mathematical sciences were of greater interest to him. At that time, chemistry was one of the compulsory subjects for first-year students, and Lyapunov continued to attend Mendeleev’s lectures, but the teachers of the mathematics department had the greatest influence on his development as a scientist.

At that time, the St. Petersburg Mathematical School, founded by the greatest scientist P.L. Chebyshev, world famous for his brilliant work on number theory, probability theory and analysis, was in its prime. Chebyshev himself and his students - Professor D.K. Bobylev, K.A. Posse, E.I. Zolotarev, A.N. Korkin - taught classes at the mathematics department of the university. Chebyshev's lectures, and subsequently the advice of the great mathematician, became decisive in the choice of topics for Lyapunov's research, and the situation in the mathematics department contributed in the best possible way to the development of the young scientist's exceptional abilities in mathematics and mechanics. Lyapunov carefully recorded Chebyshev's lectures, and in the evening of the same day he put the recording in order and rewrote it in his wonderful calligraphic handwriting. Possessing an excellent memory, he reproduced recordings of lectures with all the subtleties of incidental remarks with which Chebyshev knew how to enliven lectures. Later, in his obituary for his great teacher, Lyapunov wrote:

P.L. Chebyshev always appeared in the audience exactly at the appointed time and at the same hour began to continue the conclusions begun in the previous lecture... When the desired conclusion was obtained, P.L. Chebyshev sat down... on a chair, which was always placed for him at the first desk, and it was here that those various comments began that gave special interest to his lectures, and which the entire audience eagerly awaited.

Chebyshev's lectures were distinguished by their lively and fascinating presentation; he always cared about clarifying the fundamental aspects of the issue and the possibility of practical application of the results obtained. Lyapunov’s notes later allowed Academician A.N. Krylov courses of lectures given by Chebyshev.

Scientific activity of A.M. Lyapunova began with research on hydrostatics under the direction of D.K. Bobylev, who from 1878 headed, or, as they said then, occupied the department of mechanics. For this work in 1880, student Lyapunov received a gold medal. After graduating from the university, at Bobylev’s suggestion, he was left at the Department of Mechanics to prepare for the professorship. In addition, Alexander Mikhailovich was appointed keeper of the cabinet of practical mechanics (conservator), which was, as it were, a preparatory step to the position of professor. In 1881, in the Journal of the Physico-Chemical Society, Lyapunov published his first two articles - “On the equilibrium of heavy bodies in heavy liquids contained in a vessel of a certain shape” and “On the potential of hydrostatic pressures”. In these works, the conditions were clarified and new rigorous proofs of previously inaccurately substantiated theorems of hydrostatics were given.

A.M. Lyapunov was intensively preparing to pass his master's exams. According to the recollections of his brother, Boris Mikhailovich Lyapunov, who at that time rented a room with him, Alexander Mikhailovich studied a lot and intensely, loved to work at night. Once a week, friends and relatives of the Lyapunovs gathered at the hostess, and Ivan Mikhailovich Sechenov also came, to whom Alexander Mikhailovich gave lessons in those sections of mathematical sciences that he considered especially important for a physiologist.

In 1882, Lyapunov successfully passed his master's exams, and Chebyshev invited him to test his strength in solving the following question:

It is known that at a certain speed, ellipsoidal shapes cease to serve as equilibrium forms for a rotating fluid. Do they not then transform into some new forms of equilibrium, which, with a small increase in angular velocity, would differ little from ellipsoids?

Chebyshev, apparently, had been interested in this problem for a long time, since he proposed it to other scientists, for example, E.I. Zolotarev, S.V. Kovalevskaya, but did not offer any methods for solving it. The task was very difficult, but, nevertheless, Chebyshev proposed it to the beginning 24-year-old scientist, because he believed that every young scientist should definitely try his hand at solving problems that present significant theoretical difficulties. As Academician V.A. later said. Steklov, Lyapunov’s first student at Kharkov University:

Chebyshev even then saw extraordinary strength in the young man if he risked placing such backbreaking work on his shoulders.

Alexander Mikhailovich himself later wrote:

I don’t know if Zolotarev and Kovalevskaya tried to resolve this issue. I became very interested in the question, especially since Chebyshev did not give any instructions for solving it, and I immediately set to work.

He applied the method of successive approximations, obtained equations for the first approximation and all the necessary results for assessing the nature of the phenomenon under study according to the first approximation. But after this, it was necessary to create equations defining successive approximations for an arbitrary order and, most importantly, to prove the convergence of the resulting approximations. In this matter, difficulties were encountered that turned out to be insurmountable, and Lyapunov postponed further research into Chebyshev’s problem. However, in the course of his work, he became interested in the problem of stability of ellipsoidal shapes and began studying this issue. The results of research on stability issues formed the subject of his master's thesis, entitled "On the stability of ellipsoidal forms of equilibrium of a rotating fluid." The defense took place at St. Petersburg University in January 1885. One of the opponents was D.K. Bobylev. Summary The work was published in the Bulletine Astronomique, and almost twenty years later this work was translated into French by Ed. Davo and, at the suggestion of Professor E. Cosserat, published in the Annales de l’Universite de Toulouse. This work immediately attracted the attention of mathematicians, mechanics, physicists and astronomers around the world. After defending his dissertation, Lyapunov received a master's degree in applied mathematics and in the spring of the same 1885 he was confirmed with the rank of privatdozent. He was going to start giving a course of lectures on potential theory in the fall, but received an offer to occupy the department of mechanics at Kharkov University, which was vacant after the election of V.G. in 1881. Imshenetsky, member of the St. Petersburg Academy of Sciences. (A prerequisite for members of the Academy was to live and work in St. Petersburg.) In August 1885, A.M. Lyapunov moved to Kharkov and the most fruitful period of his scientific activity began there.

Kharkov University at that time was one of the largest in Russia and had a fairly strong staff of teachers. In 1863, due to the growth social movement, a university charter was issued, ensuring the autonomy of universities: the election of the rector, deans and professors, the right of the University Councils to establish departments, approve academic degrees and much more. However, in 1884, Emperor Alexander III approved a new reactionary charter, according to which universities were completely subordinated to the Ministry of Public Education and the trustees of educational districts. The election of university staff was abolished, freedom of teaching was restricted, centralization was brought to the point of absurdity: to transfer a lecture, almost the permission of the Ministry was required. Special instructions were issued indicating the spirit in which lectures should be given. The inspectorate, which observed everything, had immense power, the professors were constrained and humiliated - such was the difficult situation in which Lyapunov began to work at Kharkov University.

Academician Buzeskul recalls:

In those years when Alexander Mikhailovich began his teaching career at Kharkov University, there was much more communication between professors, as well as between students, than later. Lectures in all faculties were concentrated in one old building... Kharkov University has long suffered from a lack of premises. The tightness in it was terrifying. There were cases when listeners in the classroom fainted from the cramped space and stuffiness... Representatives of a wide variety of specialties met in the professor's room... Students from various faculties crowded in the corridor... In general, there were few students - from 800 to 1200. With the introduction of the statute of 1884, the number of applicants in some faculties, for example in history and philology, it immediately dropped by almost two or three times.

In the fall A.M. Lyapunov, being in the rank of privat-docent of the Department of Mechanics, began lecturing on all sections of mechanics. Until 1890, he alone conducted all teaching in the department of mechanics, including practical classes with students. Students, opposed to the new reactionary order, having learned that a new professor of mechanics had arrived from St. Petersburg, decided that he was a newly appointed mediocre official, and were unfriendly towards him. However, at the very first lecture, the unexpected happened. According to the memoirs of V.A. Steklova:

A handsome man, almost the same age as some of our comrades, entered the classroom together with the old dean, Professor Levakovsky, respected by all students, and, after the dean left, he began to read, in a voice trembling with excitement, instead of the course on the dynamics of systems, the course on the dynamics of a point, which we had already listened to from Professor Delarue. It was already the 4th year of my student life; in Moscow for a year I listened to such lecturers as Davydov, Tsinger, Stoletov, Orlov; was a student at Kharkov University for two years; I was already familiar with the mechanics course. But from the very beginning of the lecture, I heard something that I had never heard before or seen in any of the textbooks I knew. And all the unfriendliness of the course crumbled into dust; By the power of his talent, to the charm of which young people in most cases unconsciously succumb, Alexander Mikhailovich, without knowing it, conquered a biased audience in one hour. From that day on, Alexander Mikhailovich took a special place in the eyes of students; they began to treat him with exceptional respect. The majority, who were no strangers to the interests of science, began to strain every effort to get at least a little closer to the height to which Alexander Mikhailovich attracted his listeners. There was a special shame in front of him for their ignorance; most did not even dare to start talking to him only for fear of showing their ignorance to him.

Lyapunov's lectures were distinguished by the simplicity and generality of presentation, the impeccable rigor of elegant original proofs. He remained an adherent of the pedagogical methods of his great teacher P.L. Chebysheva. At lectures and at the so-called consultation hours, he sought to awaken in students an interest in science, a thirst for knowledge, and independence in work. He always sharply objected to any coercion, believing that the main thing in creative work is the initiative of the person himself, driven solely by the thirst for knowledge.

A strong young man, not much older than many of the students, constantly focused on his thoughts, he walked with a firm step along the university corridor to auditorium No. 8, where he lectured on mechanics. According to Steklov’s recollections, there was no case when he missed classes, even due to illness. During breaks and after lectures, he could be seen in the circle of colleagues closest to his specialty, always discussing scientific topics or sitting at mathematical calculations. As academician wrote. Buzeskul,

Everything base was alien to him. He was “not of this world”; he constantly hovered in the sphere of science. He was completely absorbed in the thought of her interests, of his favorite subject.

At the University of A.M. Lyapunov taught various general and special courses theoretical mechanics, integration of differential equations, probability theory. In mechanics alone, they taught six courses: kinematics, dynamics of a material point, dynamics of systems of material points, theory of attraction, theory of deformed bodies and hydrostatics. In “Review of teaching subjects and practical classes at Kharkov University for the first half of the 1886-1887 academic year.” It is recorded that private assistant professor Lyapunov had seven hours a week: two hours of lectures on the kinematics of a point, three hours of lectures on the kinematics of a system of points, two hours of practical classes on the dynamics of a point. Alexander Mikhailovich also read analytical mechanics at the Kharkov Institute of Technology (from 1887 to 1893). Lithographic courses of the lectures he gave were published in small editions by the students themselves. In 1982, a complete course of lectures given by Lyapunov during the Kharkov period was published in one volume.

Developing lecture courses and preparing for classes took a lot of time, because Alexander Mikhailovich was very responsible in his teaching activities and introduced a lot of new things into the courses he taught. Many results of research in analytical mechanics, which have now become classical, were first presented in Lyapunov’s lectures. So, A.M. Lyapunov was the first to obtain an analytical expression for the reactions of ideal holonomic constraints as functions of time. In 1900, while preparing for a course of lectures on probability theory, he proved the main limit theorem of probability theory, and for much more general conditions, than was done earlier by P.L. Chebyshev and A.A. Markov. Studying probability theory was only an episode in Lyapunov’s scientific activity, however, in this area he achieved results of fundamental importance. Academician A.N. Krylov subsequently wrote:

...He presented mechanics as a branch of mathematics, and not physics...therefore, the impeccable rigor of proofs was set by him as the main requirement, and in this regard, much belongs to him personally and is not found in other courses or treatises... Now it remains to say how Alexander Mikhailovich achieved such amazing brevity of presentation with complete clarity and rigor... It is clear that with inside here the vastness of his knowledge was manifested, the depth with which he thought through every assumption, every conclusion and proof, and the thoroughness of finishing to which he was accustomed in all his work. From the outside... it is clear that each of the most important issues various departments of mechanics was posed by him from the very beginning in the most general form... all individual cases were obtained as particular ones from the general solution found or served as examples to explain it. The second feature of the presentation is the absence of any kind of simple intermediate calculations; they are replaced by an indication of the sequence of necessary actions or transformations and the result that will be obtained.

In January 1886, having arrived in St. Petersburg during the holidays, Alexander Mikhailovich married Natalya Rafailovna Sechenova and returned back with his wife. In Kharkov, Lyapunov met professor of astronomy G.V. Levitsky, mathematicians M.A. Tikhomandritsky and K.A. Andreev. Here he met his former teacher of physics and mathematics at the Nizhny Novgorod gymnasium, Professor A.P. Gruzintsev, who worked as a private assistant professor at the Department of Physics.

At first, Lyapunov’s scientific activity, in his own words, was suspended because he had to compile courses of lectures for students, which he called “Notes.” But, despite intense pedagogical activity, Alexander Mikhailovich nevertheless published two notes in 1886 and 1887 in the “Communications of the Kharkov Mathematical Society”: “Some generalization of the Lejeune-Dirichlet formula for the potential function of an ellipsoid on an internal point” and “On the body of greatest potential” " In his last work, Lyapunov, using an original method different from the methods of the calculus of variations, showed that if there is a body whose potential reaches itself highest value, then such a body is a ball.

Having completed work on the Notes, Lyapunov resumed his energetic scientific activity. In 1888, he published in the “Communications of the Kharkov Mathematical Society” an article “On the constant screw motions of a rigid body in a liquid,” which for the first time outlined the main ideas of Lyapunov’s first method in the theory of stability. Sustainability declares itself as an indispensable element of it scientific research, starting from the very first student essay. Since 1888, Alexander Mikhailovich published a number of works devoted to the stability of motion of mechanical systems with a finite number of degrees of freedom, moving from the study of particular problems to more general ones. For 9 years from 1893 to 1902. Lyapunov published 20 works. Science completely absorbed his time and energy. He worked day after day until 4 or 5 o'clock in the morning, sometimes coming to lectures without sleeping all night. He rarely allowed himself any entertainment, sometimes going to the theater 1-2 times a year. The only exceptions were the concerts of his brother, composer S.M. Lyapunov, certainly visited by Alexander Mikhailovich.

Partly because he gave the impression of a silent, gloomy, withdrawn person to people who knew him little, that he was often so absorbed in his scientific thoughts that he looked - and did not see, listened - and did not hear... In reality, behind the external dryness and even The severity of A.M. Lyapunov concealed a man of great temperament, with a sensitive and, one might say, childishly pure soul. (V.A. Steklov).

At that time, the majority of teachers with a master's degree, contrary to the statute of 1884, were approved by the Minister of Public Education as professors without defending a doctoral dissertation. Lyapunov, although he obtained a number of fundamental results, which, according to Steklov, could already constitute an outstanding doctoral dissertation, made very high demands on himself. He believed that his dissertation was not yet completed, and for another four years he worked at Kharkov University as a private assistant professor, receiving a modest salary of 1,200 rubles. in year.

Purposefulness in solving large fundamental problems is a distinctive feature of Alexander Mikhailovich’s scientific creativity. His deep mathematical talent was combined with extraordinary perfection in his mastery of the mathematical apparatus and ingenuity in its application. The complexity of A.M.’s work Lyapunov - in the fundamental difficulty of the issues he dealt with.

Stability problems were classified as the most difficult problems in mathematics and were of interest to almost all major mathematicians, from Lagrange to Poincaré. Lyapunov's works were fundamental for the development of the theory of stability and subsequently brought him world fame. Looking through the “Communications of the Kharkov Mathematical Society”, one can see how Lyapunov gradually approaches the solution of the intended problem. In February and March 1889, he reported at a meeting of the Kharkov Mathematical Society his work “On the characteristic equation corresponding to a given system of differential equations with periodic coefficients,” and his article “On the stability of motion in one particular case of the problem” was published in the “Communications of the Kharkov Mathematical Society” about three bodies." In November 1890, he gave a report “On some systems of linear differential equations.” In March 1891, he gave a report on “The General Problem of the Theory of Stability of Movement.” In December 1891 - the message “New proof of Fuchs’ theorem relating to linear differential equations.”

In the 90s, articles often appeared in foreign literature using Lyapunov's ideas, but not referring to his work. Alexander Mikhailovich, in order to secure priority for Russian science, sent a message in 1896 to the French journal “Pure and Applied Mathematics” (Journ. de mathem. pures et appl.). However, subsequently, articles appeared in the same journal that actually used Lyapunov’s method, but did not mention his name in a word. From 1896, Lyapunov began publishing his works almost exclusively in French to make them more accessible to European scientists. He also conducted active scientific correspondence with famous French mathematicians Henri Poincaré and Emile Picard.

The results obtained by Lyapunov on stability formed the subject of his doctoral dissertation “The General Problem of Stability of Movement,” which was defended at Moscow University in 1892. Official opponents of N.E. Zhukovsky and B.K. Mlodzeevsky noted that his work, both in terms of the amount of material and scientific level, is equivalent to several doctoral dissertations. Lyapunov's dissertation was published in a separate edition in Kharkov.

In 1908, this fundamental work was translated into French and published by the University of Toulouse. The French translation was reproduced in 1949 by Princeton University Press. Interest in this research was associated with the development of military equipment, aircraft construction, and the creation of spacecraft, which, in turn, contributed to the further development of the theory of stability inherent in the works of Lyapunov. In 1992, a translation of the dissertation from French into English was published in London by Taylor and Francis. Thus, the fundamental results obtained by Lyapunov were far ahead of their time. In 1992, the world scientific community widely celebrated the 100th anniversary of Lyapunov's theory of stability.

In January 1893, Alexander Mikhailovich received the title of ordinary professor at Kharkov University. He continued lecturing and intensive scientific work, according to brother B.M. Lyapunov, “producing a dissertation every year, sometimes two,” making significant additions to the results of his dissertation. By the Kharkov period of A.M.’s life. Lyapunov includes his research on potential theory and the motion of a solid body in a liquid, which are closely intertwined with the research of his student, and later a famous scientist, Academician V.A. Steklova. Lyapunov obtained results that significantly complemented his dissertation, discovered the case of the motion of a rigid body in a liquid that now bears his name, and carried out a remarkable study on the representation of the motion of the Moon by Hill series. He was actively involved in potential theory issues. His work in this area formed the basis on which the theory of potential is based to this day. Under the influence of Lyapunov, mathematicians at Kharkov University developed a great interest in questions of mathematical physics, primarily in the main limit problems for the Laplace equation. Lyapunov discovered inaccuracies and shortcomings in potential theory - in this classical section of mathematical physics. In his memoir “Sur certaines questions se rattachant au probleme de Dirichlet” (On some questions related to the Dirichlet problem, 1897), he was the first to strictly define and clarify a number of basic provisions of potential theory.

From October 1891, Lyapunov was deputy, and from 1899 to 1902, chairman of the Kharkov Mathematical Society and editor of the publication “Communications of the Kharkov Mathematical Society”. He reported on the results of all his works of this period, devoted mainly to the theory of potential and the theory of probability, at meetings of the Society, and involved his students in the activities of the Society. Meetings were held regularly, on average twice a month. As a university professor, he took part in university-wide affairs and served on various commissions on educational issues.

Since 1872, at the department of applied mathematics of the university there was a laboratory of practical mechanics, which appeared thanks to the efforts of Professor M.F. Kovalsky. When the management of the office passed to Lyapunov, he actively began reorganizing it - revising old equipment, replacing outdated models and mechanisms, thanks to which the office acquired a modern look.

During his summer vacation, Lyapunov usually went with his wife to the Simbirsk province, but even there he continued his scientific work. In the summer, many relatives came to visit them, and young people gathered in the evenings. Alexander Mikhailovich loved to talk about the stars and the elementary concepts of astronomy. He loved nature very much and grew indoor plants and garden trees himself. In his Kharkov apartment there were palm trees and ficus trees that he had grown.

In 1900 A.M. Lyapunov was elected a corresponding member of the Academy of Sciences (on the proposal of academicians A.A. Markov and N.Ya. Sonin), and in 1901 - an ordinary academician in the department of applied mathematics, which remained vacant for seven years after the death of P.L. Chebysheva. In 1902 Lyapunov moved to St. Petersburg. The seventeen-year period of living in Kharkov and working at Kharkov University has ended. According to V.A. Steklova, Alexander Mikhailovich recalled this time with special love and called it the happiest.

In St. Petersburg, Lyapunov devoted himself entirely to scientific work. Twenty years later, he again returned to the problem of equilibrium figures, proposed to him in 1882 by Chebyshev and not completely solved by him then. Lyapunov began his work by studying the rotation of a homogeneous fluid. In February 1903, Steklov informed him about the publication of A. Poincaré’s book “Equilibrium Figures of a Rotating Liquid Mass,” a series of lectures given at the Sorbonne in 1900. Lyapunov, confident that Poincaré had solved his problem, left his job and began studying the equilibrium figures of a rotating inhomogeneous fluid. In a letter to Steklov dated February 15, 1903, he writes: “As annoying as it may be, he will have to quit his work, because ... there is no doubt that he proceeded ... from the same considerations ... otherwise he could not have taken a step on the issue under consideration.” Having received Poincaré’s book, Lyapunov found in it only a presentation of long-known results and realized that on the question of equilibrium figures, Poincaré “stands at the same point as seventeen years ago” (from a letter to Steklov dated February 21, 1903). He further writes: “... a week's break from this work turned out to be very useful for the matter, because during this period I started other work... and noticed that even in solving the first question, significant simplifications of the calculation were possible and that I was following an overly complicated path.” In the same 1903, Lyapunov published the work “Research on the theory of figures of celestial bodies,” where he proved the existence of equilibrium figures close to a sphere in the case of an inhomogeneous fluid slowly rotating around an axis. Then Lyapunov did gigantic work, both in volume and in scientific significance, on the theory of equilibrium figures, completely solving the problem posed by Chebyshev. This work “On figures of equilibrium, not much different from ellipsoids, rotating homogeneous mass Liquids" was published in four parts in 1906-1914 and occupies about 800 pages.

Lyapunov's study of equilibrium figures opened a new page in the development of celestial mechanics. The fact is that in 1902, an article by the famous English astronomer George Darwin (son of Charles Darwin) “The Stability of Pear-shaped Figure of Equilibrium of a Rotating Mass of Liquid” appeared. In this work, J. Darwin showed the stability of pear-shaped shapes and put forward a cosmogonic hypothesis about the formation of planetary satellites from a rotating mass of liquid, based on the stability of the pear-shaped shape. Poincaré's work also appeared, where the existence of many forms of equilibrium was shown, and the results that were already contained in Lyapunov's master's thesis were presented. Darwin called this work of Poincaré a revelation and, under his influence, proposed a hypothesis about the formation of double stars from one of the forms of pear-shaped figures. For him, the French scientist was elected a member of the Paris Academy of Sciences and received a gold medal from the Royal Society of Astronomers of London. The work was based on the analysis of the first approximation, that is, on the results that Lyapunov obtained back in 1883, but did not consider it possible to publish, since he considered it necessary to give a rigorous answer based on the analysis of subsequent approximations, which he failed to do then. Now it was necessary to show the fallacy of Darwin's reasoning, using only a first approximation without due care. Lyapunov ingeniously resolved all the difficulties of the problem and showed that pear-shaped figures are unstable and, thus, Darwin's cosmogonic hypothesis is untenable. These results were published in 1905, after which a controversy arose between Lyapunov and Darwin that lasted several years. Poincaré, in his lectures on equilibrium figures, limited himself to only a small remark: “The pear-shaped figure is perhaps stable... To solve the problem, it would be necessary to carry out all the calculations again, but they present significant difficulties.” As proof, Lyapunov publishes a voluminous work, where on 784 pages he sets out in detail his gigantic calculations. Only in 1917, the famous English physicist and astronomer James Jeans discovered an error in the calculations of J. Darwin and showed that Lyapunov’s theory was correct. Remembering this, Academician Steklov wrote:

If Poincaré’s research could be called a revelation that made an era in the history of science, then in what words can one evaluate the works of A.M. Lyapunov in the area under consideration.

Lyapunov was always picky about the accuracy of problem solving. If the problem could not be solved exactly, then, using approximate methods, he always estimated the size of the error. It is appropriate to quote Poincaré's statement here:

Many objections can be made, but one cannot demand the same rigor as in pure analysis

and compare it with Lyapunov’s words:

It is not permissible to use dubious reasoning as long as we are solving a specific problem... which is posed quite clearly from the point of view of analysis.

In 1908, Lyapunov was sent to the IV International Mathematical Congress in Rome, a report on which he presented at a meeting of the Physics and Mathematics Department of the Academy of Sciences. In Rome, Alexander Mikhailovich met Italian mathematicians professors Volterra, Veronese and Blaserna. Soon after returning from Italy, Lyapunov was elected a member of the Academy of Sciences in Rome (Accademia die Lincei). Since 1909, he took part in the publication of the complete works of L. Euler and was the editor of the eighteenth and nineteenth volumes.

In his scientific work, Lyapunov took on the development of an even more complex and important question about the equilibrium figures of an inhomogeneous rotating fluid. He promised to publish his results and reported that he had managed to solve the problem under more general assumptions. At the end of June 1917, he and his wife went to Odessa, where his brother B.M. lived at that time. Lyapunov. Natalya Rafailovna had long suffered from tuberculosis, and doctors prescribed her a mild climate. The difficulty of traveling through a country engulfed in revolution and the instability over time led to an exacerbation of the disease, and the wife weakened before our eyes. At the beginning of 1918, Odessa was occupied, and Lyapunov found himself in difficult situation, cut off from St. Petersburg, experienced financial difficulties. In addition, he developed cataracts, and his vision quickly deteriorated, preventing him from working fully.

In August 1918, Alexander Mikhailovich received an invitation from the Faculty of Physics and Mathematics of Novorossiysk (Odessa) University to give lectures on a topic that he himself wished to choose. Lyapunov agreed to give a course “On the Form of Celestial Bodies,” which presented the results of his latest work, a total of seven two-hour lectures, starting on September 16. The audience were mainly university professors. Always physically strong, he, according to the memoirs of B.M. Lyapunov, was very tired after lectures and had difficulty getting home.

The wife's condition kept getting worse. On October 28, Lyapunov gave his last lecture, and on October 31, N.R. Lyapunova died. For Alexander Mikhailovich the blow was too strong, although he had, of course, long ago understood the inevitability of such an outcome. On the same day A.M. Lyapunov was taken to the surgical department of the university clinic with a gunshot wound to the head and died three days later without regaining consciousness. In the note he left, he bequeathed to be buried in the same grave with his wife. Odessa at this time was cut off from the country, and only on May 3, 1919 Russian Academy Sciences at a special meeting honored the memory of the outstanding scientist. A.M. was buried. Lyapunov in Odessa. Among his papers remained a fully completed manuscript “On various forms of equilibrium of an inhomogeneous rotating fluid.” This manuscript was published for the 200th anniversary of the Academy of Sciences (Sur certaines series de figures d "equilibre d" un liquide heterogene en rotation. - L., 1925-1927).

Scientific merits of A.M. Lyapunov are recognized all over the world: he was an honorary member of St. Petersburg, Kharkov and Kazan universities, an honorary member of the Kharkov Mathematical Society, a foreign member of the Academy in Rome, and a corresponding member of the Paris Academy of Sciences.

Works by A.M. Lyapunov are devoted to the theory of stability of motion and equilibrium of mechanical systems, the theory of equilibrium figures of a uniformly rotating fluid, mathematical physics, differential equations and probability theory. The most important achievement of A.M. Lyapunov is the creation of a modern theory of stability of motion and equilibrium of mechanical systems determined by a finite number of parameters.

A.M. Lyapunov also obtained a number of significant results in the theory of linear and nonlinear differential equations. In particular, he established the existence of periodic solutions to a certain class of systems of nonlinear differential equations and gave effective method constructing such solutions, and also found out a qualitative picture of the behavior of integral curves of the equations of motion near the equilibrium position. The method for determining the stability of a system of ordinary differential equations is called the Lyapunov method.

In mathematical physics A.M. Lyapunov also obtained a number of important results. He investigated the features of the potential of a system of charges and dipoles continuously distributed on some arbitrary surface. In probability theory, he developed the method of characteristic functions, gave a proof under very broad conditions of the central limit theorem, stated but not fully proven by P.L. Chebyshev. The method used by Lyapunov to prove the theorem is now one of the main ones in probability theory.

Over the past century, the results obtained by Alexander Mikhailovich Lyapunov were significantly developed and supplemented, and the results created by him scientific directions have grown into separate fields of mathematics and mechanics and have important applications in physics, radiophysics, engineering and modern technologies.

In 1969, the USSR Academy of Sciences established the Gold Medal named after A.M. Lyapunova. The tradition of awarding an award named after an outstanding scientist was continued by the Russian Academy of Sciences, which established the A.M. Prize in 1995. Lyapunova. Awarded by the Department of Mathematics (OM RAS) to domestic scientists “For outstanding work in the field of mathematics and mechanics”

One of the streets in Moscow bears the name of the scientist.

In 2007, the National Bank of Ukraine, on the occasion of the 150th anniversary of A.M. Lyapunov issued a commemorative coin with a face value of 2 hryvnia

The following mathematical and physical objects bear the name of Lyapunov:

• Lyapunov's central limit theorem
• Lyapunov exponent
• Lyapunov fractal
• Lyapunov function
• Lyapunov stability
• Lyapunov time
• Lyapunov surface
• Lyapunov's theorem
• Lyapunov condition.

Based on materials from the website theormech.univer.kharkov.ua, Wikipedia and the book by D. Samin “100 Great Scientists” (M.: Veche, 2000).

Russian astronomers

September 30, 1820 Mikhail Vasilyevich Lyapunov is a famous Russian astronomer from the middle of the last century. He was born 185 years ago, on September 30, 1820. At the age of 19 he graduated from the Faculty of Mathematics of Kazan University, where he attended lectures by the rector of the university N. I. Lobachevsky (1792-1856) and professor of astronomy I. M. Simonov (1794-1855 ). Already in September 1840, M. V. Lyapunov began working at the university observatory as an astronomer-observer and conducted observations on the meridian circle. At the same time, Lyapunov began teaching at the university, where he conducted practical classes in astronomy.

In 1842, M. V. Lyapunov, together with N. I. Lobachevsky and professor of physics and physical geography E. A. Knorr (1805-1879), participated in an expedition to observe the total solar eclipse on June 26, 1842 in Penza. During this expedition, Lyapunov’s responsibilities were to determine the geographic coordinates of the observation point.

From 1842 to 1845, M.V. Lyapunov was on a long business trip to the Pulkovo Observatory to observe the repair of instruments at the Kazan Observatory that were damaged by the fire of 1842. At the same time, he carried out scientific work here under the guidance of V. Ya. Struve and O. V. Struve. In 1843, while in Pulkovo, M.V. Lyapunov took part in the work of a “chronometric” expedition to determine the difference in longitude of Pulkovo and Altona. On this expedition, he, together with astronomer E. E. Sabler (1810-1865), transported 78 chronometers from Pulkovo to Altona. In 1845, Lyapunov participated in the second chronometric expedition, this time to determine the geographical points of Russia. Here his duties included conducting observations in Valdai. Returning from a business trip to Pulkovo, M.V. Lyapunov began giving lectures on astronomy. At the same time, the most fruitful period of his observational activity began, during which he observed a lot on the refractor and meridian circle, determining the positions of major and minor planets, as well as emerging comets. But his most important work was the study of the great Orion Nebula, which M.V. Lyapunov began on the recommendation of O.V. Struve. The work was carried out from 1845 to 1849 using a 9-inch Fraunhofer refractor. After careful processing of the material received, in 1851 the work was completed and submitted for publication. In December 1853, V. Ya. Struve reported to the Academy of Sciences on the completion of M. V. Lyapunov’s work “Results of observations of the Great Orion Nebula.” He highly appreciated the work and noted the importance of the conclusions drawn. In general, V. Ya. Struve spoke flatteringly about Lyapunov and considered him “the first and most worthy of all the young figures at Russian observatories.”

However, so important work, dedicated to the study of the Orion Nebula and the establishment of its gaseous nature, due to the fault of O. V. Struve, was published only in 1862, when Lyapunov had already left scientific activity in the field of astronomy.

In June 1850, the young Lyapunov was appointed director of the Kazan Observatory and led it until mid-January 1855. By this time, he assisted the astronomer M. M. Gusev (1826-1866) in translating into Russian the astronomical volume of the outstanding work of Alexander Humboldt “ Space". After leaving the university, Lyapunov’s activities became purely pedagogical. From 1856 to 1864 he was the director of the Demidov Lyceum in Yaroslavl. Then, due to health reasons, he was forced to completely leave work and began raising his eldest son, Alexander Lyapunov (1857-1918), who later became a famous mathematician and mechanic, a member of the St. Petersburg Academy of Sciences. M. V. Lyapunov died on November 20, 1868.

November 5, 1870 The name of Sergei Nikolaevich Blazhko is well known not only in our country, but also abroad. He lived a long life and devoted all of it to science. S. N. Blazhko was born on November 5 (17), 1870. In 1888, he entered the Faculty of Physics and Mathematics of Moscow University and from that time, for almost seven decades, his entire life was connected with Moscow University and the university observatory. After graduating from the university, S. N. Blazhko was assigned to the position of supernumerary assistant at the observatory and worked under the leadership of V. K. Tserasky. In 1910 he became an associate professor at the department of astronomy and geodesy, and from 1918 a professor. From 1918 to 1920, S. N. Blazhko was deputy director of the Moscow Observatory, and from 1920 to 1931, director. In 1929, S. N. Blazhko was elected a corresponding member of the USSR Academy of Sciences, and in 1934 he was awarded the honorary title of Honored Scientist of the RSFSR.

The scientific activity of S. N. Blazhko is extensive, but is mainly devoted to the study of variable stars and practical astronomy. In 1895, S. N. Blazhko began systematically photographing the starry sky, using for this purpose a high-aperture wide-angle astrograph, called the “equatorial camera.” These works laid the foundation for the rich collection of the “glass library” of the Moscow Observatory. It is well known that for many decades, spectrographing meteors was a very labor-intensive operation due to the suddenness and short duration of the phenomenon. In the last century, only one spectrogram was obtained (E. Pickering in Arequipa, in 1897) and then by accident. Therefore, the initiative of S. N. Blazhko is especially interesting, who at the beginning of this century began systematic work on spectrographing meteors using an objective prism. On May 11, 1904 and August 12, 1907, S. N. Blazhko was lucky enough to obtain successful photographs of the spectra of meteors and for the first time give their correct interpretation. Thus, the spectrum of the 1904 meteor consisted of 17 lines, among which the lines of iron, hydrogen and calcium were especially clearly visible. It is interesting to note that until 1909, only five spectra were obtained throughout the world, three of which belonged to S. and N. Blazhko. In 1912, in his monograph “On Stars of the Algol Type,” which was his master’s thesis, S. N. Blazhko first published the general theory of eclipsing variable stars of the Algol type and outlined a method for determining orbital elements from photometric data. The dissertation was brilliantly defended in 1913.

S. N. Blazhko studied over two hundred variable stars of various types and was the first to discover periodic changes in the period and light curve of some short-period variables such as KK Lyrae, which were called the “Blazhko effect” in the literature. In 1919, S. N. Blazhko proposed a new method for photographing small planets, which became widespread. It consisted of obtaining three images on one plate with breaks between images and with a shift of the tube in declination.

S. N. Blazhko well understood the intricacies of astronomical instruments and was the author of a number of original designs: a blink microscope for the discovery of new variable stars, a slitless stellar spectrograph for a 15-inch astrograph, a device for leveling the brightness of stars when observing them with a meridian circle, and some others. Widely known outstanding pedagogical activity S. N. Blazhko. For about 50 years he taught various courses at Moscow University and many prominent astronomers are his students. As a result of many years of teaching, three wonderful textbooks on basic university courses were published: “Course of Practical Astronomy” (1938, 1940 and 1951), “Course of General Astronomy” (1947) and “Course of Spherical Astronomy” (1948 and 1954). For two of these books in 1952, S. N. Blazhko was awarded the State Prize of the second degree.

The contribution of S. N. Blazhko to the literature on the history of astronomy is important. In 1940, he published an interesting work “History of the Astronomical Observatory of Moscow University in connection with the teaching of astronomy at the university (1824-1920).”

S. N. Blazhko carried out a great deal of social and organizational work. He was a member of the Astronomical Council of the USSR Academy of Sciences, a member of the editorial board of the Astronomical Journal, and chairman of the Commission for awarding the F. A. Bredikhin Prize. It should be especially noted that for many years he was the permanent chairman of the Commission for the Study of Variable Stars under the Astronomical Council. For a number of years, S. N. Blazhko was the chairman of the Moscow Society of Astronomy Amateurs, and was subsequently elected an honorary member of the All-Union Astronomical and Geodesic Society and its Moscow branch. S. N. Blazhko died on February 11, 1956.