# Mstislav Vsevolodovich Keldysh

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### President of the Academy of Sciences USSR (1961-1975)

Alexander Nitusov

Creation and utilisation of electronic digital computers in the USSR was always backed-up by powerful complex of mathematical scientific schools, which were traditionally advanced since as early as the end of the 18 th century. The new possibilities introduced by appearance of the computers into solving of complicated computational problems stimulated, in their turn, progress in some domains of classical mathematics and expedited development of methods of computation mathematics and mathematical modelling.

At the end of the 1950-s V.A. Steklov Mathematical Institute [1] (MIAN) of the USSR Academy of Sciences (AN USSR ) played role of the “nest”, which had given birth to several large academic teams of notable importance. They were famous for their successful solving of scientific, economic and defence problems of national dimensions. The MIAN department of applied mathematics, which had been set up by famous Soviet mathematician M.V. Keldysh, was one of them. It was officially established in 1953 and eventually developed into a core of the Institute of Applied Mathematics AS USSR . M.V. Keldysh was leading Soviet scientist , who made major contributions to complex function theory, differential equations and applications to aerodynamics.

**Mstislav Vsevolodovich Keldysh**

Mstislav Vsevolodovich Keldysh was born in Riga (Latvia), on the 10 th of February 1911, where his father was teaching at the polytechnic institute. History of his family might seem unusual anyway within its several generations it incorporated many characteristic features of Russian cultural landscape.

His grandfather on the mother's line – A.N. Skvortsov was artillery general and a son of general. He came from nobility, mainly of Polish ancestry, however his mother (Mstislav's great-grandmother) came from a Georgian family (which once cured his father – general N. Skvortsov , when he was left by them badly wounded). Another great-grandmother was a gipsy girl from Ukraine , who had been picked by the Skvortsovs as a baby (she was seriously ill). When the girl recovered, she stayed with the family and eventually married one of Mstislav's great-grandfathers, a doctor who looked after her. It was a family joke that Mstislav had “gipsy ways”.

The other grandfather, on the father's line – Mikhail F. Keldysh (1839—1920) was born in Poland ( Warsaw ) into a family of a psalm reader at an orthodox church. He graduated from a Warsaw divinity school, however turned to medicine and studied at the medical academy of St. Petersburg . He made a long career as an army doctor and was awarded military rank of general and also nobility. His son Vsevolod Mikhailovich Keldysh (1878—1965) (Mstislav' father) was military, a general-engineer famous for his progressive mathematical calculation methods for concrete constructions stability proving. He was leading participant-designer, in construction of the Metro of Moscow, channel Moscow-Volga and some other important projects.

Mstislav Vsevolodovich Keldysh himself never concealed his noble origin, though in the 1920-s, in the period of post-revolutionary radicalism (or maximalism) it could cause serious troubles. The Keldysh family also did not escape political repressions of the 1930-s, so his career did not seem to promise big perspectives.

However he had the character. In all official forms and questionaries Keldysh had to feel he wrote boldly, “social origin – nobility”. Nevertheless he escaped dangers and eventually entered department of physics and mathematics of the Moscow State University (MSU).

His elder sister, Ludmila Vsevolodovna Keldysh was also a famous mathematician. In 1925 she graduated from the MSU and joined scientific research seminar of world famous Moscow mathematician Nikolay Nikolaevich Luzin, whose contribution to progress of the Moscow school of mathematics, and to mathematics in general, is invaluable. Basic subject of Luzin's study was *theory of sets. *Due to his efforts Moscow became recognized (world) leader in that domain. In the beginning of the 1920-s he set up mathematical seminar (as a research group) for his students and post-graduates, which the youngsters nicknamed “Luzitania” for his name's phonetic co-incidence with name of the famous British vessel. Luzin's school “nurtured” (directly or indirectly) most of the famous Soviet mathematicians of the later period. His first students were P.S. Aleksandrov, M.Ya. Suslin, D.E. Menshov and A.Ya. Khinchin. The next students included P.S. Urysohn, A.N. Kolmogorov, N.K. Bari, L.A. Lyusternik and N.G. Shnirelman . Future academician M.A. Lavrentev [2] was another participant.

In 1923, Ludmila Keldysh and Petr (Peter) Sergeevich Novikov also joined the group. Novikov (himself a famous mathematician) married her in 1935. Ludmila was awarded a doctorate in 1941 and eventually became a professor of mathematics. She made important contributions to *theory of sets * and *geometric topology *. In 1934—1964 she worked at the V.A. Steklov Institute and then received professorship at the MSU.

L. Keldysh and P. Novikov had five children – nephews of Mstislav Keldysh. Their eldest child, Leonid, went on to be a leading international figure in *solid state physics *. The second son, Andrei, became a theoretician on *algebraic numbers *, and Sergei Novikov, the third one also made a famous mathematician. He was awarded **Fields Medal [3]** in 1970. At present he is an academician.

Mstislav Keldysh himself successfully graduated from the university on the 24 th of July 1931 and received a position at the Central Aero- Hydrodynamic Institute (CAHI). The institute was one of the most modern and important scientific centres of its time. Staff of the institute was composed of the prominent scientists and most able young specialists. Keldysh was recommended there by his teacher M.A. Lavrentev, who was then one of the institute's leading scientists at the department of general theory (and later became his elder friend).

Keldysh was only 20, however, already his first publications attracted attention of academician S.A. Chaplygin , who was the institute's director and the prominent name in the earlier history of the aerodynamics and the aircraft science. S.A. Chaplygin is famous for his discovery of aerodynamic phenomena emerging in flying objects when they enter the range of higher -also supersonic- speeds, what was especially important in the age of jet-propelled aviation. Before him the lows of the aerodynamic were considered to be direct analogue to the lows of hydrodynamics. Thus Chaplygin became the first one to discover and demonstrate the difference.

Keldysh's studies were not only aimed at solving current applied problems. They also introduced new, more progressive, forms of implementation of general mathematic methods in aero- and hydrodynamics, what greatly increased their scientific value. Phenomena of the *aerodynamic flutter * was one of the most ‘urgent issues' of the 1930-s. *Flutter * – intensive vibrations of the flying plane, often followed accelerating of its speed and brought danger of its total destruction in the air. That was very serious obstacle for development of aviation. Shrewd Chaplygin recognised born talents of the young theorist mathematician, who was also very responsible person, and entrusted him with solving the flutter problem. He granted Keldysh certain freedom of scientific actions, however, under condition of eventual providing results in applicable practical form.

The *flutter phenomena * was studied by many scientists of all leading aircraft producing countries but it was the USSR which became absolute leader in that field. Here the flutter problems were solved most completely in all aspects of practical interest. That was possible also due to efficient researches of Keldysh and his colleagues. Their complex mathematical descriptions substantiated clear theoretical conclusions and following practical recommendations, which in their turn enabled development of reliable methods of elimination of airplane body self-oscillations (flutter) within the whole range of flight speeds. Their reports and publications still could be utilised as a theoretical basis for further researches. That was the work of decisive importance: the problem of flutter was solved and the further progress of high-speed aviation became a reality. That also gave big advantage to the Soviet airforce during the World War Two, since the opposite side was not so surely safe from the danger of flutter.

As importance of the research was pretty clear, M.V. Keldysh and his colleague E.P. Grossman were awarded “Stalin Premium” (grade II) soon after beginning of the war, in 1942 (later it was named “State Premium”). A year later Keldysh was decorated with his first order – “Red Banner of Labour”. He was engaged in practical work on flutter control, as scientific expert in aircraft producing industry, until the end of the war.

Another important problem of that time was connected with new airplane design with a wheel mounted in its front part and with landing on three wheels. That was result of increasing of landing and taking-off speed. Although now it is the most common way of landing, that time it confronted serious problems. Thus, when the plane reached certain speed self-amplifying oscillations began in the front gear leg what inevitably caused serious damages. Engineers and pilots called that - “ *Shimmy *”. Keldysh implemented his experience from the *flutter problem * and conducted new series of researches described in his work “ *Shimmy * of the front gear of the three wheels undercart” (1945). He solved the problem and produced complete set of engineering instructions, which proved to be very efficient. In 1946 he was awarded one more “Stalin Premium” (“State Premium”). That work of his is referred to as “model”, by mathematicians, until now.

In the middle of the 1930-s academician I.M. Vinogradov invited Keldysh to enter post-graduate study at V.A. Steklov Mathematical Institute to prepare a dissertation “Functions of Complex Variable and Harmonic Functions Representation with Arrays of Polynomials”. Keldysh submitted his thesis and was awarded a doctorate at V.A. Steklov Institute in 1938. Specialists estimated his dissertation as, “Classical study summing-up an important stage of research in a principal mathematic domain and simultaneously opening a new one”.

In the 1930-s Keldysh focused his scientific researches on *boundary value problems * in common equations and on *theory of conformal mappings*. Number of important results, connected with solvability and stability of *Dirichlet problem * solution and also with *Carleman and Neumann problems*, Keldysh obtained, in collaboration with M.A. Lavrentev, in 1937-1942. They were published in academic periodicals: *Doklady **AN SSSR, **Izvestiya Akad. Nauk SSSR Ser. Mat., * and *Matematicheskiy Sbornik *.

By the end of the war situation in the scientific organisations became more favourable for theoretical researches. Keldysh was still working at the Central Aero-Hydrodynamic Institute (CAHI) but also resumed his research at the V.A. Steklov Institute. In April of 1944 a new subdivision - department of mechanics, was set up at the institute; he headed it till 1953. Dynamics of rockets and applied celestial mechanics became the core subjects of its research.

In fact, his contribution in mathematics, in that period, was not less significant than his achievements in aircraft engineering. Notable progress in mathematical science, that followed his discoveries, was often based on his ability to present every theory or problem -no matter how complicated- with maximal simplicity, however without loosing its essence.

The same was in the case of approximation theory, functional analysis and differential equations. Keldysh possessed profound knowledge in numerous mathematic domains and efficiently combined them, often finding unexpected analogies and thus creating new, very effective, methods. All his abstract researches, such as the *theory of non-self-adjoint operators *, originated from concrete applied problems, what took place in abovementioned case of energy dissipation during oscillations in mechanical constructions. His achievements of that period were recognised and highly appreciated by the contemporary scientific society.

In 1943 Keldysh was elected a corresponding member of the USSR Academy of Sciences (AS USSR) department of physics and mathematics. In 1946 he became full academician of the AS USSR department of technical sciences (mathematics and mechanics).

In 1946 he left CAHI to head the so-called Jet-Powered Research Institute (so-called, “Scientific Research Institute–1”/SRI-1/). He was its director during the following nine years.

At the Fourth All-Union Mathematical Congress (1961) M.V. Keldysh and V.B. Libskiy made a report, “Some Problems of Spectral Theory of Non-self-adjoint Operators”. It generalised results of their research in the domain of *boundary value problems * of the common differential equations including the *theorem of completeness *, which was finally proved by Keldysh in 1951. At the same time M.V. Keldysh and academician L.I. Sedov (famous expert on space researches) published another work dedicated to applications of the *theory of complex variable functions * to problems of hydro- and aero-dynamics.

The World War II was over, the country compensated the losses and completed rebuilding of its industry and infrastructure, however beginning cold war again attracted its scientific powers to defence problems. Nuclear weapons and rockets became symbol of intensifying arms race. Keldysh was engaged in the both problems. He founded and led special mathematic design bureau, which, together with the department of V.A. Steklov institute, was integrated into Department of Applied Mathematics, established in 1953. Here he formed very strong scientific team.

As we can see the character of his activity essentially changed after the war. Keldysh chiefly turned to management and organisational work. He headed several leading mathematical institutes (e.g. Institute of Applied Mathematics AS USSR ) and numerous academic commissions. In 1961 he was elected a vice president, and a year later the president, of the USSR Academy of Sciences. Keldysh remained in that position until 1975. However his personal feelings regarding leaving scientific career for academic duties always were mixed, even confused. Thus, in 1971, at the official reception dedicated to his sixty years birthday he answered the greetings from friends and colleagues with sincere confessions of regret for being outside of practical researching activity.

Nevertheless, “The Keldysh Phenomenon”, as it was seen both by the collaborators and the whole Soviet scientific community, consisted in having the supreme academic administrator who himself was a true scholar always deeply feeling the problems, both current and perspective, and who was aware of demands to the science and tendencies of its development. All those qualities also enabled him, as the academy leader, to find optimal course aimed at practical needs irrespectively of political conditions (what was by no means an easy task). In other words, his high scientific competence made the work of all organisations he headed most efficient. The whole life of M.V. Keldysh was a good proof of that.

When he was heading the SRI-1 it was engaged in development of high-powered jet engines for cruise missiles. The work also included researches on supersonic dynamics of gases, heat protection, exchange of heat masses, etc. In 1959 the world first cruise missile was successfully tested. It demonstrated better characteristics as the similar American missile built within program “SM-64 Navaho”, which ran from 1946 to 1958 when it was cancelled to be changed for intercontinental ballistic missile. That program of SRI-1 was closely connected with pioneer mathematical project on dynamics of rockets and applied celestial mechanics (mechanics of space flight), which Keldysh ran at the Department of Applied Mechanics of the V.A. Steklov Mathematical Institute. That was essential contribution to development of the space engineering. In 1953 the institute researched optimal structures of composite missiles, ballistic spaceship descent what enabled its return from a mission and landing with a crew on board. Also the ways of the vehicle stabilisation by usage of the earth gravitation and many other projects were performed.

In 1954 M .V. Keldysh, S.P. Korolev and M.K. Tikhonravov submitted a proposal on creation of the space satellite to the USSR government. In the next year Keldysh was appointed as the chairman of the AS USSR Commission on the Satellite.

After successful launching of the first satellite in 1957, the space research program was essentially extended. The Department of Applied Mathematics, led by Keldysh, developed systems for satellites monitoring and predicting their trajectories, on development of ballistics of the space vehicles flights for minimising their energy consumption, etc.

The vehicle boost scenario with entering intermediate orbit or the planet gravitation utilisation for the vehicle flight trajectory changes were examples of brilliant solutions, which formed scientific basis for further development of the space flights. There is no need to repeat the whole well known list of the Soviet achievements in space science and engineering. Contribution of Keldysh, both as theorist of science and administrative coordinator of the state space programs, was enormous. In 1959 the Interdepartmental Scientific and Engineering Council on space researches was established at the AS USSR by governmental decision. Keldysh was appointed as its chairman. Well-balanced research program prepared and ran under his guidance enabled efficient (in all aspects) space explorations.

He also actively participated in nuclear researches. The journalists, who wrote about strategic parity of the USSR and the USA , referred to its “authors” on the Soviet side as the “three K-s”, meaning academicians I.V. Kurchatov, S.P. Korolev and M.V. Keldysh. As their names were “publicly inaccessible” for the secrecy reasons those times, the journalists “denoted” the chief of the space programs as “Theoretician of the Cosmonautics”. Now the name of Keldysh is long since a part of the common history. Academician I.M. Vinogradov, director of the Mathematical Institute AS USSR remembered, “Soon after the war (in 1946) I was visited by Y.B. Khariton and some other physicists. They were searching for a mathematician who could organise computations for nuclear researches. I recommended them to address Keldysh who could better understand every applied mathematical problem then anybody else. They really liked him”.

Researches on atom energy that time were naturally considered in military aspect and were primarily aimed at development of weapons. That was very new and complicated problem. The difficulties were exacerbated by limited volume of knowledge on various phenomena accompanying nuclear processes. Therefore creation of physical and mathematical models with their following detailed reproduction in facilitated computations was very important cognition method for that study.

All that, first of all needed great amount of computations but the available mathematical appliances were insufficient for that work. Principally new generation of powerful calculating devices – digital electronic computers were not yet in use. That was the problem of state importance. Though Keldysh himself did not design computers he was the first big consumer of new machinery. His institute should create new methods of calculation and implement them in solving all nuclear related problems with electronic computers. Same computers were also used by his team for design of rackets and in space research projects. The formidable work on new calculation methods and their realisation on computers became the basis of new domain in mathematics, which is at present a special field – computational and applied mathematics.

Keldysh not only organised those researches but also developed series of new computation methods and algorithms. They made decisive impact on development of the Soviet computation mathematics, first of all numerical solution methods in mathematical physics.

His outstanding contribution to solving of defence problems was officially appreciated on the highest level: in 1956 he was awarded an honourable title “Hero of the Socialist Labour [4]” and in 1957 was awarded the “Lenin Premium”. In 1961 he was again awarded the title “Hero of the Socialist Labour [5]”. That time it was award for contribution to development of rocket engineering and also for his participation in preparing and successful launching of the world's first manned spaceship “Vostok”, piloted by Yuri Gagarin.

Keldysh not only implemented digital computers in solving of scientific and applied problems but notably influenced development of the soviet computer engineering in general. In 1949 he headed special commission of the AS USSR Presidium, which was inspecting work of the Institute of Precession Mechanics and Computer Engineering (IPMaCE). According to the commission's final conclusion academician M.A. Lavrentev was appointed the institute's director. Lavrentev in his turn had initiated creation of the first Soviet computer MESM by S.A. Lebedev in Kiev . In 1951 Keldysh was chairman of the AS USSR commission, which inspected and accepted MESM.

In 1951, the State Commission headed by Keldysh adopted projects of computers BESM of (IPMaCE) and “Strela” of Special design Bureau 245 giving start to regular development of national computer production. In 1967 the State Commission headed by Keldysh highly appreciated famous computer BESM-6 of IPMaCE (designed by S.A. Lebedev, V.A. Melnikov, K.N. Korolev, A.A. Sokolov) and recommended it to commercial production.

From 1961 till 1975 Keldysh was the President of the USSR Academy of Sciences. His entering the office brought decisive changes into the work of its Presidium and in the social position of the academy in general. Keldysh implemented all his authority and influence in higher administrative and scientific circles so to create a team of colleagues, sharing similar progressive ideas, and thus to initiate cardinal reforms. They managed to clear some scientific fields, for example biology, from “false teachings” and to rehabilitate such “condemned” sciences as genetics and cybernetics from political accusations and ideological blame. They also created favourable conditions for progress of new domains – molecular biology, quantum electronics, etc.

Impressive success of the USSR in solving basic scientific and technical problems clearly demonstrated importance of the fundamental science as the driving force of the development. Therefore it should take proper position in the national progress. Keldysh himself, as the academy president and the official of the state level, made notable contribution to realisation of that principle. He always concentrated his efforts on principal issues and the period of his presidency is recognized as the most quick and efficient growth of the academy – basis of the fundamental science. He personally paid much attention to promising fundamental projects.

Thus, he analysed and approved new conception of the National-Level Automated System (national computer network primarily intended for supporting government functions in economy and administration) and the Common System of Computer Centres, proposed by academician V.M. Glushkov in 1963. Unfortunately that network of huge physical dimensions (one should remember geographical sizes of the USSR ) was not constructed for purely bureaucratic reasons.

He was also always engaged in space exploration projects. Not only in establishing of -more theoretical – mathematical- problems, like precise definition of trajectories and current coordinates of the geo- and lunar satellites or influence of the geoid gravitation on the (satellite) orbit evolution, but in more “applied” projects - flights of numerous space vehicles. Thus he was one of the principal persons in launching Soviet automatic stations to the moon, around the moon, of moon satellites, flights to other bodies of the solar system, flights of numerous manned space ships and stations, successful flight of the automatic station (robot) “Luna- 16” , which brought to the Earth the first samples of lunar soil and the mission “Luna- 17” – delivering automatic self-propelled robot “Lunokhod- 1” , which explored surface of the moon many months after. He was also scientific head of the “Interkosmos”, international space-research program.

Although he was always busy with global problems Keldysh was not a reserved academic personality. He also could be humorous attentive to others. For example the institute of applied mathematics participated in project “Luna- 3” – the automatic station that made the first photos from the backside of the moon. Several weeks after the triumph, he astonished collaborators by bringing them several bottles of excellent French vine (what was a rear thing in Moscow those times). The story was really an amusing one. As it turned out, a long time before a French vigneron promised a railway car of his vine to those who would first see, “What the backside of the moon looks like”. The French car did arrive to the USSR Space Research Centre and the vine was distributed among leading personnel of the mission; Keldysh remembered about mathematicians of the institute.

In 1972 the first scientific delegation of the AS USSR arrived to the USA on invitation of F. Handler – president of the American National Academy . They visited leading American research centres – Californian Institute of Technologies , Stafford University , University of Berkley , Space System Rapid Design Centre, JPL and the NASA (Johnson) Space Centre Houston. After numerous talks with American colleagues and his personal detailed observing of research work organisation at American institutes, Keldysh could answer the question, “Why do Americans steadily outnumber Russians in receiving Nobel Prizes, when their scientific level and understanding of contemporary scientific problems are more or less equal?” in some following way. “Primarily for their much better facilitation of research process. Numerous automatic systems for experimental work, for obtained data processing and rapid publishing of new results make organisational efficiency of the institutes and laboratories notably higher (than in the USSR)”. There is no need to say that on their return that dialogue had practical consequences.

In 1971, when he was sixty, Keldysh was decorated with the third gold medal [6] “Sickle and Hammer” for his organisational efforts on scientific development. Besides this (triple) highest sign of honour he was seven times (!) awarded the USSR highest civil order – “Lenin Order”.

Despite his high official position, which “opened the doors of governmental offices” Keldysh was never a “blind satellite” of the official policy in any aspect. He always remained with his personal views and opinions, although it would be too naive to imagine him constantly in open confrontation to all he disliked. Nevertheless diplomacy, inevitable attribute of his official position, was always a heavy burden to him as to born scientist. Anyway he always remained a convinced patriot of both his country and his science.

In 1975, when a heavy illness limited his physical abilities and he could not work as intensively as before Keldysh made a decision to leave his office. It was just before 250-years anniversary of the Academy. It looks likely that his physical deterioration was caused not only by the extreme overloads of the exhausting daily work but also by growing depression (or spiritual discomfort) of the last years, which resulted from increasing amount of the projects that he could not realise for various reasons.

Mstislav Vsevolodovich Keldysh died on the 24 th of June 1978 in Moscow . He was buried in the Kremlin wall (burial place for the persons of exceptional national merits).

His name was commemorated in the names of a scientific-research ship of the AS USSR, of a small planet, of a lunar crater and a square in Moscow . Former “Scientific Research Institute – 1” is now re-named after him into “M.V. Keldysh Research Centre”. At the Institute of Applied Mathematics , which he had established, there is his memorial study, which possesses a large collection of documents connected with his life and work.

Two monuments have been erected and several memorial plates are placed on walls of the houses where he lived and worked in Moscow . A monument is also erected in Riga (now Latvia ).

The gold medal coined in his honour by the USSR Academy of Sciences is awarded for outstanding scientific works on applied mathematics and mechanics and for theoretical researches on space explorations.

Scientific publications: M.V. Keldysh. Selected works, in 4 volumes.

Notes

1. Famous under abbreviation MIAN – *(Russ.) Matematicheskiy Institut Akademii Nauk *

2. **Mikhail Alekseevich Lavrentev **, prominent mathematician and physicist – www.computer-museum.ru, also in www-history.mcs.st-and.ac.uk

3. **Fields Medals ** are given once in four years to the most distinguished mathematicians aged 40 or under. As there is no Nobel Prize in mathematics, they are regarded as the highest professional honour for a mathematician. They were established by the Canadian mathematician J.C. Fields and were first awarded in 1936. (from http://www-history.mcs.st-andrews.ac.uk )

4. The highest honourable title in the USSR . The recipient was also decorated with the medal “Gold Sickle and Hammer” and given some honourable social privileges.

5. Double title “Hero of the Socialist Labour” among others provided posthumous erection of a monument (by the government) to honour the bearer.

6. Only 16 persons had triple award “Hero of the Socialist Labour” during the whole Soviet history (including M.V. Keldysh). Academicians Kurchatov, Khariton and Zeldovich (see above) were among them.

Sourses:

- Basic Russian article by collaborators of the Academician M.V. Keldysh Memorial Museum – Study (A.V. Zabrodin). - www.computer-museum.ru
- www.keldysh.ru/memory/keldysh/vera_keldysh.htm