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Akushskiy Israel Yakovlevich

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Israel Yakovlevich Akushskiy was born on the 30 th of July 1911 in Dnepropetrovsk (industrial centre in the South Ukraine) into family of the rabbi-superior of the town. After the October Revolution the father became a teacher.

The period after the revolution and Civil War (the later 1920-s, 1930-s, etc.) was far from being simple but in many ways a glorious one. General public ideology, especially among the younger generation, was focused on creation of the new society without national, religious and social separation or segregation, based on equal rights for everybody. Learning and creative labour were considered to be the top priority issues. Thousands enthusiastic young people, irrespectively of their origin, were “feeding on ideas” and did their best in learning and contributing to creation of new community, each one in his or her own professional field. That was the reality of the time to which belonged Israel Akushskiy.

Karl Adolfovich Krug
Israel Yakovlevich

Being still a student of the Moscow State University he worked as counting assistant at the scientific research institute of mathematics and mechanics. In 1936, after graduation, he received position of junior scientific collaborator at the Institute of Mathematics (V.S. Steklov[1] Mathematical Institute) which had been transferred to Moscow from Leningrad not long before. His supervisor there was L.A. Lusternik – one of creators of the functional analysis .

Although computational methods were not very popular before, approaching of the war accelerated their development. The institute was given task to produce tables for artillery ballistic and navigation tables for air force. The latter was the subject for special laboratory established in 1939 and trusted to Akushskiy. Big -for those times- amount of calculations needed advanced machinery, however, production of so-called calculation-analytic in the USSR was just beginning. By lucky coincidence the firm IBM made exhibition of its calculation complex in Moscow Polytechnic Museum . With many efforts Akushskiy managed to persuade the institute authorities to rent it and place in his laboratory. One could say that it was one of the first computer centres in Moscow .

With the beginning of the war most of the institute was evacuated to the East, only Akushskiy with small group of collaborators remained in Moscow working for the army. Calculation of navigation tables always was their main task. Sometimes he personally visited air force bases, situated hundreds kilometres off Moscow, doing “one-night business trips”.

Although he didn't have to be on the front line his work, nevertheless, was full of other risks. Thus one night Akushskiy was summoned to a higher security office. A military airplane disappeared during a mission in the Far East, the crew used his tables… . Quite naturally one needed more than great deal of self-control at such turn of events, luckily his brilliant intellect saved the situation. The unlucky airplane flying Eastward could cross the 180 th meridian. In that case the correction values, taken from navigation tables, should be added with reversed sign otherwise it would fly a “mirror course”. The inexperienced navigator could have forgotten that. Analysis of the last –available- flight data and new calculations proved Akushskiy's theory. Wreckages of the lost plane were found exactly in the suggested area. Security officers had to apologise.

Once they were given an unusual task which consisted in calculating about 50 variants of flight route Moscow-Teheran. Much later they learnt that those were preparations for the “Big three[2]” meeting in Iran in summer of 1943.

In fact the quality of his laboratory works was always high and their materials, such as navigation tables for long range bombers, many times proved their reliability. In 1942 he received his first award, that was a premium of the air force General Staff. In the same 1942 Akushskiy was dispatched to besieged by Nazis Leningrad to complete tables for naval radiolocation systems. Seeing around him constant destruction of the town and murdering of its civil population he was working day and night.

On return to Moscow, by the end of 1943, he resumed work at the laboratory and began preparations of a dissertation thesis. Akushskiy had solid reasons for that. He had not only devised theory and new methods of calculations for radio-navigation, -location, etc., but was the USSR first to implement binary arithmetic for practical computations. As soon as the war came to the end he received permission to work on his scientific thesis. In the mid-1945 he successfully submitted it and was awarded “Candidate of sciences” degree. Famous mathematician academician A.N. Kolmogorov[3], who attended the submission and spoke in support of Akushskiy, suggested him to write an article on the dissertation subject and then himself sent it to Norbert Wiener, with whom Kolmogorov had been maintaining correspondence since the war times. Akushskiy followed the advice and later, during his first Moscow visit in 1956, Wiener came to Steklov Mathematical Institute and -among other- was also interested to have a personal talk with him.

Already during the war L.A. Lusternik established scientific seminar on computation theory. Academician N.G. Bruyevich, AS USSR scientific secretary, also run a seminar – on precession mechanics. Later the both were joined and the problems of computation machinery were discussed more often. Akushskiy actively participated. From the personal experience he saw that available calculating and analog machinery would not cope with practical problems of the nearest future. Academician S.I. Vavilov - the President of AS USSR supported their proposals on new institute for computer engineering and in 1948 he already received governmental decision of approval. In the same 1948 the Academy of Sciences established the Institute of Precession Mechanics and Computer Engineering (IPMaCE). It integrated N.G. Bruyevich's department of precession mechanics, department of academician I.S. Bruk[4] and laboratory of Prof L.I. Gutenmakher (of Power-engineering Institute AS USSR), and also department of the “Steklov Mathematical Institute” headed by L.A. Lusternik to which belonged laboratory held by Akushskiy.

N.G. Bruyevich was its first director from 1948, however in the next year he was replaced by famous mathematician academician M.A. Lavrentyev, for the official reason that the institute paid insufficient attention to electronic computation devices. In 1952 Lavrentyev recommended to that position academician S.A. Lebedev, the most prominent Soviet computer pioneer, who headed IPMaCE from 1952 till 1974 and made it one of the world's most famous “classical” computer institutes.

Unfortunately the political “trends” of those times, which had nothing to do with scientific problems, complicated the work and Akushskiy moved to Alma-Ata, capital town of Kazakhstan . In Kazakhstan he established laboratory of computation mathematics which later became basis for new Institute of Mathematics and Mechanics (IMM) founded at the Kazakhstan Academy of Sciences (AS), and there he worked from 1954 till 1956. He also lectured on computation mathematics at the Kazakh State University and supervised postgraduates. Some of them later became famous scientists.

It was then when Akushskiy approached the idea of a new calculating system which should highly accelerate computation processes in electronic computers – the modular arithmetic based on “rest classes arithmetic” system. That became his main scientific issue for all remaining life. On a visit to Moscow in 1956, he shared the idea with M.A. Lavrentyev, to hear in reply that a scientist Antonin Svoboda of Czechoslovakia had sent a letter with description of similar method[5]. Svoboda wrote about designing a computer based on the same modular arithmetic . Although the priority turned to be not his, Akushskiy wasn't disappointed but grew “possessed” with the idea. He thought a lot on development of the new method, what later would bring notable practical results.

Although the IMM was “newly born” one and scientific society of Kazakhstan was just in process of formation the work itself was intensive and soon Akushskiy won both respect and love of his colleagues and students. Nevertheless, in 1956, when the president of AS Kazakhstan learnt about his intention to return to Moscow he did not object, however he wished to keep him as participant in the Academy's work. He asked Akushskiy to continue supervision of dissertations and to consult postgraduates, researches on computation mathematics and on computer engineering in general. Later, in 1970, Akushskiy was elected a corresponding member of the AS Kazakhstan.

F.V. Lukin then worked as chief engineer of Design Bureau No 1 at the Ministry of Radio-producing Industry which was also the main administrative office for computer development. He also became one of the first to pay attention to modular arithmetic. In the mid-1950-s Lukin received information about American researches on calculation system in rest classes (RCS). He thereupon informed Akushskiy, who was already back to Moscow working as a senior scientist of the department headed by D.I. Yuditskiy at the Special Design Bureau -245 (SDB-245). The Bureau was conducting research and design of the first serially produced computer “Strela” (arrow).

In 1957 Y.Y. Basilevskiy, B.I. Rameev, Y.A. Shreider, I.Y. Akushskiy and D.I. Yuditskiy – all leading members of the “Strela” team, formed the USSR first group which made attempt to work with the new calculation system. That time it was not success, not all of them realised its principles.

However, in 1960 the same Lukin, then already the director of the Scientific Research Institute of Remote Radio-communications, assigned Akushskiy an invitation to head design of a new computer, which he willingly accepted .

That computer was named T-340 and a little later it was followed by K-340-A. The both were based on the modular arithmetic; K-340-A, possessed unusual performance 1.25 mil double ops (or 2.4 mil ops). At those times average performance of computer was measured by tens of thousands ops. It was designed and assembled in a very short time and was immediately implemented in the anti-aircraft defence systems. By the way, at present, after implementation of integrated circuits it is still in use and in commercial production.

In the rest classes system (RCS) each number with many decimal places is represented with series of smaller numbers with few decimal places, which are in fact rests after division of the initial number by simple bases. All operations over each of the “rests” are performed separately and independently (in parallel) within the same computer cycle. Introduction of superfluous bases provides possibility of control and error correction during the operation performance. This is the system's advantage. Common computers can't do it. Therefore such computers are always quicker and more reliable.

That was the theory, but no written materials or other evidence about practical implementation of the rest classes system, or at least experiments with it, were available that time. Everything should be done by own efforts. Active participant of that research B.M. Amerbaev - academician of the AS Kazakhstan remembers, “F.V. Lukin attracted Akushskiy's attention to the researches … on new method for the parallel computations. Later it turned out that it possessed ability of arithmetical self-correction. That was non-traditional computer arithmetic and its development also needed original approach and solutions. During the subsequent work there were found lots of brilliant solutions in original architecture, increasing reliability, parallel computations, conveyer computers”.

In 1961 Akushskiy had a prolonged talk with A. Svoboda having met him at a mathematical congress in Leningrad . They discussed their conference reports to be made and it looked like that time Akushskiy was ahead of his “rival”. Anyway Svoboda made another report and the “ Leningrad one” he presented later, at a mathematical conference in Spain .

Academician Sergey Lebedev, the USSR leading computer expert and IPMaCE director, was very high opinion of Akushskiy both as of person and of scientist. He supported him and used to say, “I would make high-performance machines in other way but nobody is obliged to do the same as others”, and always added, “I wish you a big success”. A. Svoboda also made computer based on modular arithmetic – EPOC, in Czhechoslovakia, but its performance was much lower than in K-340-A.

In 1965-1968 the government launched new stages of development program for anti-rocket defence systems. That time new computers, or rather computation systems, needed total performance of about 0.5 milliard ops. The competition of design projects established by the government order was won by computer 5E53. Design team of that project was headed by D.I. Yuditskiy. I.Y. Akushskiy was his deputy on scientific work.

5E53 had many advantages. Usage of modular arithmetic made possible many progressive solutions, which were implemented in its architecture. First of all that was simpler hardware and higher performance, it was also increased reliability due to self-correction abilities of the rest classes system, etc. Architecture of 5E53 was different from traditional von-Neumann type and had many original elements. Thus instructions were divided in two types – arithmetic and control ones. The former were performed by RCS – processors, the latter by traditional – binary. Basic processes – computations, data retrieval were performed in conveyor mode by means of hardware. Up to eight serial operations could be done simultaneously. Separation of memory into eight serially addressed blocks (sections) also was realised on hardware level. It enabled information retrieval from one RAM block within 700 nsec. Its memory was based not on ferrite components but on integrated circuits and changeable induction cards. Computer assisted design was widely used during the whole work. It was new technology almost unknown, so most of the design programs were composed by the participants themselves.

The work was very intensive, creative and enthusiastic, everybody often spent 12 and more hours a day at the laboratory. Davlet Yuditskiy -the director- once came at two at night with oscilloscope to investigate the reasons of external interferences. One of the leading designers V.M. Radunskiy grew so concentrated on “working process” that (by mistake) he gave his wife an identification pass-card returning home after exhausting day. No wonder that the design was completed within a year and half. Experimental model of the computer was assembled and successfully tested by the beginning of 1971. In reality it was an eight-processor complex operating with clock rate of 6 MHz. Duration of its errorless operation reached 600 hours (other computers didn't exceed 100 h). The whole installation needed a site of 120 sqw m. Eight sets of project documentary were sent to the manufacturing plant.

Unfortunately that was the end of the story. In spite of the triumphant completion of that unusual project the computer itself was never produced. In spite of the numerous clear advantages of 5E53 competition with other producers was lost on the higher administrative level. The inter-ministerial commission demonstrated preference to other computer 5E66 (design M.A. Kartsev).

Yuditskiy and Akushhskiy made desperate efforts to find other customers. Some of their technical solutions had been patented in other countries leaders of computer technologies, such as the Great Britain, Japan and USA . One American company suggested cooperation for joint production of a computer based on Akushskiy's ideas and American electronic components[6]. K.A. Valiev – director of the institute of molecular electronics was already preparing for work with new American circuitry but unfortunately cooperation and all related works were suddenly stopped by the higher administrative decision. National security reasons were the official explanation.

In 1971 F.V. Lukin suddenly died. It was a heavy and painful personal blow for Akushskiy. Advanced design of 5E53 was at least ten years ahead of all comparable computers in the world but now the design team had no serious support. After intensive searches Akushskiy received permission to produce experimental computer in his town of birth Dnepropetrovsk, what looked like a good omen, but that time it was his own director who refused to help.

Akushskiy decided to retire. As academician he could continue scientific work at home without regular visiting or being employee of any institute. He also did not need any special ideas, he himself was always generating them. Besides he always had numerous students whom he kept consulting at home. He supervised about 90 future scientists.

He worked practically up to his last day. Already by the beginning of 1992 he had prepared text of the principal article on implementation of modular arithmetic in ultra high numeric range. Unfortunately he could not publish this work – a sort of his scientific testament. The scientist died on the 2 nd of April 1992 of a heart attack.

At present Israel Yakovlevich Akushskiy is recognised as founder of non-traditional computer arithmetic.

In the beginning of the 1960-s his computers were not only the world's first to step over performance barrier of 1 mil ops but also numbered thousands hours of the continual faultless operation. His methods based on modular arithmetic enabled efficient computations with ultra-high numbers of thousands of decimal places. His methods also made possible solution of numerous problems from theory of numbers that remained unsolved from the times of Gauss, Euler and Fermat.

I .Y. Akushskiy published more than 200 works many of which were popular both in the USSR and abroad (among them 12 monographs). Many of his 90 inventions were patented in other countries. He supervised 80 “Candidate of sciences”[7] and 10 doctoral dissertations.


1. “V.S. Steklov Mathematical Institute” played very important role in development of the Soviet computer programming. It is one of the principal mathematical scientific centres of Moscow .

Vladimir Andreevich Steklov (1864-1926) graduated from the Kharkov University as mathematician, after highly successful university career, in 1887. He remained there under Alexander Lyapunov and in 1893 was awarded Master's degree with thesis on equations of a solid body moving in an ideal non-viscous fluid. He also worked on problems from potential theory, electrostatics and hydromechanics. He reduced them to boundary-value problems of Dirichlet type, where Laplace 's equation must be solved on a surface, using rigorous mathematical analysis, and was awarded doctorate in 1902. His supervisor A. Lyapunov moved to St. Petersburg in 1902 and Steklov followed him in 1906, to hold the chair of mathematics. In 1910 he was elected to the Russian Academy of Sciences, in 1919 became its vice-president. Being strongly against the Tsarist Regime and sympathising with progressive students he became very popular teacher. Together with his excellent lecturing skills it attracted many students to study at the Department of Mathematics and Physics. Steklov essentially contributed to applied mathematics. He wrote General Theory of Fundamental Functions. H e proved to be a brilliant scientific administrator too. For eight years he worked tirelessly to maintain and, in the Soviet time, to enlarge the activity of the Academy, so to reorganise it bringing science and practical requirements closer together. In 1921 he founded the Institute of Physics and Mathematics and was its director until his death in 1926. In 1934 it was split into two separate Institutes of Physics and of Mathematics (V.A. Steklov Mathematical Institute) and transferred to Moscow.

2.The “Big Three” meeting – the historical meeting of the heads of the anti-Hitler coalition states: J. Stalin, F. Roosevelt and U. Churchill in Teheran, in 1943. All arrangements of the Stalin's trip there were perfect, he even resided President Roosevelt in the Soviet embassy. It was better protected, therefore safer.

3. A ndrey Nikolaevich Kolmogorov (1903 – 1987) was one of the developers of probability theory. He later used this work to study the motion of the planets and the turbulent flow of air from a jet engine

4. Corresponding member of the AS USSR Isaak Semenovicn Bruk – see (

5. According to some sources (, in 1950 Swoboda was delivering lectures and noticed that in analog computers there was no big structural difference between adder and multiplier but in digital systems they differed principally. He asked students to find digital realisation to make both processes comparably easy and one of them Miro Valah suggested idea of digital coding which was later named “rest classes system”. It was a fruitful idea and after years of research by A. Svoboda, M. Valah, N. Szabo, R. Tanaka, etc. it was realised in the first Czechoslovakian electronic modular computer EPOC ( Electronny POCytach ). (from article by B. Malashevich, D . Malashevich, “Soviet modilar and ternary computers”)

6. A notable episode for those –cold war- times, considering American embargo on trade with computer-related technologies and components with the USSR .

7. Could be compared with Master's degree.


  1. I.Y. Akyshskiy biography at the “Virtual computer museum” (Russ.).
  2. B.N. Malinovskiy. “History of computing in persons”, Kiev, KIT, 1995.
  3. B. Malashevich. Development of computers in Zelenograd: unknown super-computers. (
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