A doctor’s son in revolutionary Petrograd
Leonid Vitalyevich Kantorovich was born on 19 January 1912 in St Petersburg into a Russian Jewish family. His father, Vitaliy Moiseevich Kantorovich, was a popular doctor; his mother was Paulina Grigoryevna Zaks. He was the youngest of five children: his two elder brothers followed their father into medicine, and he had two elder sisters.
Among his first memories, he later wrote, were the February and October revolutions of 1917. During the civil war the family spent a year in Belarus. In 1922, when Leonid was ten, his father died, and he was brought up by his mother, who played a central role in his education. He traced the first stirrings of his interest in science, and of independent thinking, to about 1920.
A prodigy at Leningrad University
In 1926, aged just fourteen, Kantorovich entered the mathematics faculty of Leningrad State University, where he also enjoyed the vivid lectures of the historian Yevgeny Tarle on political economy and modern history. His teachers included Vladimir Smirnov, Grigorii Fichtengolz and Boris Delaunay, and his friends among the students included Sergei Sobolev and Dmitrii and Vera Faddeev, all of whom became leading mathematicians.
He began research in his second year, at fifteen, and solved problems posed by the great Moscow mathematician Nikolai Luzin on analytical operations on sets, which he presented at the First All-Union Mathematical Congress in Kharkov in 1930. He graduated that year, aged eighteen, and at twenty was already lecturing at three institutions; MacTutor records that students, seeing his youthful face, told him to sit down and wait for the professor to arrive. He became a full professor in 1934, at twenty-two, and received his doctorate in 1935, when the Soviet Union restored academic degrees.
Pure mathematics
Kantorovich’s achievements in pure mathematics alone would have made his name. In the 1930s, one of the great decades of functional analysis, he opened a new direction: the systematic study of spaces of functions in which some pairs of elements can be ordered. These partially ordered spaces, today called Kantorovich spaces, proved very fruitful, and brought him into contact with John von Neumann, Garrett Birkhoff, Albert Tucker and Maurice Fréchet, whom he met at the Moscow Topological Congress of 1935. At Torsten Carleman’s invitation he published a memoir on functional equations in the Swedish journal Acta Mathematica, and he won prizes in Leningrad and all-Union competitions for young researchers in 1937 and 1938. The theory was gathered in Functional Analysis in Semiordered Spaces (1950), written with his colleagues B. Z. Vulikh and A. G. Pinsker.
At the same time he worked on practical methods, from approximate conformal mapping to the approximate solution of differential equations, summed up in Approximate Methods of Higher Analysis (1936), written with Vladimir Krylov. After the war he showed how the abstract tools of functional analysis could power numerical computation, in a paper whose title, Functional Analysis and Applied Mathematics, seemed paradoxical at the time. It won him the Stalin Prize in 1949. His name is also attached to the Kantorovich inequality and theorem on the convergence of iterative methods such as Newton’s method, and to the Kantorovich–Rubinstein metric in probability theory and the modern theory of optimal transport.
The plywood problem
Kantorovich came to economics, as he put it, by accident. In 1938 the laboratory of the Leningrad Plywood Trust asked the young professor for help with a puzzle: how to schedule work on eight lathes so as to get the most output of several kinds of plywood in fixed proportions. The obvious method, comparing the values at every corner of the set of possible solutions, was useless, because even simple problems had an enormous number of corners.
He realised that the same mathematical form appeared everywhere: in allocating work to equipment, using sowing land, cutting materials with minimal waste, using complex resources and routing transport. He devised what he called the “method of resolving multipliers”, and in 1939 Leningrad University published his booklet The Mathematical Method of Production Planning and Organization. In essence it contained the main ideas of what the world would later call linear programming, including the economic meaning of the multipliers as a kind of shadow price.
The work remained unknown in the West for many years. George Dantzig, Tjalling Koopmans and others independently developed linear programming in the late 1940s, and Kantorovich learned of their work only in the mid-1950s. Kantorovich himself, with characteristic fairness, noted in his Nobel autobiography that the transport problem had been stated before him, by A. Tolstoy in 1930 and later by Frank Hitchcock. In 1960, at Koopmans’s initiative, his 1939 booklet was translated and published in the American journal Management Science.
War and the siege of Leningrad
During the Second World War Kantorovich taught at military engineering schools. MacTutor records that he was given the rank of major and evacuated with his institute to Yaroslavl, where he also worked on defence problems and wrote a textbook of probability with military applications. Wikipedia credits him with work on the safety of the Road of Life, the ice road across Lake Ladoga that supplied besieged Leningrad, calculating safe distances between vehicles according to the thickness of the ice and the air temperature. He was awarded the Order of the Patriotic War and the medal For the Defence of Leningrad.
Even in wartime he continued to think about economics, and in 1942 wrote the first version of the book that would become his most important economic work.
Optimal planning in a planned economy
After the war Kantorovich put his methods to practical use. In 1948–50, at the Leningrad railway-carriage works, the geometer V. A. Zalgaller used linear programming under his guidance to calculate the best way of cutting steel sheets, saving material. He also became interested in computing, working on programming automation and on early computer design; with Mark Gavurin and Vera Faddeeva he used punched-card tabulating machines, with ingenious parallel methods, to compute tables of Bessel functions.
His 1942 manuscript was finally published in 1959 as The Best Use of Economic Resources. It applied his optimal approach to the central questions of Soviet economics: planning, prices, rent, investment efficiency and the decentralisation of decisions. His argument that a planned economy needed rational prices, including a uniform interest rate for investment decisions, was a bold departure in Soviet economics, and he recalled that some Soviet economists met the new methods guardedly. A conference of the Academy of Sciences nevertheless endorsed the new direction, and a generation of mathematician-economists was trained in Leningrad, Moscow and beyond.
Novosibirsk, Moscow and the Nobel Prize
Kantorovich was elected a corresponding member of the USSR Academy of Sciences in 1958 and a full academician in 1964. In 1960 he moved to the new scientific town of Akademgorodok near Novosibirsk, where he led work on mathematics and economics in the Siberian branch of the Academy and trained many talented students. He received the Lenin Prize in 1965. From 1971 he headed a research laboratory at the Institute of National Economic Planning in Moscow, introducing senior managers to new methods, and advised government bodies.
In 1975 he shared the Nobel Memorial Prize in Economic Sciences with Tjalling Koopmans “for their contributions to the theory of optimum allocation of resources.” The Royal Swedish Academy of Sciences called him the leading representative of the mathematical school in Soviet economic research. He remains the only economist from the Soviet Union to have received the prize. He also received honorary doctorates from universities including Glasgow, the Sorbonne, Cambridge and Pennsylvania.
The man and his background
In 1938 Kantorovich married Natalya Ilyina, a physician; they had a son and a daughter, both of whom became mathematical economists. His student Semen Kutateladze described a man of striking contrasts: shy in private yet outspoken in public, no orator yet a master of argument, gentle by nature but capable of an iron grip when his ideas needed defending.
Kantorovich was born into a Jewish family in the last years of imperial Russia and made his career entirely within the Soviet system, where Jewish identity was officially a nationality rather than a faith and religious life was suppressed. He wrote little about his background in his published autobiography. His story belongs to the remarkable generation of Soviet scientists of Jewish origin whose work shaped twentieth-century mathematics and economics.
Death and legacy
Leonid Kantorovich died in Moscow on 7 April 1986, aged seventy-four, and was buried in the Novodevichy Cemetery. Over his career he published more than three hundred papers and books.
Linear programming, the technique he first described for a plywood factory, became one of the most widely used tools of the modern world. Airlines schedule crews and planes with it, refineries blend fuel, farmers plan crops, shipping firms route cargo and factories plan production by solving the kind of problem he set out in 1939. In economics his insight that efficient allocation and prices are two sides of the same problem shaped the theory of planning and markets alike, and in mathematics his name lives on in Kantorovich spaces and in the theory of optimal transport.
Sources & further reading
Leonid Vitaliyevich Kantorovich, Biographical, NobelPrize.org · Leonid Vital’evich Kantorovich, MacTutor History of Mathematics, University of St Andrews · Leonid Kantorovich, Jewish Virtual Library · Leonid Kantorovich, Wikipedia · Researched from the sources above and checked against them. Spotted an error? Tell us.
A life of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.