Leonid Vitaliyevich Kantorovich (Russian: Леони́д Вита́льевич Канторо́вич (19 January 1912 – 7 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programming. He was the winner of the Stalin Prize in 1949 and the Nobel Prize in Economics in 1975.

Leonid Vital'evich Kantorovich's father was Vitaliy Moiseevich Kantorovich, a popular medical doctor specialising in sexually transmitted diseases, and his mother was Paulina Grigoryevna Zaks. Leonid Vital'evich had two elder sisters Lidiya and Nadezhda, and two elder brothers Nikolay and Georgiy who followed their father in becoming medical doctors. The first events to impact on the young child Leonid was the general strike and disorder that broke out in St Petersburg in February 1917 and then the violent revolution of October 1917 when workers stormed the Winter Palace and disposed the government. Civil war then raged throughout the country during 1918-20 and the Kantorovich family went to Belarus (then known as Byelorussia) where they spent a year of this difficult period. Kantorovich was a child prodigy and he writes about his interest in science beginning when he was eight years old:-

״My first interest in sciences and the first displays of self-dependent thinking manifested themselves about 1920.״

In 1922, when he was ten years old, his father died and from that time on he was brought up by his mother who played an important role in his upbringing. He entered the Mathematics Faculty of Leningrad State University in 1926, when he was only 14 years old. He attended lectures by Vladimir Ivanovich Smirnov, Grigorii Mickhailovich Fichtengolz (1888-1959), one of the founders of the Leningrad school of real analysis, and Boris Nikolaevich Delone. Among his fellow students, he was friends with Isidor Pavlovich Natanson (1906-1964), Sergei Lvovich Sobolev, Solomon Grigor'evich Michlin (1908-1990), Dmitrii Konstantinovich Faddeev and Vera Nikolaevna Zamyatin (who was known as Vera Nikolaevna Faddeeva after her marriage in 1930). In his second year at university, still only aged fifteen, Kantorovich began research as a member of Grigorii Mickhailovich Fichtengolz's descriptive function theory seminar and he writes:-

״I think my most significant research in those days was that connected with analytical operations on sets and on projective sets (1929-30) where I solved some of Nikolai Nikolaevich Luzin's problems. I reported these results to the First All-Union Mathematical Congress in Kharkov (1930).״

He graduated in 1930 at the age of eighteen having reached the level equivalent to a doctorate and continued to undertake research in the Mathematical Department of the Faculty of Physics and Mathematics of Leningrad State University. Note that at this stage, the Soviet Union had abolished doctoral degrees and he would only formally receive the degree in 1935 when the award of such degrees was reinstated. He was appointed as an assistant in the Naval Engineering School in 1930. In the following year he was appointed as a research associate in the Research Institute of Mathematics and Mechanics of Leningrad State University and, from 1932, an associate professor in the Department of Numerical Mathematics. By 1932, therefore, he held these three positions and, being still only 20 years of age, his youthful appearance caused some surprise among his students who at first refused to believe that the "youngster" was their lecturer and not a fellow-student. When he came to give his first lecture, several students shouted to him to sit down and wait for the professor to arrive.

He published his first book in 1933, coauthored with Vladimir Ivanovich Krylov (1902-1994) and Vladimir Ivanovich Smirnov, entitled Calculus of variations. In 1934 the Second All-Union Mathematical Congress was held in Leningrad and attracted around 700 participants. Kantorovich gave two lectures, "On conformal mappings of domains" and "On some methods of approximate solution of partial differential equations". His research was also highlighted in the lecture "Leningrad studies in analysis" given by Vladimir Ivanovich Smirnov. In 1934 he qualified as a professor and, in the following year, he participated in the Moscow Topological Congress. There he met John von Neumann, George David Birkhoff, Albert William Tucker, Maurice Fréchet and other mathematicians, and he maintained his contacts with these mathematicians concerning his work on partially-ordered spaces.

From 1934 to 1960 he was a professor of mathematics at Leningrad State University. In 1935 he made a major breakthrough when he defined what are now called K-spaces.

K-spaces are vector lattices in which every nonempty order bounded subset has an infimum and supremum:-

Kantorovich spaces have provided the natural framework for developing the theory of linear inequalities which was a practically uncharted area of research those days.

In 1936 he published On one class of functional equations (Russian) in which he applied semiordered spaces to numerical methods.

He was awarded first prize in mathematics at the Leningrad competition for young research workers in 1937 and at the All-Union competition of young research workers in 1938, he received the prize for his paper Functional analysis using the theory of semi-ordered spaces. Also in 1938 he married Natalya Ilyina who, like his two brothers and father, was a medical doctor; they had two children, a son and a daughter, who both became mathematical economists.

His interest in economics began in 1938.

Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production mentioned in the above quote.

World War II was having a major impact on research and scientific publications. He was drafted into the armed forces, given the military rank of a major and, in 1941, the Institute of Industrial Construction where he was teaching became the Higher Technical School of Military Engineering. This was moved from Leningrad to Yaroslavl, 300 km north of Moscow and Kantorovich was evacuated there. As well as teaching at the Higher Technical School of Military Engineering he also undertook various tasks relating to defence.

In 1949, the work was awarded the State Prize and later was included in the book, 'Functional Analysis in Normed Spaces' (Russian), written with G P Akilov (1959).

He held the chair of mathematics and economics in the Siberian branch of the USSR Academy of Sciences in Novosibirsk (1961-1971), then directed research at Moscow's Institute of National Economic Planning (1971-76). Kantorovich was a joint winner of the 1975 Nobel Prize for economics with Tjalling C Koopmans, ... for their contributions to the theory of optimum allocation of resources.

As the starting point of their work in this field, both have studied the problem - fundamental to all economic activity - of

Despite the differences of opinion and attempts to assign Kantorovich to one economic school or another, all the scientists under consideration here emphasise his outstanding contribution to the development of economic sciences.

His remarkable contribution to mathematics, economics and computers was published in over 300 papers and books. It is interesting to note that, in the 1980s, Kantorovich suggested that his contributions might be divided into the following nine distinct areas: (1) descriptive function theory and set theory; (2) constructive function theory; (3) approximate methods of analysis; (4) functional analysis; (5) functional analysis and applied mathematics; (6) linear programming; (7) hardware and software; (8) optimal planning and optimal prices; and (9) the economic problems of a planned economy.

Kantorovich received a great many honours for his remarkable contributions, the most prestigious being the Nobel prize which we have already mentions. He was elected to many academies and scientific societies including the International Econometric Society (1966), the Hungarian Academy of Sciences (1967), the American Academy of Arts and Sciences (1969), the Academy of Sciences of German Democratic Republic (1977), the National Engineering Academy of Mexico (1977), Yugoslavian Academy of Science and Arts (1980), the International Control Institute of Ireland (1984). He was awarded an honorary doctorate by the universities of Glasgow (1966), Warsaw (1966), Grenoble (1966), Nice (1968), Helsinki (1969), Munich (1970), Paris (Sorbonne) (1975), Cambridge (1976), Pennsylvania (1976), the Indian Statistical Institute in Calcutta (1978), and Martin-Luther University, Halle-Wittenberg (1984). He received the Stalin prize (1949), a diploma of the Operations Research Society of America (1960), Lenin Prize (1965), Bronze medal of the Prague Higher Economic School (1981), and the Silver medal of Operational Research Society of Birmingham (1986).

Following his death from cancer in April 1986, he was buried at Novodevichy Cemetery in Moscow.

From an article by: J J O'Connor and E F Robertson

לאוניד ויטַלייביץ' קנטורוביץ'

(‏19 בינואר 1912 - 7 באפריל 1986) היה מתמטיקאי וכלכלן סובייטי יהודי, חתן פרס נובל לכלכלה בשנת 1975. נחשב למפתח התכנון הליניארי שבעבורו זכה בפרס נובל, וכן ערך מחקרים חשובים בתחום אנליזה פונקציונלית, תורת הקירובים ואי-שוויון קנטורוביץ'.

ביוגרפיה

לאוניד קנטורוביץ' נולד בסנקט פטרבורג למשפחת רופאים ממוצא יהודי. בשנת 1926 בהיותו, בן 14 בלבד, החל את לימודיו באוניברסיטת לנינגרד. בין היתר למד אצל גריגורי פיכטנגולץ. לאחר סיום לימודיו בפקולטה למתמטיקה החל ללמד ובשנת 1934 מונה לפרופסור. בשנת 1935 הוא קיבל תואר דוקטור על סמך כלל העבודות שבוצעו על ידו.

בשנת 1938 קנטורוביץ' ייעץ לבית חרושת לייצור עץ לבוד. הוא הבין שמדובר בבעיית אופטימיזציה תוך אילוצים רבים. השיטה שהוא פיתח נהפכה עם הזמן לבסיס של תכנון ליניארי.

החל משנת 1939 קנטורוביץ לימד באוניברסיטה למהנדסים צבאיים בלנינגרד. בשנת 1948 קבוצת מתמטיקאים בראשותו צורפה לפרויקט הגרעין הסובייטי. בשנת 1949 זכה בפרס סטלין עבור עבודותיו בתחום המתמטיקה.

בשנת 1958 קנטורוביץ' נבחר לחבר בהתכתבות של האקדמיה למדעים של ברית המועצות. באותה תקופה שימש ראש קתדרה למתמטיקה חישובית באוניברסיטת לנינגרד ובמקביל עבד במכון למתמטיקה על שם סטקלוב בלנינגרד.

עבודותיו של קנטורוביץ' בתחום הכלכלה זכו לביקורת צוננת מכלכלנים סובייטים שאף האשימו אותו בגישה אנטי-מרקסיסטית, אולם תפקידו ותאריו הרבים בתחום המתמטיקה הגנו עליו מפני מתנגדיו.

בשנת 1960 ממשלת ברית המועצות החליטה להקים מרכז מדעי בנובוסיבירסק. במסגרת זו הועברו לעיר מדענים ממספר מרכזים מדעיים ותיקים. קנטורוביץ' הקים קתדרה למתמטיקה חישובית באוניברסיטת נובוסיבירסק ועבד במכון למתמטיקה של האקדמיה למדעים שהוקם בעיר.

בתחילת שנות ה-60 רעיונותיו של קנטורוביץ' בתחום הכלכלה החלו להתקבל בקרב כלכלנים סובייטים. בשנת 1964 קנטורוביץ' נבחר לחבר באקדמיה למדעים ובשנת 1965 זכה בפרס לנין עבור פיתוח שיטות של תכנון ליניארי ויישומיהן בתחום הכלכלה.

בשנת 1971 קנטורוביץ' חזר למוסקבה והחל לעבוד באקדמיה לכלכלה לאומית של מועצת השרים של ברית המועצות. בשנת 1975 הוענק לקנטורוביץ' פרס נובל לכלכלה. בשנת 1976 הוא החל לעבוד במכון לבעיות מערכתיות ליד האקדמיה למדעים.

קנטורוביץ' נפטר בשנת 1986 ונקבר בבית העלמין נובודוויצ'י במוסקבה.

https://he.wikipedia.org/wiki/%D7%9C%D7%90%D7%95%D7%A0%D7%99%D7%93_...