Nikolai Luzin
Encyclopedia
Nikolai Nikolaevich Luzin, (also spelled Lusin) (9 December 1883, Irkutsk
– 28 January 1950, Moscow
), was a Soviet
/Russia
n mathematician
known for his work in descriptive set theory
and aspects of mathematical analysis
with strong connections to point-set topology. He was the eponym
of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.
in 1901 at Moscow University, where his advisor was Dimitri Egorov. Luzin went through a personal crisis in the years 1905 and 1906. He wrote to Pavel Florensky
that: You found me a mere child at the University, knowing nothing. I don't know how it happened, but I cannot be satisfied any more with analytic functions and Taylor series ... it happened about a year ago. ... To see the misery of people, to see the torment of life, to wend my way home from a mathematical meeting ... where, shivering in the cold, some women stand waiting in vain for dinner purchased with horror - this is an unbearable sight. It is unbearable, having seen this, to calmly study (in fact to enjoy) science. After that I could not study only mathematics, and I wanted to transfer to the medical school. ... I have been here about five months, but have only recently begun to study.
From 1910 to 1914 he studied at Göttingen, where he was influenced by Edmund Landau
. He then returned to Moscow and received his Ph.D. degree in 1915. During the Russian Civil War
(1918–1920) Luzin left Moscow
for the Polytechnical Institute Ivanovo-Voznesensk (now called Ivanovo State University of Chemistry and Technology
). He returned to Moscow in 1920. On 5 January 1927 Luzin was elected as a corresponding member of the USSR Academy of Sciences and became a full member
of the USSR Academy of Sciences first at the Department of Philosophy and then at the Department of Pure Mathematics (12 January 1929).
In the 1920s Luzin organized a famous research seminar at Moscow University. His doctoral students included some of the most famous Soviet mathematicians: Pavel Aleksandrov
, Nina Bari
, Aleksandr Khinchin
, Andrey Kolmogorov
, Alexander Kronrod
, Mikhail Lavrentyev
, Alexey Lyapunov
, Lazar Lyusternik
, Pyotr Novikov, Lev Schnirelmann
and Pavel Urysohn
.
conjecture and was unexpected to most mathematicians at that time.
His Ph.D. thesis entitled Integral and trigonometric series (1915) made a large impact on the subsequent development of the metric theory of functions. A set of problems formulated in this thesis for a long time attracted attention from mathematicians. For example, the first problem in the list, on the convergence of the Fourier series for a square-integrable function, was solved by Lennart Carleson
in 1966.
In the theory of boundary properties of analytic functions he proved an important result on the invariance of sets of boundary points under conformal mappings (1919).
Luzin was one of the founders of the descriptive set theory
. He also made contributions to complex analysis
, theory of differential equations, and numerical methods.
which consisted of former Luzin's students Lazar Lyusternik and Lev Shnirelman along with Alexander Gelfond
and Lev Pontryagin claimed that “there appeared active counter-revolutionaries among mathematicians.” Some of these mathematicians were pointed out, including the advisor of Luzin, Dmitri Egorov
. In September 1930, Dmitri Egorov was arrested on the basis of his religious beliefs. After arrest, he left the position of the director of the Moscow Mathematical Society. The new director became Ernst Kolman. As a result, Luzin left the Moscow Mathematical Society and Moscow State University. Egorov died on 10 September 1931, after a hunger strike
initiated in prison. In 1931, Ernst Kolman made the first complaint against Luzin.
In July–August 1936, Luzin was criticised in Pravda
in a series of anonymous articles whose authorship later was attributed to Ernst Kolman. It was alleged that Luzin published “would-be scientific papers,” “felt no shame in declaring the discoveries of his students to be his own achievements,” stood close to the ideology of the “black hundreds,” orthodoxy, and monarchy
“fascist-type modernized but slightly.” Luzin was tried at a special hearing of the Commission of the Academy of Sciences of the USSR, which endorsed all accusations of Luzin as an enemy under the mask of a Soviet citizen. One of the complaints was that he published his major results in foreign journals. This method of political insinuations and slander was used against the old Muscovite professorship many years before the article in Pravda.
The political offensive against Luzin was launched not only by Joseph Stalin
's repressive ideological authorities, but also by a group of Luzin's students headed by Pavel Alexandrov, who may have been pressured to it by threats to reveal his homosexual relationship with Andrey Kolmogorov
. Although the Commission convicted Luzin, he was neither expelled from the Academy nor arrested. There has been some speculation about why his punishment was so much milder than that of most other people condemned at that time, but the reason for this does not seem to be known for certain. Historian of mathematics
A.P. Yushkevich speculated that at the time, Stalin was more concerned with forthcoming Moscow Trials
of Lev Kamenev
, Grigory Zinoviev
and others, and that the eventual fate of Luzin was of little interest to him. Still, Luzin was never rehabilitated
even after Stalin's death.
Irkutsk
Irkutsk is a city and the administrative center of Irkutsk Oblast, Russia, one of the largest cities in Siberia. Population: .-History:In 1652, Ivan Pokhabov built a zimovye near the site of Irkutsk for gold trading and for the collection of fur taxes from the Buryats. In 1661, Yakov Pokhabov...
– 28 January 1950, Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
), was a Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
/Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for his work in descriptive set theory
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
and aspects of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
with strong connections to point-set topology. He was the eponym
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...
of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.
Life
He started studying mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in 1901 at Moscow University, where his advisor was Dimitri Egorov. Luzin went through a personal crisis in the years 1905 and 1906. He wrote to Pavel Florensky
Pavel Florensky
Pavel Alexandrovich Florensky was a Russian Orthodox theologian, philosopher, mathematician, electrical engineer, inventor and Neomartyr sometimes compared by his followers to Leonardo da Vinci.-Early life:Pavel Aleksandrovich Florensky was born on January 21, 1882, into the family of a railroad...
that: You found me a mere child at the University, knowing nothing. I don't know how it happened, but I cannot be satisfied any more with analytic functions and Taylor series ... it happened about a year ago. ... To see the misery of people, to see the torment of life, to wend my way home from a mathematical meeting ... where, shivering in the cold, some women stand waiting in vain for dinner purchased with horror - this is an unbearable sight. It is unbearable, having seen this, to calmly study (in fact to enjoy) science. After that I could not study only mathematics, and I wanted to transfer to the medical school. ... I have been here about five months, but have only recently begun to study.
From 1910 to 1914 he studied at Göttingen, where he was influenced by Edmund Landau
Edmund Landau
Edmund Georg Hermann Landau was a German Jewish mathematician who worked in the fields of number theory and complex analysis.-Biography:...
. He then returned to Moscow and received his Ph.D. degree in 1915. During the Russian Civil War
Russian Civil War
The Russian Civil War was a multi-party war that occurred within the former Russian Empire after the Russian provisional government collapsed to the Soviets, under the domination of the Bolshevik party. Soviet forces first assumed power in Petrograd The Russian Civil War (1917–1923) was a...
(1918–1920) Luzin left Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
for the Polytechnical Institute Ivanovo-Voznesensk (now called Ivanovo State University of Chemistry and Technology
Ivanovo State University of Chemistry and Technology
Ivanovo State University of Chemistry and Technology or ISUCT is a research facility and a university located in Ivanovo, the administrative center of Ivanovo Oblast, Russia....
). He returned to Moscow in 1920. On 5 January 1927 Luzin was elected as a corresponding member of the USSR Academy of Sciences and became a full member
Academician
The title Academician denotes a Full Member of an art, literary, or scientific academy.In many countries, it is an honorary title. There also exists a lower-rank title, variously translated Corresponding Member or Associate Member, .-Eastern Europe and China:"Academician" may also be a functional...
of the USSR Academy of Sciences first at the Department of Philosophy and then at the Department of Pure Mathematics (12 January 1929).
In the 1920s Luzin organized a famous research seminar at Moscow University. His doctoral students included some of the most famous Soviet mathematicians: Pavel Aleksandrov
Pavel Sergeevich Alexandrov
Pavel Sergeyevich Alexandrov , sometimes romanized Aleksandroff or Aleksandrov was a Soviet Russian mathematician...
, Nina Bari
Nina Bari
Nina Karlovna Bari was a Soviet mathematician known for her work on trigonometric series. She was killed by a train in the Moscow Metro, and her colleagues speculated that she committed suicide, prompted by the death of her mentor Nikolai Luzin ten years earlier, a man who may have been her lover....
, Aleksandr Khinchin
Aleksandr Yakovlevich Khinchin
Aleksandr Yakovlevich Khinchin was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory. He was born in the village of Kondrovo, Kaluga Governorate, Russian Empire. While studying at Moscow State University, he became one of the first followers...
, Andrey Kolmogorov
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
, Alexander Kronrod
Alexander Kronrod
Aleksandr Semenovich Kronrod was a Soviet mathematician and computer scientist, best known for the Gauss-Kronrod quadrature formula which he published in 1964. Earlier his computations informed theoretical physics...
, Mikhail Lavrentyev
Mikhail Lavrentyev
Mikhail Alekseevich Lavrentyev or Lavrentiev was an outstanding Soviet mathematician and hydrodynamicist.-Biography:...
, Alexey Lyapunov
Alexey Lyapunov
Alexey Andreevich Lyapunov was a Soviet mathematician and early pioneer of computer science. One of the founders of cybernetics, Lyapunov was member of the Soviet Academy of Sciences and a specialist in the fields of real variable function theory, mathematical problems of cybernetics, set theory,...
, Lazar Lyusternik
Lazar Lyusternik
Lazar Aronovich Lyusternik was a Soviet mathematician....
, Pyotr Novikov, Lev Schnirelmann
Lev Schnirelmann
Lev Genrikhovich Schnirelmann , also Shnirelman, Shnirel'man was a Soviet mathematician who sought to prove Goldbach's conjecture...
and Pavel Urysohn
Pavel Samuilovich Urysohn
Pavel Samuilovich Urysohn, Pavel Uryson was a Jewish mathematician who is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology...
.
Research work
The first significant result of Nikolay Luzin was a construction of an almost everywhere divergent trigonometric series with monotonically converging to zero coefficients (1912). This example disproved the Pierre FatouPierre Fatou
Pierre Joseph Louis Fatou was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory...
conjecture and was unexpected to most mathematicians at that time.
His Ph.D. thesis entitled Integral and trigonometric series (1915) made a large impact on the subsequent development of the metric theory of functions. A set of problems formulated in this thesis for a long time attracted attention from mathematicians. For example, the first problem in the list, on the convergence of the Fourier series for a square-integrable function, was solved by Lennart Carleson
Lennart Carleson
Lennart Axel Edvard Carleson is a Swedish mathematician, known as a leader in the field of harmonic analysis.-Life:He was a student of Arne Beurling and received his Ph.D. from Uppsala University in 1950...
in 1966.
In the theory of boundary properties of analytic functions he proved an important result on the invariance of sets of boundary points under conformal mappings (1919).
Luzin was one of the founders of the descriptive set theory
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
. He also made contributions to complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, theory of differential equations, and numerical methods.
The Luzin affair of 1936
On 21 November 1930 the declaration of the “initiative group” of the Moscow Mathematical SocietyMoscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
which consisted of former Luzin's students Lazar Lyusternik and Lev Shnirelman along with Alexander Gelfond
Alexander Gelfond
Alexander Osipovich Gelfond was a Soviet mathematician, author of Gelfond's theorem.-Biography:Alexander Gelfond was born in St Petersburg, Russian Empire in the family of a professional physician and amateur philosopher Osip Isaakovich Gelfond. He entered the Moscow State University in 1924,...
and Lev Pontryagin claimed that “there appeared active counter-revolutionaries among mathematicians.” Some of these mathematicians were pointed out, including the advisor of Luzin, Dmitri Egorov
Dmitri Egorov
- External links :...
. In September 1930, Dmitri Egorov was arrested on the basis of his religious beliefs. After arrest, he left the position of the director of the Moscow Mathematical Society. The new director became Ernst Kolman. As a result, Luzin left the Moscow Mathematical Society and Moscow State University. Egorov died on 10 September 1931, after a hunger strike
Hunger strike
A hunger strike is a method of non-violent resistance or pressure in which participants fast as an act of political protest, or to provoke feelings of guilt in others, usually with the objective to achieve a specific goal, such as a policy change. Most hunger strikers will take liquids but not...
initiated in prison. In 1931, Ernst Kolman made the first complaint against Luzin.
In July–August 1936, Luzin was criticised in Pravda
Pravda
Pravda was a leading newspaper of the Soviet Union and an official organ of the Central Committee of the Communist Party between 1912 and 1991....
in a series of anonymous articles whose authorship later was attributed to Ernst Kolman. It was alleged that Luzin published “would-be scientific papers,” “felt no shame in declaring the discoveries of his students to be his own achievements,” stood close to the ideology of the “black hundreds,” orthodoxy, and monarchy
Monarchy
A monarchy is a form of government in which the office of head of state is usually held until death or abdication and is often hereditary and includes a royal house. In some cases, the monarch is elected...
“fascist-type modernized but slightly.” Luzin was tried at a special hearing of the Commission of the Academy of Sciences of the USSR, which endorsed all accusations of Luzin as an enemy under the mask of a Soviet citizen. One of the complaints was that he published his major results in foreign journals. This method of political insinuations and slander was used against the old Muscovite professorship many years before the article in Pravda.
The political offensive against Luzin was launched not only by Joseph Stalin
Joseph Stalin
Joseph Vissarionovich Stalin was the Premier of the Soviet Union from 6 May 1941 to 5 March 1953. He was among the Bolshevik revolutionaries who brought about the October Revolution and had held the position of first General Secretary of the Communist Party of the Soviet Union's Central Committee...
's repressive ideological authorities, but also by a group of Luzin's students headed by Pavel Alexandrov, who may have been pressured to it by threats to reveal his homosexual relationship with Andrey Kolmogorov
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
. Although the Commission convicted Luzin, he was neither expelled from the Academy nor arrested. There has been some speculation about why his punishment was so much milder than that of most other people condemned at that time, but the reason for this does not seem to be known for certain. Historian of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
A.P. Yushkevich speculated that at the time, Stalin was more concerned with forthcoming Moscow Trials
Moscow Trials
The Moscow Trials were a series of show trials conducted in the Soviet Union and orchestrated by Joseph Stalin during the Great Purge of the 1930s. The victims included most of the surviving Old Bolsheviks, as well as the leadership of the Soviet secret police...
of Lev Kamenev
Lev Kamenev
Lev Borisovich Kamenev , born Rozenfeld , was a Bolshevik revolutionary and a prominent Soviet politician. He was briefly head of state of the new republic in 1917, and from 1923-24 the acting Premier in the last year of Lenin's life....
, Grigory Zinoviev
Grigory Zinoviev
Grigory Yevseevich Zinoviev , born Ovsei-Gershon Aronovich Radomyslsky Apfelbaum , was a Bolshevik revolutionary and a Soviet Communist politician...
and others, and that the eventual fate of Luzin was of little interest to him. Still, Luzin was never rehabilitated
Rehabilitation (Soviet)
Rehabilitation in the context of the former Soviet Union, and the Post-Soviet states, was the restoration of a person who was criminally prosecuted without due basis, to the state of acquittal...
even after Stalin's death.
External links
- Lorentz G.G., Mathematics and Politics in the Soviet Union from 1928 to 1953
- Kutateladze S.S., The Tragedy of Mathematics in Russia
- Kutateladze S.S., Roots of Luzin's Case