Nikolai Luzin | |
|---|---|
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| Born | (1883-12-09)9 December 1883 |
| Died | 28 February 1950(1950-02-28) (aged 66) Moscow,Russian SFSR, Soviet Union |
| Citizenship | Russian Empire Soviet Union |
| Alma mater | Moscow State University |
| Known for | Contributions todescriptive set theory,mathematical analysis,point-set topology;Luzin's theorem,Lusin spaces,Luzin sets; |
| Scientific career | |
| Fields | Mathematician |
| Institutions | Moscow State University Steklov Mathematical Institute Polytechnical Institute Ivanovo-Voznesensk |
| Thesis | The Integral and Trigonometric Series (1915) |
| Doctoral advisor | Dmitri Egorov |
| Doctoral students | Pavel Alexandrov Nina Bari Aleksandr Khinchin Andrey Kolmogorov Alexander Kronrod Mikhail Lavrentyev Alexey Lyapunov Lazar Lyusternik Pyotr Novikov Lev Schnirelmann Pavel Urysohn |
Nikolai Nikolayevich Luzin (also spelledLusin; Russian:Никола́й Никола́евич Лу́зин,IPA:[nʲɪkɐˈlajnʲɪkɐˈlajɪvʲɪtɕˈluzʲɪn]ⓘ; 9 December 1883 – 28 February 1950) was a Soviet and Russianmathematician known for his work indescriptive set theory and aspects ofmathematical analysis with strong connections topoint-set topology. He was theeponym ofLuzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted hisset-theoretic orientation, and went on to apply it in other areas of mathematics.
He started studyingmathematics in 1901 atMoscow State University, where his advisor wasDmitri Egorov. He graduated in 1905.
Luzin underwent great personal turmoil in the years 1905 and 1906, when his materialistic worldview had collapsed and he found himself close to suicide. In 1906 he wrote toPavel Florensky, a former fellow mathematics student who was now studying theology: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 andTaylor 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. The correspondence between the two men continued for many years and Luzin was greatly influenced by Florensky's religious treatiseThe Pillar and Foundation of Truth (1908).[1]
From 1910 to 1914 Luzin studied atGöttingen, where he was influenced byEdmund Landau. He then returned to Moscow and received his Ph.D. degree in 1915. During theRussian Civil War (1918–1920) Luzin left Moscow for thePolytechnical Institute Ivanovo-Voznesensk (now calledIvanovo State University of Chemistry and Technology). He returned to Moscow in 1920.
In the 1920s Luzin organized a famous research seminar at Moscow State University. His doctoral students included some of the most famous Soviet mathematicians:Pavel Alexandrov,Nina Bari,Aleksandr Khinchin,Andrey Kolmogorov,Aleksandr Kronrod,Mikhail Lavrentyev,Alexey Lyapunov,Lazar Lyusternik,Pyotr Novikov,Lev Schnirelmann andPavel Urysohn.
On 5 January 1927 Luzin was elected as a corresponding member of theAcademy of Sciences of the Soviet Union and became afull member of the Academy of Sciences of the Soviet Union first at the Department of Philosophy and then at the Department of Pure Mathematics (12 January 1929). In 1929 he was elected as a member of thePolish Academy of Sciences and Letters inKraków.
Luzin's first significant result was a construction of an almost everywhere divergenttrigonometric series with monotonic convergence to zero coefficients (1912). This example disproved thePierre Fatou conjecture and was unexpected to most mathematicians at that time.
At approximately the same time, he proved what is now calledLusin's theorem inreal analysis.
His Ph.D. thesis titledIntegral and trigonometric series (1915) had 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 theFourier series for asquare-integrable function, came to be called Luzin's conjecture and was solved byLennart Carleson[2] in 1966 (Carleson's theorem).
In the theory of boundary properties ofanalytic functions he proved an important result on the invariance of sets of boundary points underconformal mappings (1919).
Luzin was one of the founders ofdescriptive set theory.[3] Together with his studentMikhail Suslin, he developed the theory ofanalytic sets.
He also made contributions tocomplex analysis, the theory ofdifferential equations, andnumerical methods.[4]
In a letter to M. Ya. Vygodsky dating from 1932, Luzin expresses sympathy with Vygodsky'sinfinitesimal approach to developing calculus. He mocks accusations ofbourgeois decadence against Vygodsky's textbook, and relates his own youthful experience with what he felt were unnecessary formal complications of the traditional development of analysis. Typical is his youthful reaction to his teachers' insistence that the derivative is a limit: "They won't fool me: it's simply the ratio of infinitesimals, nothing else." A recent study notes that Luzin's letter contained remarkable anticipations of modern calculus with infinitesimals.[5]
On 21 November 1930, the declaration of the "initiative group" of theMoscow Mathematical Society which consisted of Luzin's former students Lazar Lyusternik andLev Schnirelmann along withAlexander Gelfond andLev Pontryagin claimed that "there appeared active counter-revolutionaries among mathematicians".[6] Some of these mathematicians were pointed out, including the advisor of Luzin,Dmitri Egorov. In September 1930, Egorov was arrested on the basis of his religious beliefs. He then left the position of director of the Moscow Mathematical Society and was replaced byErnst Kolman. As a result, Luzin left the Moscow Mathematical Society and Moscow State University. Egorov died on 10 September 1931, after ahunger strike initiated in prison. In 1931, Kolman brought the first complaint against Luzin.
In 1936 theGreat Purge began. Millions of people were arrested or executed, including leading members of the intelligentsia. In July–August of that year, Luzin was criticized inPravda in a series of anonymous articles whose authorship later was attributed to Kolman.[7] 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", and stood close to the ideology of the "black hundreds", orthodoxy, andmonarchy "fascist-type modernized but slightly."[8] One of the complaints was that he published his major results in foreign journals.
The article triggered a special hearing on Luzin's case by the Commission of the Academy of Sciences of the Soviet Union, where the allegations were reviewed and formalized. At the hearing,Alexandrov,Lyusternik,Khinchin,Kolmogorov and some other students of Luzin accused him of plagiarism fromPyotr Novikov andMikhail Suslin and various forms of misconduct, which included denying promotions to Kolmogorov and Khinchin. According to some researchers, Alexandrov and Kolmogorov had been involved in a homosexual relationship in the 1930s, a fact the police used to pressure them into testifying against their former teacher.[9]Sergei Sobolev,Gleb Krzhizhanovsky andOtto Schmidt incriminated Luzin with charges of disloyalty to Soviet power. The methods of political insinuations and slander had been used against the old Muscovite professorship already several years before the article inPravda.
The hearings were completed in five sessions between July 7, 1936, and July 15, 1936, and people testifying, as well as the nature of accusations, changed from one session to another. In the initial session, the accusations were separated into accusations of scientific misconduct, which included plagiarism; accusations of professional misconduct, which mostly involved accusations of nepotism in promotions and reviews; and political accusations, which were the most serious. The initial review on July 7, which most prominently featured Alexandrov and Kolmogorov, concluded in a warning to Luzin regarding plagiarism while stressing the overall importance of his work, cleared him politically, yet recommended to relieve him of administrative duties.
However, this outcome did not seem to satisfy the instigators of the case, so that from the second hearing on, the nature of accusations shifted: now the primary focus was that Luzin published his papers extensively in France rather than in Soviet journals, and his pre-Soviet sympathies were brought to the forefront.
The special hearing of the Commission of the Academy of Sciences of the Soviet Union endorsed all accusations of Luzin as an "enemy under the mask of a Soviet citizen."[8] Although the Commission convicted Luzin, he was neither expelled from the academy nor arrested, but his department in theSteklov Institute was closed and he lost all his official positions. 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 mathematicsAdolph P. Yushkevich speculated that at the time,Stalin was more concerned with the forthcomingMoscow trials ofLev Kamenev,Grigory Zinoviev and others, whereas the eventual fate of Luzin was of a little interest to him.[10]
The 1936 decision of the Academy of Sciences was not canceled after Stalin's death.[8][11] The decision was finallyreversed on January 17, 2012.[12][13]
In 1976, Martian craterLuzin was named in his honor.[14]
Лузин, Н. Н. (1931)."О методе академика А. Н. Крылова составления векового уравнения".Известия Академии наук СССР. VII Seriya.7:903–958.JFM 57.1455.01.
is devoted to theKrylov subspace methodThe police soon learned of Kolmogorov and Alexandrov's homosexual bond, and they used that knowledge to obtain the behavior that they wished.
