Search Results for Luzin


Biographies

  1. Nikolai Luzin (1883-1950)
    • Nikolai Nikolaevich Luzin .
    • Nikolai Nikolaevich Luzin was born in Irkutsk, and his birthplace was not, as is incorrectly stated in a number of sources, Tomsk.
    • One might expect that Nikolai would have shown a special talent for mathematics at the Gymnasium, but this was far from the case ([',' P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.','15] and [',' P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • For Luzin this was torture.
    • Fortunately the tutor was a talented young man who quickly discovered that, despite Luzin's poor performance in mathematics, he could solve hard problems but often using a novel method that the tutor had never seen before.
    • Soon the tutor had shown Luzin that mathematics was not a subject where one had to learn long lists of facts, but a topic where creativity and imagination played a major role.
    • In 1901 Luzin left the Gymnasium and at this time his father sold his business and the family moved to Moscow.
    • There Luzin entered the Faculty of Physics and Mathematics at Moscow University intending to train to become an engineer.
    • At first Luzin lived in the new family home in Moscow, but Luzin's father began to gamble on the stock exchange with the money he had made from the sale of his business.
    • The family soon hit hard times as Luzin's father lost all their savings and the family had to leave their home.
    • Luzin, together with a friend, moved into a room owned by the widow of a doctor.
    • Luzin stayed on by himself in the room but he clearly got on well with the owners since he later, in 1908, married the widow's daughter.
    • At Moscow University Luzin studied under Bugaev, learning from him the theory of functions which was to influence greatly the direction his research would eventually take.
    • However, although Luzin appeared to lack talent in mathematics, one of his teachers Egorov spotted his great talent, invited him to his home, and began to set him hard problems.
    • This had a major effect on Luzin, who was a close friend of Florensky, as we shall describe below.
    • After graduating in the autumn of 1905 Luzin seemed unsure whether to devote himself to mathematics.
    • In fact Luzin's crisis had hit him in the spring of 1905 and, on 1 May 1906, Luzin wrote to Florensky from Paris where Egorov had sent him five months earlier in an attempt to get him through the crisis (see [',' C E Ford, The influence of P A Florensky on N N Luzin, Historia Mathematica 25 (1998), 332-339.','9]):- .
    • Luzin was not only upset by seeing the prostitutes, he also says in the letter how he had been affected by the 'terrible days' of the 1905 Revolution.
    • There are letters from Egorov at this time pleading with Luzin not to give up mathematics.
    • After returning to Russia, Luzin studied medicine and theology as well as mathematics.
    • However in April 1908 he wrote of the joy he was finding in number theory (see [',' C E Ford, The influence of P A Florensky on N N Luzin, Historia Mathematica 25 (1998), 332-339.','9]):- .
    • Largely Luzin's crisis seems to have been solved by Florensky to whom Luzin wrote in July 1908:- .
    • His interest in mathematics slowly returned but it was not until 1909 that Luzin seems to have finally committed himself completely to mathematics.
    • In 1910 Luzin travelled abroad visiting Gottingen where he was influenced by Edmund Landau.
    • However, the work was of fundamental importance as is stated in [',' P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.','15] and [',' P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • The influence of Luzin's dissertation on the future development of the theory of functions cannot be overestimated.
    • In 1914 Luzin and his wife separated for a short time and again Florensky seems to have helped them through the difficult time.
    • He wrote to Luzin's wife (see [',' C E Ford, The influence of P A Florensky on N N Luzin, Historia Mathematica 25 (1998), 332-339.','9]):- .
    • Florensky seems to have given good advice since Luzin and his wife returned to a successful marriage.
    • In 1917 Luzin was appointed as Professor of Pure Mathematics at Moscow University just before the Revolution.
    • The Revolution caused Luzin to rethink some of the same thoughts as he had done at the time of his crisis and again he exchanged letters with Florensky.
    • Over the next ten years Luzin and Egorov built up an impressive research group at the University of Moscow which the students called 'Luzitania'.
    • Whereas Egorov was reserved and formal, Luzin was extroverted and theatrical, inspiring real devotion among these students and young colleagues.
    • inspired by Luzin.
    • Luzin's main contributions are in the area of foundations of mathematics and measure theory.
    • From 1917 onwards, Luzin studied descriptive set theory.
    • He stated the fundamental problem ([',' P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.','15] and [',' P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • Much of Luzin's work on set theory involved the study of effective sets, that is sets which can be constructed without the axiom of choice.
    • Keldysh describes this work in [',' L V Keldysh, The ideas of N N Luzin in descriptive set theory, Russian Mathematical Surveys 29 (5) (1974), 179-193.','12] and [',' L V Keldysh, The ideas of N N Luzin in descriptive set theory (Russian), Uspekhi Mat.
    • Luzin proceeded from the point of view of the French school (Borel, Lebesgue), which greatly influenced him.
    • But whereas the French had analysed set-theoretical constructions carried out with the help of the Axiom of Choice, Luzin went considerably further and considered difficulties arising within the theory of effective sets.
    • Luzin's school was at its peak during the years 1922 to 1926, but then Luzin concentrated on writing his second monograph on the theory of functions and spent less time with the young mathematicians in the school.
    • In 1927 Luzin was elected as a member of the USSR Academy of Sciences.
    • In 1931 Luzin himself turned to a new area when he began to study differential equations and their application to geometry and to control theory.
    • His work in this area led him to study the bending of surfaces which is described in [',' P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.','15] and [',' P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • up to 1938, when Luzin, by means of a subtle analysis of these equations, established that the existence of a principal base is rather rare.
    • It has been drawn to our attention by [',' L Mazliak, Private communication','19], that in 1936, Luzin was the victim of a violent political campaign organized by the Soviet authorities through the newspaper Pravda.
    • The aim was obviously to get rid of Luzin as a representative of the old pre-Soviet mathematical school of Moscow: his master, Egorov, had been himself the victim of such a campaign in 1930 (based on his religious sympathies) and died shortly after in 1931 in despair and misery.
    • A contemporary record of the "Luzin affair" has been miraculously preserved and recently edited in Moscow by Demidov and Levchin [',' S S Demidov and B V Levshin, Delo akademika Nikolaya Nikolaevicha Luzina (the academician N N Luzin affair) (Moscow, 1999).','3], [',' F Smithies, Review of Reference [3] above, Mathematical Reviews, 2001k:01066.
    • It shows that Luzin had had a narrow escape from a tragic fate as the Soviet authorities may have feared the international consequences of a too strong attack on a scientist so famous abroad.
    • The main visible consequence of the Luzin affair was that, from this precise moment, Soviet mathematicians began to publish almost exclusively in Soviet journals and in Russian.
    • Luzin always had an interest in the history of mathematics and late in his career he wrote important articles on Newton and on Euler.
    • As a teacher his remarkable talents are described by Kuznetsov ([',' P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.','15] or [',' P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • Keldysh and Novikov wrote in [',' L V Keldysh and P S Novikov, The work of N N Luzin in descriptive set theory (Russian), Uspekhi Mat.
    • Thanks to his exceptional intuition and his ability to see deeply into the heart of a question, Luzin frequently predicted mathematical facts whose proof turned out to be possible only after many years and required the creation of completely new mathematical methods.
    • The 1936 Luzin affair .
    • Honours awarded to Nikolai Luzin .
    • 2.nPlanetary featuresnCrater Luzin on Mars .
    • http://www-history.mcs.st-andrews.ac.uk/Biographies/Luzin.html .

  2. Mikhail Yakovlevich Suslin biography
    • Beginning in session 1914-15, Suslin began to work with Nikolai Nikolaevich Luzin who had just returned to Moscow after studying at Gottingen for several years under Edmund Landau.
    • Suslin was not the only student joining Luzin's group, for D E Menshov, A Ya Khinchin and P S Aleksandrov also joined.
    • Luzin suggested that his students work on Borel sets and asked Suslin to read Henri Lebesgue's 1905 paper Sur les functions representables analytiquement Ⓣ.
    • At the same time Suslin was working with P S Aleksandrov on a problem suggested by Luzin, namely investigating whether the converse of a result found by Aleksandrov was true.
    • In March 1917 Luzin requested that Suslin carry on his studies so that he might gain a professorship.
    • Luzin wrote again in September 1917 requesting a studentship to support him during the two years.
    • However, the Russian Revolution was now causing problems for everyone working in Moscow and Luzin decided that he would be able to work better in a quieter place [',' P S Aleksandrov, Pages from an autobiography, Russian Math.
    • In 1918 Luzin moved for a while to Ivanovo (which was then still called Ivanovo-Voznesensk).
    • Acting on his advice, A Ya Khinchin, D E Menshov and M Ya Suslin also moved there and, like Luzin, taught at the Ivanovo Polytechnic Institute.
    • A recommendation from Luzin was expected.
    • Until the end of Luzin's life a portrait of Suslin stood on his desk, the only portrait of Suslin that I have seen.

  3. Nina Bari biography
    • In the Moscow School of Mathematics she came under the influence of Nikolai Nikolaevich Luzin but he was only one of a number of world-class mathematicians teaching at the university at this time, including Sergei Alekseevich Chaplygin, Dimitri Fedorovich Egorov, Vyacheslaw Vassilievich Stepanov and Nikolai Egorovich Zhukovsky.
    • This was the period of intensive development of the Moscow real variable school, headed by N N Luzin, under whose guidance Nina Bari started her own mathematical work while still an undergraduate.
    • To see Luzin in those years was to see a display of what is called an inspired relationship to science.
    • Bari began research at the Institute, with Luzin as her thesis advisor, but continued to hold her teaching posts.
    • In addition to support from Luzin, she was strongly influenced by Dmitrii Evgenevich Menshov who had undertaken research with Luzin but returned to Moscow State University as a lecturer in 1922.
    • The vigorous school at Moscow State University headed by Luzin began to run out of steam in the last few years of the 1920s as he concentrated on writing monographs.
    • She edited the complete works of Luzin and was the editor of two important mathematics journals.
    • It has been claimed that this was suicide due to depression caused by Luzin's death eleven years earlier.

  4. Dmitrii Menshov biography
    • Perhaps the most significant event for Menshov, however, was that Luzin returned from Gottingen to Moscow in the autumn of 1914 and began to lecture on functions of a real variable.
    • Menshov attended Luzin's lecture course, and when Luzin posed the open problem of whether the Denjoy integral and the Borel integral were equivalent, he was able to solve the problem.
    • He showed Luzin his solution to the problem that Luzin had just posed and before the end of 1914 the two had begun a firm mathematical friendship.
    • Luzin quickly established a School of Mathematics at Moscow University and Menshov became one of his fist research students along with P S Aleksandrov, M Ya Suslin, and A Ya Khinchin.
    • Menshov's first degree was awarded in 1916 for the thesis which he wrote on The Riemann theory of trigonometric series which was examined by Egorov and Luzin.
    • At this time Luzin and other members of his research school were in Ivanovo so Menshov was certainly in the mainstream of the exciting mathematics that was being developed.

  5. Pavel Aleksandrov biography
    • In Aleksandrov's second year of study he came in contact with Luzin who had just returned to Moscow.
    • After Luzin's lecture I turned to him for advice on how best to continue my mathematical studies and was struck most of all by Luzin's kindness to the man addressing him - an 18-year old student ..
    • I then became a student of Luzin, during his most creative period ..
    • To see Luzin in those years was to see a display of what is called an inspired relationship to science.
    • After Aleksandrov's great successes Luzin did what many a supervisor might do, he realised that he had one of the greatest mathematical talents in Aleksandrov so he thought that it was worth asking him to try to solve the biggest open problem in set theory, namely the continuum hypothesis.
    • Luzin and Egorov had built up an impressive research group at the University of Moscow which the students called 'Luzitania' and they, together with Privalov and Stepanov, were very welcoming to Aleksandrov on his return.
    • In fact Aleksandrov always included Emmy Noether and Hilbert among his teachers, as well as Brouwer in Amsterdam and Luzin and Egorov in Moscow.

  6. Mikhail Alekseevich Lavrent'ev biography
    • It was during this trip to Gottingen that Aleksii Mikhailovich met another Russian, Nikolai Nikolaevich Luzin, who was studying there with Edmund Landau.
    • Aleksii Mikhailovich and Nikolai Nikolaevich became good friends and, after returning to Russia, Luzin often visited the Lavrent'ev home in Kazan.
    • Luzin had a very strong influence on Aleksii Mikhailovich's young son.
    • At Moscow University, Lavrent'ev had been taught by his father's friend Nikolai Nikolaevich Luzin among others and, after graduating, he continued to undertake research on set theory and topology advised by Luzin.
    • He studied under Luzin from 1922 to 1926, then in 1927, after successfully defending his candidate's thesis on set theory, he was sent to France to study in Paris for six months.

  7. Lyudmila Vsevolodovna Keldysh biography
    • Nikolai Nikolaevich Luzin gave a lecture in Ivanovo-Voznesensk which Lyudmila Keldysh and other high school pupils attended.
    • This lecture firmly established in Keldysh's mind that she wanted to study mathematics and, if possible, become a professional mathematician like Luzin.
    • She had joined Luzin's research seminar in 1923, the same year as Petr Sergeevich Novikov joined the research group.
    • Her name became known after her initial result, which was first published in 1930 in Luzin's lecture notes [Lecons sur les ensembles analytiques et leurs applications Ⓣ(1930)].
    • She continued working in Luzin's research group and also began working at the V A Steklov Mathematical Institute of the USSR Academy of Sciences as soon as it moved from St Petersburg to Moscow around 1934.

  8. Charles De la Vallée Poussin (1866-1962)
    • In 1930 Vallee Poussin was revising his 1916 tract Lebesgue integrals: Set functions: Baire classes when Luzin's Lectures on analytic sets and their applications was published.
    • The paper [',' F A Medvedev, Letters of C de la Vallee-Poussin to N N Luzin (Russian), Istor.-Mat.
    • 27 (1983), 301-312.','5] contains three letters written by Vallee Poussin to Luzin dated 4 February 1933, 8 March 1933 and 21 March 1933.
    • Vallee Poussin comments in these letters on the fact, which is of great interest to him, that Luzin used slightly different classifications of the same sets as he had studied.
    • He gives high praise to Luzin's book.

  9. Lennart Carleson biography
    • In 1913 Luzin conjectured that if a function f is square Lebesgue integrable then the Fourier series of f converges pointwise to f almost everywhere.
    • Kolmogorov proved results in 1928 which seemed to suggest that Luzin's conjecture must be false but Carleson amazed the world of mathematics when he proved Luzin's long-standing conjecture in 1966.
    • The citation emphasizes not only Carleson's fundamental scientific contributions, the best known of which perhaps are the proof of Luzin's conjecture on the convergence of Fourier series, the solutions of the corona problem and the interpolation problem for bounded analytic functions, the solution of the extension problem for quasiconformal mappings in higher dimensions, and the proof of the existence of 'strange attractors' in the Henon family of planar maps, but also his outstanding role as scientific leader and advisor.

  10. Ivan Ivanovich Privalov (1891-1941)
    • We should mention that Nikolai Nikolaevich Luzin, although seven years older that Privalov, was a student at the same time.
    • In 1911 he went to the University of Gottingen (with his friend Luzin) for the summer semester and there he attended lectures by David Hilbert, Felix Klein, and Edmund Landau.
    • Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals.
    • Sergei Alekseevich Chaplygin and Nikolai Nikolaevich Luzin explained Privalov's approach to research (see for example [',' P I Kuznetsov and E D Solomentsev, Ivan Ivanovich Privalov (on the ninetieth anniversary of his birth), Russian Math.

  11. Sergei Alekseevich Chaplygin biography
    • On 3 July 1936, Nikolai Nikolaevich Luzin, Professor of Pure Mathematics at Moscow University, was the victim of a violent political campaign organized by the Soviet authorities through the newspaper Pravda.
    • The article claimed that Luzin combined:- .
    • The article about Luzin is completely outrageous: Supposing that he committed the sin of misjudging some applicant for a scientific degree or title, but how is it possible to jump to the conclusion of sabotage from that?! ..
    • There remains the critical evaluation of Luzin's contributions.

  12. Wacaw Sierpiski (1882-1969)
    • However Egorov and Luzin heard that he had been interned and arranged for him to be allowed to go to Moscow.
    • Sierpiński spent the rest of the war years in Moscow working with Luzin.
    • Sierpiński continued to collaborate with Luzin on investigations of analytic and projective sets.

  13. Dimitri Fedorovich Egorov (1869-1931)
    • Nikolai Nikolaevich Luzin was Egorov's first student and became a member of the school Egorov created in Moscow dealing with functions of a real variable.
    • Egorov and Luzin are now considered as joint founders of the influential Moscow School of Pure Mathematics.
    • In 1931 the Society put the following editorial into their journal (see for example [',' A L Shields, Luzin and Egorov, Part 2, The Mathematical intelligencer 11 (2) (1989), 5-8.','14]):- .

  14. Vyacheslaw Vassilievich Stepanov (1889-1950)
    • He was supervised there by Dimitri Fedorovich Egorov but also influenced by Nikolai Nikolaevich Luzin who was a student of Egorov, then from 1909 an assistant lecturer.
    • Luzin, who was a little ahead of Stepanov, had travelled abroad visiting Gottingen where he had been inspired by Edmund Landau.
    • He returned to Moscow in 1915 and, much influenced by Egorov and Luzin, he worked on periodic functions and differential equations.

  15. Pavel Urysohn (1898-1924)
    • However his interest in physics soon took second place for after attending lectures by Luzin and Egorov at the University of Moscow he began to concentrate on mathematics.
    • Luzin was a dynamic mathematician and it was he who persuaded Urysohn to stay on in order to study for a doctorate during 1919-21.

  16. Maurice Fréchet (1878-1973)
    • Let us record just a few of the names: Pavel Sergeevich Aleksandrov, Rene-Louis Baire, L E J Brouwer, Bela Kerekjarto, Kazimierz Kuratowski, Henri Lebesgue, Paul Levy, Nikolai Nikolaevich Luzin, P Mahlo, Paul Montel, Frigyes Riesz, Wacław Sierpiński, Pavel Samuilovich Urysohn, Edwin Wilson, and Stanisław Zaremba.
    • In the earliest of these letters the young Russian scholars express their gratitude to Frechet for having created the theory of abstract spaces on which their earliest investigations were based and cite as the source of their first published works problems posed by N Luzin in his analysis seminar at Moscow University.

  17. Lev Shnirelman (1905-1938)
    • There he was taught by outstanding mathematicians such as Khinchin, Luzin and Urysohn.
    • He was advised by Luzin while working for his postgraduate degrees.

  18. Andrey Kolmogorov biography
    • Luzin and Egorov were running their impressive research group at this time which the students called 'Luzitania'.
    • Kolmogorov graduated from Moscow State University in 1925 and began research under Luzin's supervision in that year.

  19. Petr Sergeevich Novikov (1901-1975)
    • He graduated in 1925 then, remaining at Moscow University, he undertook research under Luzin's supervision.
    • After early work on set theory, influenced by Luzin and his school, he began to publish results in mathematical physics from 1938.

  20. Abraham Plessner biography
    • In Moscow, he joined the research group of Nikolai Nikolaevich Luzin.
    • In 1936, Luzin was the victim of a violent political campaign organized by the Soviet authorities through the newspaper Pravda.

  21. Adolph Pavlovich Yushkevich biography
    • They were taught mathematics by Egorov, Luzin and other outstanding mathematicians.

  22. Leonid Vital'evich Kantorovich biography
    • 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.

  23. Elias Stein biography
    • He held this position for two years during which time a whole series of his papers appeared in print: Interpolation of linear operators (1956), Functions of exponential type (1957), Interpolation in polynomial classes and Markoff's inequality (1957), Note on singular integrals (1957), (with G Weiss) On the inerpolation of analytic families of operators action on Hpspaces (1957), (with E H Ostrow) A generalization of lemmas of Marcinkiewicz and Fine with applications to singular integrals (1957), A maximal function with applications to Fourier series (1958), (with G Weiss) Fractional integrals on n-dimensional Euclidean space (1958), (with G Weiss) Interpolation of operators with change of measures (1958), Localization and summability of multiple Fourier series (1958), and On the functions of Littlewood-Paley, Luzin, Marcinkiewicz (1958).

  24. Boris Vladimirovich Gnedenko biography
    • This town, east of Moscow, was a centre for the textile industry and it had figures highly in the history of mathematics with people such at Luzin and Khinchin teaching at the polytechnic there.

  25. Antoni Zygmund biography
    • Among other topics, he worked on summability of numerical series, summability of general orthogonal series, trigonometric integrals, sets of uniqueness, summability of Fourier series, differentiability of functions, smooth functions, approximation theory, absolutely convergent Fourier series, multipliers and translation invariant operators, conjugate series and Taylor series, lacunary trigonometric series, series of independent random variables, random trigonometric series, the Littlewood-Paley, Luzin and Marcinkiewicz functions, boundary values of analytic and harmonic functions, singular integrals, partial differential equations and interpolation operators.

  26. Stanisaw Saks (1897-1942)
    • We should mention, in addition, that he was also influenced by Luzin's work.

  27. Aleksandr Yakovlevich Khinchin (1894-1959)
    • At university in Moscow Khinchin worked with Luzin and others.

  28. Boris Nikolaevich Delone biography
    • In this new Mathematics Institute, Delone became a colleague of Sergei Bernstein, N N Luzin, V I Smirnov, R O Kuzmin, N S Koshlyakov, N Y Kochin, S L Sobolev and D K Faddeev.

  29. Anatolii Asirovich Goldberg biography
    • Aleksandr Sergeevich Kovanko, who we just mentioned, had been a student of Dimitri Fedorovich Egorov and had participated in Nikolai Nikolaevich Luzin's famous school at the University of Moscow in the 1920s.

  30. Ivan Matveevich Vinogradov biography
    • During his time as head of the Steklov Institute, Vinogradov discussed with Luzin the research areas which should be emphasised in the Soviet mathematical Institutes.

  31. Allen Shields biography
    • Soon after George Piranian returned from his leave, he began working with Shields and they published the joint paper The sets of Luzin points of analytic functions (1957).

  32. Christian Goldbach (1690-1764)
    • V (Moscow, 1966), 31-34.','6], [',' N N Luzin, Introduction to L Euler’s letters to C Goldbach (Russian), Istor.-Mat.


History Topics

  1. function concept
    • Luzin points out in [',' N Luzin, Function I, Amer.
    • Monthly 105 (1) (1998), 59-67.','17] and [',' N Luzin, Function II, Amer.

  2. References for function concept
    • N Luzin, Function I, Amer.
    • N Luzin, Function II, Amer.

  3. References for 20th century time
    • F A Medvedev, N N Luzin on non-Archimedean time (Russian), Istor.-Mat.


Societies etc

  1. Trinity Cambridge Mathematical Society
    • Nikolai Luzin, in 1930, conjectured that it was impossible to dissect a square into a finite number of squares all of different sizes.


Honours

  1. International Congress Speaker
    • Nikolai Nikolaevich Luzin, Sur les voies de le theorie des ensembles.

  2. Planetary features
    • Luzin .


References

  1. References for Nikolai Luzin
    • References for Nikolai Luzin .
    • Biography and analysis of Luzin's work, Collected Works of Luzin 3 Vols (Moscow, 1953-59).
    • S S Demidov and B V Levshin, Delo akademika Nikolaya Nikolaevicha Luzina (the academician N N Luzin affair) (Moscow, 1999).
    • N K Bari and L A Lyusternik, The work on N N Luzin on the metric theory of functions (Russian), Uspekhi Mat.
    • S S Demidov, A N Parshin and S M Polovinkin, On the correspondence of N N Luzin with P A Florensky (Russian), Istor.-Mat.
    • S S Demidov, A N Parshin, S M Polovinkin and P V Florensky, The correspondence of N N Luzin with P A Florensky (Russian), Istor.-Mat.
    • V S Fedorov, The work of N N Luzin on the theory of functions of a complex variable (Russian), Uspekhi Mat.
    • C E Ford, The influence of P A Florensky on N N Luzin, Historia Mathematica 25 (1998), 332-339.
    • V K Goltsmann and P I Kuznetsov, The work of N N Luzin on differential equations and numerical methods (Russian), Uspekhi Mat.
    • L V Keldysh, The ideas of N N Luzin in descriptive set theory, Russian Mathematical Surveys 29 (5) (1974), 179-193.
    • L V Keldysh, The ideas of N N Luzin in descriptive set theory (Russian), Uspekhi Mat.
    • L V Keldysh and P S Novikov, The work of N N Luzin in descriptive set theory (Russian), Uspekhi Mat.
    • P I Kuznetsov, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 195-208.
    • P I Kuznetsov, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • M A Lavrentev, Nikolai Nikolaevich Luzin, Russian Mathematical Surveys 29 (5) (1974), 173-178.
    • M A Lavrentev, Nikolai Nikolaevich Luzin (Russian), Uspekhi Mat.
    • E R Phillips, Nikolai Nikolaevich Luzin and the Moscow school of the theory of functions, Historia Mathematica 5 (1978), 275-305.
    • A L Shields, Luzin and Egorov, The Mathematical intelligencer 9 (4) (1987), 24-27.
    • A L Shields, Luzin and Egorov, Part 2, The Mathematical intelligencer 11 (2) (1989), 5-8.

  2. References for Dimitri Fedorovich Egorov
    • P S Aleksandrov, F A Medvedev and A P Juskevic, Letters of D F Egorov to N N Luzin (Russian), Istor.-Mat.
    • V I Bogachev, On the history of the discovery of the Egorov and Luzin theorems (Russian), Istor.-Mat.
    • A L Shields, Luzin and Egorov, The Mathematical intelligencer 9 (4) (1987), 24-27.
    • A L Shields, Luzin and Egorov, Part 2, The Mathematical intelligencer 11 (2) (1989), 5-8.

  3. References for Arnaud Denjoy
    • M Luzin, A letter to Arnaud Denjoy in 1926 (Polish), Wiadom.
    • F A Medvedev (trans.), N N Luzin's letters to A Denjoy, Istor.-Mat.
    • A P Yushkevich, Letters of A Denjoy to N N Luzin (Russian), Istor.-Mat.

  4. References for Ivan Matveevich Vinogradov
    • N N Luzin, A letter from N N Luzin to I M Vinogradov (Russian), With comments by M I Kratko and G A Savina, Ocherki Istor.

  5. References for Otto Yulyevich Schmidt
    • S S Demidov, A letter of N N Luzin to O Yu Shmidt (Russian), Istor.-Mat.
    • S S Demidov, Lettre de N N Luzin a O Yu Schmidt, in Proceedings of the seminar on the history of mathematics 7 (Inst.

  6. References for Sergei Alekseevich Chaplygin
    • K K Rybnikov, N N Luzin, O Yu Shmidt, and S A Chaplygin - instructors at Moscow Forestry Technical Institute (Russian), Istor.-Mat.

  7. References for Leonid Vital'evich Kantorovich
    • Yu G Reshetnyak and S S Kutateladze, N N Luzin's letter to L V Kantorovich (Russian), Vestnik.

  8. References for Wacaw Sierpiski
    • G Sinkiewicz, On the collaboration of Waclaw Sierpinski and Nikolai Luzin (Polish), Kwart.

  9. References for Maurice Fréchet
    • A P Yushkevich, A letter of N N Luzin to M.

  10. References for Charles De la Vallée Poussin
    • F A Medvedev, Letters of C de la Vallee-Poussin to N N Luzin (Russian), Istor.-Mat.

  11. References for Christian Goldbach
    • N N Luzin, Introduction to L Euler's letters to C Goldbach (Russian), Istor.-Mat.

  12. References for Aleksei Krylov
    • N S Ermolaeva, New materials for the biography of N N Luzin (Russian), Istor.-Mat.


Additional material

  1. The 1936 Luzin affair
    • The 1936 Luzin affair .
    • [The case of Academician Nikolai Nikolaevich Luzin] .
    • This book gives a full account of the "Luzin affair" of 1936, when an attempt was made to discredit the Russian mathematician Nikolai Luzin and have him expelled from the Academy of Sciences.
    • The authors describe the background of Moscow mathematics from 1920 onwards; an important school, in real-variable theory, was led by Luzin, and was nicknamed ("Luzitania").
    • The Egorov affair alarmed Luzin, who had only recently returned from a long trip abroad; he gave up his university work, took refuge in the Central Aero-Hydrodynamics Institute in Leningrad, and worked in the Steklov Institute there.
    • Kolman attacked Luzin in print, associating him with Egorov and other reactionaries, and alleged that he was tainted with Fascism; this denunciation prevented Luzin from going to the international congress at Zurich in 1932.
    • Very much later an OGPU file was discovered alleging that Luzin had met Hitler and received instructions from him.
    • The attack on Luzin began after he was asked to report on some school tests, and reported in an invited article in Izvestiya on 27 June 1936 that he found the standard surprisingly high.
    • An anonymous article on 3 July, almost certainly by Kolman, accused Luzin of .
    • It also described Luzin as "an enemy in a Soviet mask".
    • On the same day a meeting of members of the Steklov Institute passed a vote of censure on Luzin, and asked the Presidium of the Academy to examine Luzin's position as head of the commission on the qualifications of prospective members.
    • A meeting of Moscow mathematicians on 7 July passed an anti-Luzin resolution.
    • The tone of the first three meetings (7, 9 and 11 July) grew more and more aggressive towards Luzin; he was attacked by S.
    • Aleksandrov agreed that Luzin had taken over Suslin's work, but kept his criticisms on an ethical level, with no hint of political wrong-doing.
    • On the third day Sobolev raised the question of Luzin's exclusion from the Academy.
    • On the same day Luzin attended the meeting by invitation; he defended himself for publishing his theoretical work abroad, on the grounds that it had no immediate practical value; he also attacked Kolman's mathematical competence.
    • Luzin made a statement, promising to take account of the criticisms, and to publish primarily in the Soviet Union; his statement was received with understanding and sympathy.
    • At the sitting on 15 July, the tone was sympathetic to Luzin, who was defended by several members.
    • Krzhizhanovskii, as chairman, adhered closely to the formal resolution; he summarised the conclusion as saying that Luzin's behaviour was not on the level that should be expected from an Academician, and that he had been given a warning.
    • Pravda continued its anti-Luzin campaign in articles on 15 July and on 6 August, but they provoked little notice.
    • Luzin himself lost his university post and his role in selecting new members of the Academy, but remained an Academician.
    • Krylov and Luzin himself and some of the up-and-coming young men such as Aleksandrov, Sobolev and A.
    • Nevertheless, the Soviet mathematical community recovered remarkably rapidly from the Luzin affair.
    • http://www-history.mcs.st-andrews.ac.uk/Extras/Luzin.html .

  2. W H Young addresses ICM 1928
    • The main invited lectures were by D Hilbert, J Hadamard, U Puppini, E Borel, O Veblen, G Castelnuovo, W H Young, V Volterra, H Weyl, T von Karman, L Tonelli, L Amoroso, M Frechet, R Marcolongo, N Luzin, F Enriques, G D Birkhoff.


Quotations

  1. A quotation by Luzin
    • A quotation by Nikolai Luzin .


Famous Curves

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JOC/BS August 2001