Lusitania is a Moscow school of mathematics created by the famous Russian mathematician N. N. Luzin . Formed in the late 1910s - early 1920s , disintegrated in the mid -1930s, both due to natural mathematical development, and for external, including political, reasons (see the Luzin Case ).
Content
History
The first students to create the core of Lusitania were P. S. Alexandrov , M. Ya. Suslin , D. E. Menshov , A. Ya. Khinchin , and somewhat later, V. N. Veniaminov, P. S. Uryson , and A N. Kolmogorov , V. V. Nemytsky , N. K. Bari , S. S. Kovner, V. I. Glivenko, L. A. Lyusternik , L. G. Shnirelman . Later, in the mid-1920s, came P.S. Novikov , L.V. Keldysh , E.A. Selivanovsky. From the very beginning of Lusitania, close contact with it was maintained by older mathematicians, students of D. F. Egorov — I. I. Privalov and V. V. Stepanov , as well as the Polish mathematician Vaclav Sierpinski , who ended up in Moscow in 1915. [one]
According to the memoirs of L. A. Lyusternik, the very word "Lusitania" arose in the autumn of 1920 . [2] One of the main meeting places of the “Lusitans” was the apartment of N. N. Luzin (No. 8) in house No. 25 on Arbat Street (the house was preserved, a memorial plaque was installed).
| Lusitania was considered an "order" , whose "commander" was N. N. Luzin, and " grand master " - D. F. Egorov. Lusitania was a truly unique and unique collective of young people who lived not only an intense, intense mathematical life, but also a life that was directly joyful and fun. [3]P.S. Alexandrov |
The activities of Lusitania were overshadowed by two unexpected deaths: on October 21, 1919, M. Ya Suslin died of typhus in the native village of Krasavka (Saratov province), and on August 17, 1924, in France, during the bathing in the Atlantic Ocean, the “keeper of the secrets of Lusitania” died - P. S. Uryson. [3]
Scientific activity
The interests of the participants were concentrated mainly around some questions of analysis ( trigonometric series , integration theory), descriptive set theory, and function theory.
In set theory, the following fundamental results were obtained. When solving the problem of the cardinality of Borel sets , P. S. Aleksandrov showed that all Borel sets are obtained from closed sets using one new operation that he constructed. M. Ya. Suslin then proved that the class of sets obtained by this operation is much wider than Borel sets, and called them A-sets (in honor of Alexandrov).
One of the first striking results in the theory of trigonometric series belonged to A. N. Kolmogorov: he constructed an example of a summable function whose Fourier series diverges almost everywhere.
Later, many former members of Lusitania contributed to the development of other fields, for example, probability theory (A.N. Kolmogorov, A. Ya. Khinchin), geometry and topology (P.S. Aleksandrov, P.S. Uryson), algebra and logic (A. N. Kolmogorov, P. S. Novikov), calculus of variations and functional analysis (L. A. Lyusternik) and others. The Luzin school had a tremendous impact on the formation of Soviet mathematics. Among its former participants and their students, a huge number of outstanding mathematicians, this is schematically depicted in the form of the so-called "Luzin tree." [four]
The atmosphere of communication
Despite the fact that the existence of Lusitania coincided with the general devastation in the country and the most difficult period in the history of Moscow University, the atmosphere of this school was characterized by humor, theatricality and the spirit of the mystery. In his memoirs, L. A. Lyusternik calls this "intellectual mischief." [5] [6]
For example, in Lusitania, a hierarchy of members was introduced using the so-called " Alephs " (a letter traditionally used to denote power in set theory ). Each entrant was given the title of "Aleph Zero." For each achievement, a unit was added to the index. P.S. Aleksandrov and P.S. Uryson received the high titles of Aleph-5. NN Luzin himself was awarded the title "Aleph-17", and the corresponding sign became the emblem of the school. [7]
A comic poem written by one of the students of that time conveys the atmosphere that prevailed at that time in Lusitania: [2]
Despising classic analysis, |
And the comic hymn “Lusitania” composed by the participants contained the following words: [1]
| Our god is Lebesgue The idol is an integral. We narrow the scope of life, So ordered us Our commander Luzin. |
See also
- Luzin, Nikolai Nikolaevich
- Egorov, Dmitry Fedorovich
- The Luzin Case
- Name and Math
Notes
- ↑ 1 2 M.A. Lavrentiev . "Nikolai Nikolaevich Luzin . "
- ↑ 1 2 Lyusternik L. A. Speech at the anniversary meeting of the Moscow Mathematical Society // UMN . - 1965. - T. 20 , No. 3 (123) . - S. 21-30 .
- ↑ 1 2 Aleksandrov P.S. Pages of an autobiography. Part II // UMN . - 1980. - T. 35 , no. 3 (213) . - S. 241–278 .
- ↑ D. Huylebrouck, P. Maritz. Around the graves of Petrovskii and Pontryagin // Mathematical Intelligencer . - 2003. - T. 25 , no. 2 . - S. 55-73 . - DOI : 10.1007 / BF02984835 .
- ↑ P.S. Aleksandrov. Luzin School of Mathematics // Quantum . - 1977. - No. 10 . - S. 13-21 .
- ↑ N. N. Luzin (on the centenary of his birth) // Quantum . - 1983. - No. 12 . - S. 7-11 .
- ↑ Sound memoirs from the collection of V. D. Duvakin
Links
- Lyusternik L. A. Youth of the Moscow Mathematical School // UMN . - 1967. - T. 22 , No. 1 (133) . - S. 137–161 .
- Lyusternik L. A. Youth of the Moscow Mathematical School // UMN . - 1967. - T. 22 , No. 2 (134) . - S. 199–239 .
- Lyusternik L. A. Youth of the Moscow Mathematical School // UMN . - 1967. - T. 22 , No. 4 (136) . - S. 147–185 .
- P.S. Alexandrov. Luzin School of Mathematics // Quantum . - 1977. - No. 10 . - S. 13-21 .
- Sound memoirs from the collection of V. D. Duvakin
- S. S. Demidov, V. D. Esakov. The Luzin Affair in the collective memory of the scientific community
- The Case of Academician Luzin / Ed. Demidova S.S., Levshina B.V. - RKHGI, 1999 .-- 368 p.
- The history of mathematics. Nikolai Nikolaevich Luzin