Nikolai Luzin (nonfiction)

Nikolai Luzin.

Nikolai Nikolaevich Luzin (also spelled Lusin; Russian: Никола́й Никола́евич Лу́зин; IPA: [nʲɪkɐˈlaj nʲɪkɐˈlaɪvʲɪtɕ ˈluzʲɪn] 9 December 1883 – 28 January 1950) was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology.

Luzin underwent great personal turmoil in the years 1905 and 1906, when his materialistic worldview had collapsed and he found himself close to suicide.

From 1910 to 1914 Luzin studied at Göttingen, where he was influenced by Edmund Landau.

Luzin's first significant result was a construction of an almost everywhere divergent trigonometric series with monotonic convergence to zero coefficients (1912). This example disproved the Pierre Fatou conjecture and was unexpected to most mathematicians at that time. At approximately the same time, he proved what is now called Lusin's theorem in real analysis.

He 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.

His Ph.D. thesis titled Integral 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 the Fourier series for a square-integrable function, was solved by Lennart Carleson in 1966 (Carleson's theorem).

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 descriptive set theory. Together with his student Mikhail Yakovlevich Suslin, he developed the theory of analytic sets.

He also made contributions to complex analysis, the theory of differential equations, and numerical methods.

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.

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.

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 1929 he was elected as a member of the Polish Academy of Sciences and Letters in Kraków.

In the 1930s, Luzin was the victim of a violent political campaign organized by the Soviet authorities; see Luzin affair.

Fiction cross-reference

• Gnomon algorithm
• Mathematics (nonfiction)

Nonfiction cross-reference

• Nina Bari (nonfiction)
• Andrey Kolmogorov (nonfiction)
• Edmund Landau (nonfiction)
• Luzin affair (nonfiction)
• Mathematician (nonfiction)
• Mikhail Yakovlevich Suslin (nonfiction)

External links:

• Nikolai Luzin @ Wikipedia