World of Mathematics on Nikolai Nikolaievich Lusin
Although he came to mathematics relatively late in life, Nikolai Nikolaievich Lusin made significant contributions in the area of , measure theory, and set . In fact, he is considered one of the founders of the famous Moscow school of function theory, which had its heyday in the 1920s. Lusin was also known in academic circles for his brilliant lectures and unconventional approach to solving problems.
Lusin was the only son of a trade official and his wife, born in Irkutsk on December 9, 1883. In about 1894 the family moved to Tomsk so the boy could attend the city's excellent gymnasium (a classical college-preparatory school). However, the move was something of a disaster, since Lusin began to do so poorly in mathematics that his father had to hire a tutor. It soon became apparent that Lusin was gifted in mathematics, but that he had difficulty solving problems using the prescribed methods. Instead, he would use his own unconventional techniques to come up with the answers, which puzzled and infuriated his teachers.
Lusin left the gymnasium in 1901 when his father sold his business and moved the family to Moscow. With Moscow University now close at hand, Lusin enrolled in the School of Physics and Mathematics with the intention of becoming an engineer. The family fell on hard times soon thereafter when Lusin's father lost his savings, forcing the young man to move into a boarding house. This misfortune did not seem to affect Lusin unduly, since he was able to continue his studies at the university.
As at the gymnasium, though, Lusin did only mediocre work. One professor, however, noticed his unusual way of thinking and began inviting Lusin to his home for private lessons away from the inhibiting atmosphere of the formal classroom. The professor, D.F. Egorov, posed many difficult problems to Lusin and was astounded to see how quickly the student could solve them, albeit in unconventional ways. Thanks in part to this special help and guidance, Lusin graduated from Moscow University in 1905.
At this point, Lusin was unsure whether to dedicate himself to mathematics. He went through a period in which he wanted to become a doctor, precipitated partially by his observation of the many prostitutes and other impoverished people in Moscow and partly because of the effects of Russia's 1905 Revolution. He felt that studying mathematics was perhaps too trivial a way for him to spend his time. Nevertheless, Lusin's true nature soon reasserted itself, and he began studying at the university in 1908. He also married his wife that year.
By about 1909 Lusin had completely devoted his energies to the study of mathematics. He began working on his master's thesis, and in 1910 became an assistant lecturer in pure mathematics at the university. With Egorov, Lusin wrote joint papers on function theory that launched the Moscow school. In 1915 Moscow University awarded Lusin a doctoral degree after he defended his thesis, "The Integral and Trigonometric Series," although the work was intended to fulfill only his master's degree. While some members of the doctoral committee were not impressed with the dissertation, those who were prevailed in granting Lusin the more advanced degree.
In 1917, Lusin accepted an appointment as full professor of pure mathematics at the university. By 1927, he and Egorov had established an elite research group there, which their students fondly dubbed "Luzitania." Many of Russia's best mathematicians of the period emerged from this collection of researchers. From this time on, Lusin dedicated himself to the study of descriptive set theory--particularly concentrating on the question, "Can we regard a line atomistically as a set of points"" In 1919, he proved an important result concerning the invariance of sets of boundary points under conformal mappings.
From 1922 to 1926 the Moscow school was at its height. Beginning in 1926, however, Lusin spent much of his time writing a monograph on function theory. Deprived of his energizing influence, his students began drifting off into different research areas. The prestigious Soviet Academy of Sciences elected Lusin as a member in 1927, and he spent the rest of his life working there.
In 1931, Lusin entered a new field of study: and their application to control theory and . This eventually led him to investigate the bending of surfaces (the foundation of topology). From 1935, Lusin also served as chairperson of the Steklov Institute's Department of the Theory of Functions of Real Variables.
Lusin died in Moscow on February 28, 1950.
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