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Nina Bari's father was a doctor. She attended L O Vyazemska's School for Girls and showed great potential in mathematics. In 1918 she entered the Faculty of Mathematics and Physics at Moscow State University.
In the Moscow School of Mathematics she came under the influence of Luzin. Also in this strong mathematical group were Stepanov, Aleksandrov and Urysohn. She graduated in 1921 and began teaching. However soon after this the Research Institute of Mathematics opened at Moscow State University and Bari became began research there in addition to her teaching posts.
Bari worked under Luzin for her doctorate on the theory of trigonometrical series. This was awarded in 1926 and after this Bari became a research assistant at the Institute of Mathematics and Mechanics in Moscow.
During 1927 - 29 she spent time in Paris, attending lectures by Hadamard, and also visited Lvov and Bologna. In 1932 she became a full professor at Moscow State University.
The year Bari graduated from Moscow State University, V V Nemytski entered there to read mathematics. They became close friends sharing not only mathematical interests but also a love of hiking in the mountains. They were eventually married.
Bari was an outstanding research mathematician who wrote over fifty research articles. In  her final publication, a research monograph on trigonometric series, is described as follows:-
The range and depth of topics covered is quite extensive, and most of her work in the field is included. But even within so long a monograph, the subject could not be completely exhausted. ... It has become a standard reference for mathematicians specializing in the theory of functions and the theory of trigonometric series.Bari also wrote textbooks, Higher Algebra (1932) and The Theory of Series (1936). She edited the complete works of Luzin and was the editor of two important mathematics journals. She also translated Lebesgue's famous book on integration into Russian.
She died by falling in front of a train on the Moscow Metro. It has been claimed that this was suicide due to depression caused by Luzin's death eleven years earlier. One of her students wrote after her death:-
The untimely death of N K Bari is a great loss for soviet mathematics and a great misfortune for all who knew her. The image of Bari as a lively, straightforward person with an inexhaustible reserve of cheerfulness will remain forever in the hearths of all who knew her.References (3 books/articles)
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