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Bernshtein, Sergei Natanovich

(1880–1968), mathematician. Born in Odessa, Sergei Bernshtein studied mathematics at both the Sorbonne and Göttingen, receiving his doctorate from the former in 1904. His dissertation presented the solution to Hilbert’s Nineteenth Problem, which dealt with analytic solutions of elliptic differential equations. Three famous mathematicians—Jacques Hadamard, Émile Picard, and Henri Poincaré—accepted his thesis. Upon arriving in Russia in 1905, however, Bernshtein learned that he would need to take general examinations and submit new dissertations for both master’s and doctoral degrees in order for his credentials to be recognized; he completed this work at Kharkov University.

In his master’s dissertation (1908), Bernshtein solved Hilbert’s Twentieth Problem, which involved the analytic solution of Dirichlet’s problem for a wide class of nonlinear elliptic equations. In his doctoral dissertation (1913), Bernshtein presented the result that had earned him the Royal Belgium Academy of Sciences Prize in 1911 and the honor of delivering the plenary talk at the 1912 International Congress of Mathematicians in Cambridge. Nevertheless, in Russia these achievements did not assure Bernshtein a position of the rank he deserved. Only in 1920 did he become a full professor at Kharkov University. Later he was elected to be a full member of the Ukrainian (1925), Soviet (1929), and French (1955) Academies of Science.

In the early 1930s, Bernshtein was subjected to political attacks because he refused to greet Stalin on behalf of the First Mathematical Congress of the USSR, held in Kharkov in 1930. Fearing arrest, he moved to Leningrad in 1933. He lived in Moscow from 1943, working at the Mathematical Institute of the USSR Academy of Sciences and at Moscow State University.

Bernshtein wrote more than 230 research papers on mathematical analysis, differential equations, approximation theory, probability theory, mathematical statistics, and mathematical genetics. His three articles on the last topic, published between 1922 and 1924, contained the fundamental “stationarity principle,” from which Bernshtein mathematically derived Mendel’s experimental laws of heredity.

Bernshtein devised the first axiomatization of probability theory (1917) and produced the earliest systematic textbook on this topic, four editions of which were published between 1927 and 1946. The fifth did not appear because of Bernshtein’s refusal to remove passages dealing with Mendel’s heredity theory, which was being vigorously contested at that time (1948) in the USSR by the Stalin-backed Lysenko school.

Bernshtein broke new ground (the “constructive theory of functions”) in approximation theory, focusing on connections between the behavior of functions and the rate of convergence of their polynomial approximations. He devoted two monographs to this topic, published in Paris in 1926 and Moscow in 1937. The earlier work was awarded a prize by the French Academy of Sciences. Bernshtein was awarded the State Prize of the USSR in 1941 in recognition of his scholarly achievements, and the USSR Academy of Sciences published his four-volume collected works between 1952 and 1964. His fundamental results are reflected in theorems bearing his name and in several important mathematical concepts.

Bernshtein engaged in teaching for nearly 40 years (1908–1947). His lectures were distinguished by their depth and originality of material. Several of his students became prominent scholars, among them Sholem Mandel’broit (1899–1983), Ezhi Neiman (1894–1981), Iakov Geronimus (1898–1984), and Nobel Laureate in Economics Leonid Kantorovich (1912–1986).

Suggested Reading

Naum Il’ich Akhiezer, Akademik S. N. Bernshtein (Kharkov, Ukr., 1955); Vasilii Leonidovich Goncharov, “Sergei Natanovich Bernshtein,” Uspekhi matematicheskikh nauk 5 (1950): 172–183; V. Videnskii, “Sergei Natanovich Bernshtein,” Kvant 1 (1997): 17–21.



Translated from Russian by I. Michael Aronson