Sergei Natanowitsch Bernstein

Sergei Bernstein

Sergei Natanovich Bernstein ( Russian Сергей Натанович Бернштейн ., Scientific transliteration Sergei Natanovič Bernštejn ; born February 22 ^{. Jul} / 5. March  1880 ^greg. In Odessa ; † 26. October 1968 in Moscow ) was a Russian mathematician .

Life

He was the brother of the psychiatrist Alexander Nikolajewitsch Bernstein (1870-1922) and the uncle of the physiologist Nikolai Alexandrowitsch Bernstein and the civil engineer Sergei Alexandrowitsch Bernstein .

Bernstein studied in Paris ( Sorbonne , University of Electrical Engineering École supérieure d'électricité ) and Göttingen (1902/03) and received his doctorate at the Sorbonne in 1904 and again in 1913 (candidate status) in Russia at the University of Kharkiv , since foreign doctoral degrees were not permitted there . Between 1907 and 1932 he was a professor at Kharkiv University. In 1925 he became a member of the All-Ukrainian Academy of Sciences .

In 1933 he became a professor at the university and at the Polytechnic Institute in Leningrad and from 1943 in Moscow, where he died in 1968.

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In his first doctoral thesis, Bernstein solved Hilbert's 19th problem on solving elliptic partial differential equations. In his second doctoral thesis he devoted himself to Hilbert's 20th problem: He proved the existence of analytical solutions to the Dirichlet problem for a large class of nonlinear elliptic partial differential equations.

Bernstein is best known for his work on approximation theory, an area in which Chebyshev worked in Russia . In 1911 he introduced the Bernstein polynomials named after him for the constructive proof of Weierstrass' theorem . At the International Congress of Mathematicians in Cambridge in 1912, he also formulated a conjecture that tightened Weierstrass' theorem and that was proven by Chaim Müntz and Otto Szász . Bernstein also dealt with probability theory. As early as 1917 he tried to axiomatize the theory of probability (which Andrei Kolmogorow finally developed convincingly in general). He presented studies on the central limit theorem, the law of large numbers, stochastic processes and the application of e.g. B. in genetics.

He is known for Bernstein's theorem, an analogue of Liouville's theorem from function theory for minimal surfaces. Bernstein had shown in the 1910s that in the Euclidean space of two dimensions a complete minimal surface (graph of a function ) is a hypersurface (affine function ). The problem of whether the theorem also applies to higher dimensions became known as the Bernstein problem of differential geometry ( Wendell Fleming in the 1960s, who also provided a new proof). De Giorgi proved in 1965 that the theorem also holds for d = 3 (minimal graphs ) and Frederick Almgren proved it in 1966 for d = 4. James Simons extended the sentence to all dimensions in 1968 . In 1969 De Giorgi, Bombieri and Enrico Giusti showed that this statement is wrong for all spatial dimensions . ${\displaystyle d}$ ${\displaystyle f\colon \mathbb {R} ^{2}\to \mathbb {R} }$ ${\displaystyle f(x)=nx+m}$ ${\displaystyle f\colon \mathbb {R} ^{d}\to \mathbb {R} }$ ${\displaystyle d\leq 7}$ ${\displaystyle d\geq 8}$

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (Sur les liaisons entre quantités aléatoires).

In Moscow, Bernstein published Chebyshev's Collected Works .

Awards

Bernstein received the following awards and memberships:

• Corresponding member since 1924 and Academician of the Russian Academy of Sciences since 1929
• Member of the German Mathematicians Association (1926)
• Corresponding member since 1928 and academician of the Académie des sciences since 1955
• Member of the French Mathematical Society (1944)
• Stalin Prize (1942)
• Order of the Red Banner of Labor (1944)
• Order of Lenin (1945, 1953)

literature

• AP Youschkevitch: Bernstein, Sergey Natanovich . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 15 , Supplement I: Roger Adams - Ludwik Zejszner and Topical Essays . Charles Scribner's Sons, New York 1978, p. 22-24 .

Remarks

1. ↑ He submitted his thesis, which corresponds to a doctorate in the West, as early as 1908.
2. ↑ Website of the National Academy of Sciences of Ukraine ( Memento of the original dated December 3, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. - Member page Бернштейн Сергій Натанович, accessed November 29, 2016 
3. ↑ In the theory of functions the functions fulfill the Laplace equation and are harmonic functions, with the minimal areas the partial differential equation (minimal area equation) is more complicated, but also of the elliptic type
4. ↑ SN Bernstein, Sur une théorème de géometrie et ses applications aux équations dérivées partielles du type elliptique, Comm. Soc. Math. Kharkov, Vol. 15, 1915-1917, pp. 38-45
5. ↑ Bernstein, On a geometric theorem and its application to the partial differential equations of the elliptic type, Math. Z., Volume 26, 1927, pp. 551–558
6. ^ Bernstein Problem, Encyclopedia of Mathematics, Springer
7. ↑ About Sergei Bernstein in the Mathematical Encyclopedia Wörtebuch. Retrieved September 20, 2018 (Russian). 
8. ↑ Sergei Bernstein on the Official Website of the Russian Academy of Sciences - (Russian), accessed September 20, 2018

Web links

• John J. O'Connor, Edmund F. Robertson :  Sergei Natanowitsch Bernstein. In: MacTutor History of Mathematics archive .
• Literature by and about Sergei Natanowitsch Bernstein in the catalog of the German National Library
• Author profile in the database zbMATH