Military Wiki
Sergei Natanovich Bernstein
Sergei Natanovich Bernstein
Sergei Natanovich Bernstein
Born (1880-03-05)5 March 1880
Odessa, Kherson Governorate, Russian Empire
Died 26 October 1968(1968-10-26) (aged 88)
Moscow, Soviet Union
Residence Russian Empire, Soviet Union
Nationality Soviet
Alma mater University of Paris
Known for Bernstein's inequality in analysis
Bernstein inequalities in probability theory
Bernstein polynomial
Bernstein's theorem (approximation theory)
Bernstein's theorem on monotone functions
Bernstein problem in mathematical genetics

Sergei Natanovich Bernstein (Russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as Bernshtein; 5 March 1880 – 26 October 1968) was a Russian and Soviet mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.[1][2]


Partial differential equations

In his doctoral dissertation, submitted in 1904 to the Sorbonne, Bernstein solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations.[3] His later work was devoted to Dirichlet's boundary problem for non-linear equations of elliptic type, where, in particular, he introduced a priori estimates.

Probability theory

In 1917, Bernstein suggested the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.

In the 1920s, he introduced a method for proving limit theorems for sums of dependent random variables.

Approximation theory

Through his application of Bernstein polynomials, he laid the foundations of constructive function theory, a field studying the connection between smoothness properties of a function and its approximations by polynomials.[5] In particular, he proved the Weierstrass approximation theorem[6][7] and Bernstein's theorem (approximation theory).


  • S. N. Bernstein, Collected Works (Russian):
    • vol. 1, The Constructive Theory of Functions (1905–1930), translated: Atomic Energy Commission, Springfield, Va, 1958
    • vol. 2, The Constructive Theory of Functions (1931–1953)
    • vol. 3, Differential equations, calculus of variations and geometry (1903–1947)
    • vol. 4, Theory of Probability. Mathematical statistics (1911–1946)
  • S. N. Bernstein, The Theory of Probabilities (Russian), Moscow, Leningrad, 1946

See also

  • A priori estimate
  • Bernstein algebra
  • Bernstein's inequality (mathematical analysis)
  • Bernstein inequalities in probability theory
  • Bernstein polynomial
  • Bernstein's problem
  • Bernstein's theorem (approximation theory)
  • Bernstein's theorem on monotone functions
  • Bernstein–von Mises theorem
  • Stone–Weierstrass theorem


  1. Youschkevitch, A. P.. "BERNSTEIN, SERGEY NATANOVICH". Dictionary of Scientific Biography. 
  2. Lozinskii, S. M. (1983). "On the hundredth anniversary of the birth of S. N. Bernstein". p. 163. Digital object identifier:10.1070/RM1983v038n03ABEH003497. 
  3. Akhiezer, N.I.; Petrovskii, I.G. (1961). "S. N. Bernshtein's contribution to the theory of partial differential equations". 
  4. Linnik, Ju. V. (1961). "The contribution of S. N. Bernšteĭn to the theory of probability". pp. 21–22. Digital object identifier:10.1070/rm1961v016n02abeh004103. MR0130818. 
  5. Videnskii, V. S. (1961). "Sergei Natanovich Bernshtein — founder of the constructive theory of functions". p. 17. Digital object identifier:10.1070/RM1961v016n02ABEH004102. 
  6. S. Bernstein (1912–13) "Démonstration du théroème de Weierstrass, fondeé sur le calcul des probabilités, Commun. Soc. Math. Kharkow (2) 13: 1-2
  7. Kenneth M. Lavasseur (1984) A Probabilistic Proof of the Weierstrass Theorem, American Mathematical Monthly 91(4): 249,50


  • O'Connor, John J.; Robertson, Edmund F.. "MacTutor History of Mathematics archive". University of St Andrews. .

External links

This page uses Creative Commons Licensed content from Wikipedia (view authors).