Sergei Bernstein

Sergei Bernstein
Born	Sergei Natanovich Bernstein (1880-03-05)5 March 1880 Odessa, Kherson Governorate, Russian Empire
Died	26 October 1968(1968-10-26) (aged 88) Moscow, 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
Scientific career
Fields	Mathematics
Institutions	University of Paris University of Göttingen University of Kharkiv Leningrad University Steklov Institute of Mathematics
Doctoral advisor	Charles Émile Picard David Hilbert
Doctoral students	Yakov Geronimus Sergey Stechkin

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

Work[]

Partial differential equations[]

In his doctoral dissertation, submitted in 1904 to 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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.^[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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).

International Congress of Mathematicians[]

Bernstein was an invited speaker at the International Congress of Mathematicians (ICM) in Cambridge, England in 1928 and in Bologna in 1928 and a plenary speaker at the ICM in Zurich.^[8] His plenary address Sur les liaisons entre quantités aléatoires was read by Bohuslav Hostinsky.^[9]

Publications[]

• 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

Notes[]

References[]

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

External links[]

• Sergei Bernstein at the Mathematics Genealogy Project
• Sergei Natanovich Bernstein and history of approximation theory from Technion — Israel Institute of Technology
• Author profile in the database zbMATH