Sergei Bernstein

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

Bernstein was born into a Jewish family living in Odessa. Sergei was brought up in Odessa but his father died on 4 February 1891 just before he was eleven years old. He graduated from high school in 1898. After this, following his mother's wishes, he went with his elder sister to Paris. Bernstein's sister studied biology in Paris and did not return to the Ukraine but worked at the Pasteur Institute. After one year studying mathematics at the Sorbonne, Bernstein decided that he would rather become an engineer and entered the

In his doctoral dissertation, submitted in 1904 to the Sorbonne, Bernstein solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations.^[4] 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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.^[5] It was later superseded by the measure-theoretic approach of Kolmogorov.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.^[6] In particular, he proved the Weierstrass approximation theorem^[7][8] and Bernstein's theorem (approximation theory). Bernstein polynomials also form the mathematical basis for Bézier curves, which later became important in computer graphics.

International Congress of Mathematicians

Bernstein was an invited speaker at the

• 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

Wikimedia Commons has media related to Sergei Bernstein.

• 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