Sergei Natanovich Bernstein (russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as ; 5 March 1880 – 26 October 1968) was a Ukrainian and Russian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

of Jewish origin known for contributions to

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

, differential geometry,

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

, and

approximation theory In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by ''best'' and ''simpler'' wil ...

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. His later work was devoted to Dirichlet's boundary problem for non-linear equations of elliptic type, where, in particular, he introduced

a priori estimate In the theory of partial differential equations, an ''a priori'' estimate (also called an apriori estimate or ''a priori'' bound) is an estimate for the size of a solution or its derivatives of a partial differential equation. ''A priori'' is Lati ...

Probability theory

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 It was later superseded by the measure-theoretic approach of

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

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

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the p ...

Approximation theory

Through his application of

Bernstein polynomial In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial that is a linear combination of Bernstein basis polynomials. The idea is named after Sergei Natanovich Bernstein. A numerically stable way to evaluate ...

s, he laid the foundations of constructive function theory, a field studying the connection between smoothness properties of a function and its approximations by polynomials. In particular, he proved the

Weierstrass approximation theorem Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...

and Bernstein's theorem (approximation theory). Bernstein polynomials also form the mathematical basis for

Bézier curve A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape ...

s, which later became important in computer graphics.

International Congress of Mathematicians

Bernstein was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(ICM) in Cambridge, England in 1912 and in Bologna in 1928 and a plenary speaker at the ICM in Zurich. His plenary address ''Sur les liaisons entre quantités aléatoires'' was read by

Bohuslav Hostinsky Bohuslav ( uk, Богуслав, yi, באָסלעוו or ''Boslov'') is a city on the Ros River in Obukhiv Raion, Kyiv Oblast (province) of Ukraine. Population: . It hosts the administration of Bohuslav urban hromada, one of the hromadas of Ukra ...

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

Notes

References

External links

*
Sergei Natanovich Bernstein
and history of approximation theory from Technion — Israel Institute of Technology
Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur ...

{{DEFAULTSORT:Bernstein, Sergei 1880 births 1968 deaths Scientists from Odesa People from Odessky Uyezd Odesa Jews Soviet mathematicians Approximation theorists Mathematical analysts PDE theorists Probability theorists 19th-century mathematicians from the Russian Empire 20th-century Russian mathematicians Expatriates from the Russian Empire in France University of Paris alumni Moscow State University faculty National University of Kharkiv academic personnel Corresponding Members of the Russian Academy of Sciences (1917–1925) Full Members of the USSR Academy of Sciences Stalin Prize winners Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Burials at Novodevichy Cemetery