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, structure, space, models, and change. History On ...

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 Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

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 function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

Work

Partial differential equations

In his doctoral dissertation, submitted in 1904 to

Sorbonne Sorbonne may refer to: * Sorbonne (building), historic building in Paris, which housed the University of Paris and is now shared among multiple universities. *the University of Paris (c. 1150 – 1970) *one of its components or linked institution, ...

, Bernstein solved

Hilbert's nineteenth problem Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less ...

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 equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The functi ...

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 po ...

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 polyn ...

s, he laid the foundations of

constructive function theory In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Berns ...

, 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) In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912. For approximation by trigonometric polynomials, the result is as follows: Let ''f'': , 2 ...

. 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 t ...

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.

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 mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...

{{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