| Sergei Natanovich Bernstein | |
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Sergei Natanovich Bernstein
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| Born | 5 March 1880 Odessa, Imperial Russia |
| Died | 26 October 1968 (aged 88) Moscow, USSR |
| Residence | USSR |
| Fields | Mathematics |
| Institutions | University of Paris |
| Alma mater | University of Paris |
| Doctoral advisor | Charles Émile Picard David Hilbert |
| Doctoral students | Vladimir Brzhechka Yakov Geronimus Vasilii Goncharov Boris Rymarenko Sergey Stechkin |
| 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; March 5, 1880, Odessa – October 26, 1968, Moscow) was a Russian and Soviet mathematician known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.[1][2]
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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.
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the first axiomatic foundation of probability theory, based on the underlying algebraic structure.[4] It was later superseded by the measure-theoretic approach of Kolmogorov.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 1920-s, he introduced a method for proving limit theorems for sums of dependent random variables.
Bernstein 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 Bernstein's theorem (approximation theory).