Sergei Natanovich Bernstein (, sometimes Romanized as ; 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. 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 estimates. 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 It was later superseded by the measure-theoretic approach of Kolmogorov. 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. In particular, he proved the Weierstrass approximation theorem 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 International Congress of Mathematicians (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 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 External links Sergei Natanovich Bernstein and history of approximation theory from Technion — Israel Institute of Technology Author profile in the database zbMATH 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