Bernstein, S. N., Démonstration du Théorème de Weierstrass fondée sur le calcul des Probabilités, Comm. Soc. Math. Kharkow 13 (1912/13), 1-2. This is Bernstein's famous paper where he presented a probabilistic proof of the Weierstrass Theorem, and introduced what we today call Bernstein polynomials. Note that his proof is somewhat "overinvolved". We nowadays present this proof in a slightly more elegant form. This paper is reprinted in Russian in Bernstein's collected works.

Bernstein, S. N., Sur les recherches récentes relatives à la meilleure approximation des fonctions continues par les polynômes, in Proc. of 5th Inter. Math. Congress, Vol. 1, 1912, 256-266. Also appears in Russian translation in Bernstein's Collected Works.

Akhieser, N. I., Academician S. N. Bernstein and his Work on the Constructive Theory of Functions (in Russian), Izdat. Harkov. Gosudarstv. Univ., Kharkov, 1955; translated into German as Das Akademiemitglied S. N. Bernstein und seine Arbeiten zur konstruktiven Funktionentheorie, translated and with a preface by Ralitza K. Kovacheva and Heinz H. Gonska. in Mitt. Math. Sem. Giessen No. 240 (2000), xiv + 97 pages. The original is an expanded form of the survey paper by N. I. Akhiezer with the same title which appeared in Uspehi Mat. Nauk (N.S.) 6 (1951), no. 1(41), 3-67, which was written by Akhieser on the occasion of Bernstein's 70th birthday.

Aleksandrov, P. S., Akhiezer, N. I., Gnedenko, B. V., and A. N. Kolmogorov, Sergei Natanovich Bernstein: Obituary, (in Russian) Uspekhi Mat. Nauk 24 (3) (1969), 211-218, translation in Russian Math. Surveys 24 (3) (1969), 169-176.