Nikolsky was born in Talitsa, which was at that time located in Kamyshlovsky Uyezd of the Russian Empire. He had been an Academician since 28 November 1972. He also had won many scientific awards. At the age of 92 he was still actively giving lectures in Moscow Institute of Physics and Technology. In 2005, he was only giving talks at scientific conferences, but was still working in MIPT, at the age of 100. He died in Moscow in November 2012 at the age of 107.

Nikolsky made fundamental contributions to functional analysis, approximation of functions, quadrature formulas, enclosed functional spaces and their applications to variational solutions of partial differential equations. He created a large scientific school of functions' theory and its applications. He authored over 100 scientific publications, including 3 monographs, 2 college textbooks and 7 school textbooks.

• Approximation of functions of several variables and imbedding theorems, Springer Verlag 1975 (Russian original, Nauka, Moscow 1969)
• Treatise on the shift operator, Springer Verlag 1986 (Russian original, Moscow 1980)
• Operators, functions and systems. An easy reading. Volume 1: Hardy, Hankel and Toeplitz, American Mathematical Society 2002
• with Valentin Petrovich Ilyin and Oleg Besov: Integral representation of functions and embedding theorems, 2 vols., Wiley 1978, 1979
• as editor: Theory and applications of differentiable functions of several variables, American Mathematical Society 1967
• Quadrature formulae, Delhi, Hindustan Publ. Corp. 1964
• Курс математического анализа (Course in mathematical analysis, Russian), 2 vols., Nauka 1975
• with Ya. S. Bugrov [ru]: Differential equations, multiple integrals, series, theory of functions of a complex variable, Mir Publ., Moscow 1983

• List of publications, downloadable here: Russian Academy of Sciences
• For Nikolsky's centenary
• Sergey Nikolsky at the Mathematics Genealogy Project