The son of a district marshal and justice of the peace, Selivanov was born into a noble family in Penza Oblast, where he attended secondary school.
In 1885 he completed in Saint Petersburg his Russian magister degree with dissertation entitled "Теория алгебраического решения уравнений" ("Theory of the algebraic solution of equations").
During those years he also lectured at the St. Petersburg Technological Institute from 1888 to 1900, and from 1889 at the Bestuzhev Women's University, where he met his wife (Yelena Pavlovna Podashevsky, marriage in 1908), who was his student.
In 1890 he received the Russian doctorate in Moscow with thesis "Об уравнениях пятой степени с целыми коэффициентами" ("On the solution of equations of the fifth degree with integer coefficients").
His work was praised by Hermite, as was his first publication,[1] in which he linked the differentiability of an indefinite integral to a parameter with its uniform convergence (newly introduced by Weierstrass at the time).