In addition to the university courses in analytical mathematics, differential equations, and probability theory, he was also active in preparing syllabi and teaching manuals for Russian schools and military academies.

He is credited with an early discovery of the Cauchy–Schwarz inequality, proving it for the infinite dimensional case in 1859, many years prior to Hermann Schwarz's research on the subject.

Bunyakovsky was elected to the post of the Vice President of the Russian Academy of Sciences on 8 April 1864 (in fact since 10 August 1863 г.).

[citation needed] In 1875, the St. Petersburg Academy of Sciences issued a medal and established a prize, bearing Viktor Yakovlevich Bunyakovsky's name, for his outstanding mathematical research.

Bunyakovsky wrote a research article titled: "On possibility of introduction of certain measures of trust to results of some sciences and statistics mainly", which was published in Sovremennik in Russia in 1848.

[8] Bunyakovsky printed a research article titled: "On the probability of number of divisions of Russian army in 1883–1885", which was published in Zapiski Academii Nauk in Russia in 1885.

[8] Bunyakovsky developed a number of practical applications as far as the probability theory is concerned, publishing his research articles in the Russian magazines Sovremennik and Zhurnal Ministerstava Narodnogo Prosvesheniya.

Bunyakovsky made a significant scientific contribution to the problem of the naval department pension fund creation, publishing his research articles in Morskoi Sbornik magazine in 1858.

[8] Bunyakovsky formulated an empirical law of deaths in 1869, making it possible to solve the problems on the calculation of both capital insurance and life-time incomes in finances.