Georg Cantor was born in St. Petersburg in 1845 to a family of a merchant, George Woldemar Cantor, and Marie Böhm -Cantor, daughter of Franz Böhm, St. Petersburg violinist, the best virtuosic soloist at St. Petersburg theaters.

Georg Cantor was born house 24 in the 11th line of Vasilevsky Island in Petersburg, attended Petrischule at the Lutheran Church of St. Peter. Members of their extended family belonged to the academic, court, artistic and commercial circles of St. Petersburg. There were eight violinists in the family, two court younger ladies (cameryoungfrau), a head waiter, a university professor, a professor of the Conservatory, an artist, and merchants. Georg Cantor played the violin and loved music and St. Petersburg all his life. The family moved to Germany when Georg Cantor was 11 years old.

As an adult, when creating his own set-theoretic work, Cantor repeatedly appealed to musical images. Moreover, those were musical images that helped him in 1872 to feel the lack of an irrational number as a limit when defining arithmetic continuity, and introduce the principle of one-to-one correspondence as a fundamental to his theory.

Many mathematicians were pondering on the continuum arithmetization problem and the number conception. Those were Charles Measure (1869, 1872), Karl Weierstrass, Edward Heine (1872), Cantor (1872) and Dedekind (1872). The arguments were based on the convergent series. Dedekind (son of a lawyer) gave a perfect legal definition of a number (1872), but these approaches did not make it possible to estimate the amount of numbers in general and in particular, the irrational numbers. The Set Theory, created by Cantor in the eighties, contained a scale of infinities that helped introduce the comparison of sets of power. This association was only possible with a rich cultural and musical basis in Cantor's researches.

Cantor's work attracted interest in Russia. In 1902, P. Florensky issued a statement of Cantor's ideas. In 1907, I.Zhegalkin made a presentation on the theory of sets (Transfinite numbers) at Moscow State University. In 1908, A.Vasilev published some Cahtor`s works translated by P.S.Yushkevich. The researches of the Moscow school of function theory were headed by Egorov and Luzin and based on the set theory.