[4] His father Nikita (Mkrtich) Ivanovich Mergelov, a former private entrepreneur (Nepman), his mother Lyudmila Ivanovna Vyrodova, the daughter of the manager of the Azov-Black Sea bank, who was shot in 1918.

In 1936 Sergey's father was building a paper mill in Yelets, but soon together with his family was deported to the Siberian settlement of Narym, Tomsk Oblast.

In 1937, the mother and son were acquitted by the court's decision and returned to Kerch, and in 1938 Lyudmila Ivanovna obtained (from the USSR Prosecutor General Andrei Yanushyevich Vyshinsky) the rehabilitation of her husband.

In 1941, in connection with the offensive of the Hitler armies to the South, the Mergelov family left Kerch and settled in Yerevan.

In 1944, at age 16, he passed the examinations via extern for grades 9-10, graduated from high school and immediately entered the Physics and Mathematics Faculty of the Yerevan State University (YSU).

He drew attention to himself at the university, where he during a year passed the first and second courses, and soon began attending lectures of academician Artashes Shahinian, the founder of the Armenian mathematical school.

There he gave full freedom to fantasy, writing puzzles for children by conducting competitions to solve particularly difficult tasks and organizing mathematical games.

Although Mergelyan introduced to defend the Ph.D. dissertation, all three official opponents - Academician Lavrentyev, Sergey Nikolsky and Corresponding Member Alexander Gelfоnd - petitioned the Academic Council to award him the Doctor of Science degree.

The petition of opponents was satisfied (for this it was necessary to call the members of the scientific council, which took time), and Mergelyan became the youngest doctor of physical and mathematical sciences in the USSR at the age of 20 (at 21).

Until today this is a record of getting the highest scientific degree (Doctor of Science) at such a young age in former USSR and present Russia.

When he was 24 he became a corresponding member of the Academy of Sciences of the Soviet Union, which, from the point of view of young age, is yet another absolute record among USSR scientists.

In 1963 he was elected Deputy Academician of the Secretary of the Department of Mathematics of the Academy of Sciences of the Soviet Union (Nikolai Nikolaevich Bogolyubov).

The theorem completed a long series of studies, begun in 1885, and composed of the classical results of Karl Weierstrass, Carl Runge, J. Walsh, Mikhail Lavrentyev, Mstislav Keldysh and others.