He attended research seminars in Kiev University and soon started to work under the supervision of the well-known contemporary mathematician Nikolay Krylov. In 1924, at the age of 15, Nikolay Bogolyubov wrote his first published scientific paper "On the behavior of solutions of linear differential equations at infinity". In 1925 he entered Ph.D. program at the Academy of Sciences of the Ukrainian SSR and obtained the degree of Kandidat Nauk ("Candidate of Sciences", equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled "On direct methods of variational calculus". In 1930, at the age of 21, he obtained the degree of Doktor nauk ("Doctor of Sciences", equivalent to Habilitation), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field.