After Army service, he graduated from Faculty of Mechanics and Mathematics, Moscow State University in 1952.

In 1953-1975 Korolev worked at the Institute of Precise Mechanics and Computer Engineering of academician S.A. Lebedev, and became his deputy.

In 1960 he was awarded the degree "Kandidat in Physical and Mathematical Sciences" for a thesis on the theory of machine translation.

He headed the team which wrote control software for ballistic missile defense, using the computers M-40 and M-50.

Korolev has held a chair at the Moscow State University Department of Computational Mathematics and Cybernetics since its founding in 1970.