He studied nuclear physics at Sofia University where he became a research associate in the theoretical department.
He worked at Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste (1967).
From 1983 to 1985 he led the faculty of physics and was a member of the academic council and vice-rector of Sofia University from 1985 to 1986.
From 1986 to 1989 Mateev was vice-chairman of the Scientific Committee for Higher Education.
In 2003 he was selected as an academician in physics from the Bulgarian Academy of Sciences.