A leading Slovak mathematician, educator, diplomat and a promoter of science. He systematically focused on the theory of higher-order differential equations and their applications. He was the closest fellow worker of Prof. Otakar Borůvka, whom he was bound to by a sincere and deep friendship.

After graduating from the Faculty of Science, Charles University in Bratislava in 1950, he worked as an assistant at the Slovak Technical University in Bratislava for a year, followed by two years at the Military Technical Academy in Brno. In 1953, he came to the Faculty of Science of the Charles University in Bratislava, which became his main workplace. First he worked there as an assistant professor, from 1960 as a docent and from 1965 as a professor. He defended his dissertation in the same year. In the academic year of 1964-1965, he was the dean of the faculty. In 1968, he became a deputy of the officer and later minister of education of the Slovak Socialist Republic. He contributed immensely to the decision to build modern premises of the Charles University in Mlýnská dolina. In 1973-1977 he worked in Paris as a permanent delegate of the Czechoslovak Socialist Republic to UNESCO. When he came back from Paris, he returned to his Alma Mater – the Comenius University in Bratislava – where he got heavily involved in organizing the formation of the independent Faculty of Mathematics and Physics of the Charles University and became its first dean (1980).

He was a member of the Presidium of the Slovak Academy of Sciences (SAS), a member of the Scientific Committee for Mathematics and the Czechoslovak National Committee for Mathematics at the Czechoslovak Academy of Sciences (CSAS). In 1982 he was appointed a corresponding member of CSAS and SAS; in 1987 he became a SAS academic and in 1998 a CSAS academic. He also held other positions, lately that of the Chairman of the Slovak Commission for Granting Scientific Degrees and the Chairman of the Union of Slovak Mathematicians.

In the 1990s, he actively collaborated with foreign mathematicians, mostly from the United States (Prof. John Graef), Finland (Prof. Ilpo Laine) and Japan (Prof. Kusano). These professional and friendly relationships ended forever when Prof. Greguš died suddenly in 2002.

Apart from extensive scientific and educational work, he was active in the editorial boards of scientific journals. In his enthusiasm and ardor for the development of mathematics, he participated in the establishment of the Mathematical Seminar at the Department of Mathematical Analysis in the 1960s, which has been running until now. In the 1970s and 1980s , he promoted the concept of combining science and practice, which resulted in the formation of contacts between production companies, mathematicians and physicists, and later in numerous successful collaborations that still exist today. However, his primary goal has always been the education of graduates with high-quality theoretical knowledge, capable of asserting themselves in various competitive environments.