Professor Islam was a theoretical physicist by profession. He worked as Post Doctoral Fellow in the University of Maryland, USA from 1963 to 1965. During 1967-1971 he worked at the Cambridge Institute of Theoretical Astronomy. He worked in the California Institute of Technology from 1971 to 1972 and then joined Washington University as Senior Research Associate. Later, he joined London King’s College as Lecturer in Applied Mathematics. From 1975 to 1978 he worked as Fellow of Science Research Council, University College, Cardiff. He joined City University, London in 1978 and was soon promoted to Reader. He worked there until 1984. He also worked as a visiting member in the Institute of Advanced Studies, Princeton during this time. Upon his return to Bangladesh in 1984, he joined the Department of Mathematics, Chittagong University and founded the Research Center for Mathematical and Physical Sciences (RCMPS) of which he was the Director till his death. He was also a syndicate member of Chittagong University of Engineering and Technology (CHUET).
Bangladesh Academy of Science awarded Dr. Islam with a Gold Medal in 1985. In 1994, he received the National Science and Technology Medal. In 1998, he received the Medal Lecture Award in the 3rd World Academy of Science in the Abdus Salam Centre for Science and Theoretical Physics located in Italy. In 2001, he was awarded the Ekushey Padak for his research in Bengali. He received the Bangladesh Science Academy Gold Medal in 1985. In 2011, in recognition of his contribution, Dhaka University awarded him with the Razzaq-Shamsun Lifetime Achievement Award in Physics.