Between 1977 and 2012 he is employed at the Faculty of Science, University of Kragujevac, responsible for teaching Physical Chemistry. He was Assistant Professor, Associate Professor, and – from 1984 – Full Professor. After retirement, in October 2012, he is Emeritus Professor at the same Faculty.
In 1990 he was elected Full Professor of Physical Chemistry at the Faculty of Physical Chemistry, University of Belgrade, but did not accept the position. In 1995 he habilitated at the Jozsef Attila University in Szeged (Hungary). Eventually – in 1996 – he was elected Full Professor in the Institute of Physical Chemistry of the same University but did not accept the position.

Ivan Gutman held various courses in the field of physical, computer and theoretical chemistry. In addition to “Physical Chemistry”, what he was teaching continuously from 1977 to 2012, he taught the following courses: “Chemical Thermodynamics”, “Quantum Chemistry and Molecular Structures”, “Quantum Chemistry”, “Theoretical Organic Chemistry”, “Elaboration of Experimental Data in Chemistry”, “Informatics for Chemists”, “Programming in Chemistry”,  “Computer Chemistry”, “History of Chemistry”, and “History and Philosophy of Chemistry”. At the Faculty of Science in Kragujevac he organized a seminar “Mathematical Methods in Chemistry” that was continuously active between Spring 1981 and Spring 2006, and on which over 1000 seminars were held.

Since 1975 he is member of the Mathematical Institute of the Serbian Academy of Sciences in Belgrade. In 1981 he obtained a Ph. D. degree in mathematics, at the Faculty of Electrical Engineering, University of Belgrade, by defending a thesis entitled “Contribution to the Spectral Theory of Trees”. His supervisor was Dragoš Cvetković.

Since 1988 he is member of the Serbian Academy of Sciences and Arts; full member is since 1997. Since 2005 he is member of the International Academy of Mathematical Chemistry. Since 2006 he is member of the Academy of Nonlinear Sciences (Moscow). Since 2012 he is member of Academia Europaea (London).

On several occasions he stayed abroad as research fellow or visiting professor. Five times he was fellow of the Alexander von Humboldt Foundation, and worked at the Institute for Quantum Chemistry of the Free University in West Berlin (1977), at the Max–Planck–Institute for Radiation Chemistry in Mulheim, Germany (1980 and 1985), at the Institute for Organic Chemistry and Biochemistry, University of Freiburg, Germany (2000), at the Mathematical Institute, University of Bayreuth, Germany (2000), and at the Computer–Chemistry Center, University of Erlangen (2003). In 1988 he was at the University of Trondheim, Norway, as fellow of the Royal Norwegian Council for Scientific and Industrial Research. In 1989 and 1990 he was (on two occasions) at the Vanderbilt University, Nashville, USA, as a Fulbright fellow. In 1989 he was also fellow of the Japan Society for Promotion of Science, staying at the Ochanomizu University, Tokyo. In 1995 he was, as Lady Davis fellow, visiting professor at the Hebrew University in Jerusalem, Israel. In 1996 he was at the Institute of Advanced Studies of the Hebrew University in Jerusalem. In 1997, as fellow of the Third World Academy of Science, he was at the University of Santa Clara, Cuba. In 1996 and 2001, as DAAD fellow, he stayed at the Technical University Ilmenau, Germany. He was visiting professor also at the Technical High School Ilmenau, DR Germany (1982), University of South Carolina, Columbia, USA (1983), Academia Sinica, Taipei, Taiwan (1992/93), József Attila University, Szeged, Hungary (1994–96), University of Montreal, Canada (1998), Johannes Kepler University, Linz, Austria (1999), Andean University, Mérida, Venezuela (2000), University of Bielefeld, Germany (2001 and 2002), University of Malta, Msida, Malta (2004), Nankai University, Tianjin, China (2005 and 2007), National Autonomous University of Mexico, Mexico City, Mexico (2006), Catholic University of the Nord, Antofagasta, Chile (2009), State University of Novi Pazar, Serbia (2014). He also visited a number of other universities and research institutions and lectured on many of them. In 2012/13 he was distinguished adjunct professor at the King Abdulaziz University, Jeddah, Saudi Arabia.

Since 1971 he published over 1260 scientific papers and is author of a few books (published by Springer, Berlin 1977, 1986, 1988, and 1989, North Holland, Amsterdam 1988, Nova, Huntington, New York, 2001, 2002, Springer, New York 2012). His works are quoted over 20,000 times in scientific papers by other authors, and over 2700 times in more than 280 books and textbooks. He is interested also in problems of teaching chemistry in elementary and secondary schools, as well as in history of natural sciences and mathematics. He published numerous articles and held scores of lectures on popular science.