After graduating from Newcastle upon Tyne University's mathematics department, Ahmet Tosun Terzioğlu went to Frankfurt University for his post-graduate studies. He then taught between 1968 and 1994 at the University of Michigan, Wuppertal University and Middle East Technical University (ODTÜ). He served consecutively as the head of ODTÜ's mathematics department and its dean of the science and literature faculty.
Terzioğlu also served as the head of TÜBİTAK between 1992 and 1997.
Terzioğlu worked as the founding rector at Sabancı University between 1997 and 2009. He was one of the first three emeritus members of the university, where he also taught in its engineering and natural sciences department.
He was also the president of the board of the Mathematics Association between 1989 and 2008. He is the author of more than 50 academic articles and four books in the field of mathematics.