He graduated with honours from the Department of Mathematics of the Faculty of Science at Istanbul University in 1991. He completed his master's degree at Ohio State University (Columbus, OH) in 1996 and his doctorate at the University of Utah (SLC, UT) in 2001. From 2002, he was appointed to the academic staff of the American University of Sharjah (AUS) in the United Arab Emirates. After working there as an assistant professor between 2002 and 2008 and as an associate professor between 2008 and 2014, he was appointed full professor in 2014.
Between 2014 and 2016, he served as Director of the Graduate School of Natural and Applied Sciences at Yıldız Technical University (YTÜ), and between 2016 and 2019 as a member of the Board of Directors of the Yıldız Technical University Foundation. In 2017, he joined the Faculty of Engineering and Natural Sciences at Istanbul Sabahattin Zaim University and was subsequently appointed Dean of the Faculty. In 2018, he was elected a member of the Zaim Teknopark Board of Directors. As of 2022, he was appointed Vice Rector. Prof. Dr. İsmail Küçük was appointed Rector of İZÜ by Presidential Decree dated 18 March 2026. Prof. Küçük is married and the father of three children.