Professor Clemens career combines a strong interest in research in the mathematical area of algebraic geometry with a lifelong interest in undergraduate and pre-college mathematics education and in nurturing mathematics and mathematics education in the developing world. After his Ph.D. degree in 1966, he spent two years as a Peace Corps volunteer in Santiago, Chile. Subsequently he spent two years as a visiting member of the Institute for Advanced Study, Princeton, NJ, before returning to Chile as a Fulbright Fellow in 1970. He then spent five years as an assistant, then associate professor at Columbia University in New York City before joining the Mathematics Department of the University of Utah in 1975. He has twice been an invited speaker at the International Congress of Mathematicians (1974, 1986) and received the University of Utah Distinguished Research Award in 1983.

In 2000 Professor Clemens received the Silver Medal of the Italian Mathematical Union, and in 2001 he was named a Distinguished Professor at the University of Utah. In 2002 Professor Clemens left Utah to accept a professorship in mathematics and mathematics education at Ohio State University.

He has served as a member of the Mathematics Sciences Education Board. Other educational activities in Utah include five years as director of the Institute for the Theory and Application of Mathematics, an arm of the Mathematics Department dedicated to university-wide and community outreach, and, between 1994 and 2002, math coordinator for the 'Ndahoo'aah Program, combining the teaching of traditional culture with math and computer preparation in the predominantly Navajo high schools of southeastern Utah.

From 2007-2010 Professor Clemens chaired the U.S. National Committee on Mathematics and has served on the U.S. National Committee on Mathematics Instruction. He was Secretary of the Commission for Development and Exchanges of the International Mathematical Union from 1994-2002 and coordinates the IMU’s Developing Countries Strategy Group since its inception in 2003. From 1999 through 2006 he directed the Park City Mathematics Institute, an Institute for Advance Study sponsored summer program of mathematics and mathematics teaching at the secondary, undergraduate, graduate and research level.

Professor Clemens' research contributions include a solution, with Phillip Griffiths, of a long-standing conjecture as to whether any solution space to a system of polynomial equations, which admits a many-to-one parametrization in fact admits a one-to-one parametrization. His current research interests are centered on deformation theory, that is, the study of the obstructions to continuously deforming subspaces when one changes the coefficients in the polynomial equations defining a solution space.
In the area of mathematics development and education, Professor Clemens is currently consulting with the World Bank backed “Millennium Science Initiative” on an African mathematics component, and he is currently a member of the Mathematics Standing Committee of the U.S. National Assessment for Educational Progress (NAEP), established by the U.S. Congress to monitor U.S. student achievement every four years (the so-called ‘nation’s report card’).