In 1985, Garfield received a Bachelor of Science degree in computer mathematics. After college, he joined Bell Laboratories, but soon after decided to continue his education and attended the University of Pennsylvania, studying combinatorial mathematics for his PhD. Garfield studied under Herbert Wilf and earned a Ph.D. in combinatorial mathematics from Penn in 1993. His thesis was "On the Residue Classes of Combinatorial Families of Numbers". Shortly thereafter, he became a Visiting Professor of mathematics at Whitman College in Walla Walla, Washington.