He studied in Zürich, Switzerland at the Eidgenössische Technische Hochschule, receiving his diploma in 1947 and a D.Sc.
While in Minnesota, he wrote Differential Geometry (1963), a textbook treating "classical problems with modern methods".
According to Robert Hermann in 1979, "Among today's treatises, the best one from the point of view of the Erlangen Program is Differential Geometry by H. Guggenheimer, Dover Publications, 1977.
"[3] In 1967 Guggenheimer published Plane Geometry and its Groups (Holden Day), and moved to New York City to teach at Polytechnic University, now called New York University Tandon School of Engineering.
In 1995 Guggenheimer presented The Scholar's Haggadah[7], which makes a bilingual comparison of variances in the traditions of Passover observance, including Ashkenazic, Sephardic, and Oriental sources.
[9] They have two sons, Michael, a professor of Arabic,[10] and Tobias I. S., an architect,[11] and two daughters Dr. Esther Furman, a biochemist,[12] and Hanna Y. Guggenheimer, an artist.