Wall received his Ph.D. from the University of Wisconsin-Madison in 1927. He was a professor of pure mathematics at the University of Texas at Austin (1946-1971) where he directed the doctoral work of over 60 students. Wall employed the discovery-based method of teaching in his classroom. His research interests included continued fractions, Hellinger integrals, group theory, and infinite processes.
From the guide to the H. S. Wall Papers 2000-088, 2002-076; 2006-073; 2006-121; 2006-137., 1902, 1929-1974, 2006, (Dolph Briscoe Center for American History, The University of Texas at Austin)