A native of Brooklyn and a 1933 graduate of Brooklyn College, Wallman received his Ph.D. in mathematics from Princeton University in 1937, under the supervision of Solomon Lefschetz and became a faculty member at the Massachusetts Institute of Technology, where he was associated with the Radiation Laboratory. During World War II he did classified work at MIT, possibly involving radar. In 1948, he left MIT to become a professor of electrotechnics at the Chalmers University of Technology in Gothenburg, Sweden, which awarded him the Chalmers medal in 1980 and where he eventually retired. In 1950 he was elected as a foreign member to the Swedish Royal Academy. He was elected a member of the Royal Swedish Academy of Engineering Sciences in 1960 and of the Royal Swedish Academy of Engineering Sciences in 1970.
The disjunction property of Wallman is named after Wallman, as is the Wallman compactification, and he co-authored an important monograph on dimension theory with Witold Hurewicz. Wallman was also a radio enthusiast, and in the postwar period co-authored a book comprehensively documenting what was known at the time about vacuum tube amplification technology, including new developments such as showing how the central limit theorem could be used to describe the rise time of cascaded circuits. At Chalmers, Wallman helped build the Electronic Differential Analyser, an early example of an analog computer, and performed pioneering research in biomedical engineering combining video displays with X-ray imaging.
- Biography of Wallman at the Chalmers University of Technology (in Swedish).
- Henry Wallman at the Mathematics Genealogy Project.
- The Princeton Mathematics Community in the 1930s, interviews with Albert Tucker, transcripts 33, 36, and 41 Archived 2015-03-10 at the Wayback Machine.
- Chalmers medalists, Chalmers University of Technology.
- "Notes", Bulletin of the American Mathematical Society, 56 (2): 212–215, 1950, doi:10.1090/S0002-9904-1950-09396-3; Schneckenburger, Edith R. (1950), "News and Notices", American Mathematical Monthly, 57 (6): 433–435, JSTOR 2307663.
- Hurewicz, W.; Wallman, H. (1941), Dimension Theory, Princeton University Press. Reviews: Menger, Karl (May 29, 1942), "Dimension", Science, 95 (2474): 554–556, doi:10.1126/science.95.2474.554-a; MR0006493 (reviewed by Hassler Whitney); Smith, P. A. (1942), "Dimension theory", Bulletin of the American Mathematical Society, 48 (9): 641–642, doi:10.1090/S0002-9904-1942-07723-8.
- Valley, George E. Jr.; Wallman, Henry (1948), Vacuum Tube Amplifiers, MIT Radiation Laboratory Series 18, New York: McGraw-Hill.. Reviews: Ridenour, Louis N. (1948), "Vacuum tube amplifiers", Massachusetts Institute of Technology Radiation Laboratory Series; Giacoletto, L. J. (1949), "Institute News and Radio Notes", Proceedings of the I.R.E., 37 (8): 907, doi:10.1109/JRPROC.1949.229980; Frankland, Scott (1998), Vacuum tube electronics: Reviews of the major texts (PDF), Perkins Electro-Acoustical Research Laboratory.
- Johansson, Magnus (1996), "Early analog computers in Sweden—with examples from Chalmers University of Technology and the Swedish Aerospace Industry" (PDF), IEEE Annals of the History of Computing, 18 (4): 27–33, doi:10.1109/85.539913.
- Chalmers Bioscience Program background material 2004, Gunnar Bjursell and Catharina Hiort.