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In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.
Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection
For more information about Paul R. Halmos (1916-2006) and about the Paul R. Halmos Photograph Collection, please see the introduction to this article on page 1. A new page featuring six photographs will be posted at the start of each week during 2012.
Halmos photographed harmonic analyst Henry Helson (1927-2010) in March of 1966 in Irvine, California. Helson earned his Ph.D. in 1951 from Harvard under advisor Lynn Loomis. In 1955, he joined the faculty at the University of California, Berkeley, and went on to advise 20 Ph.D. students during his career there. (Sources: Mathematics Genealogy Project and “A Tribute to Henry Helson,” by Donald Sarason, et al., AMS Notices 58:2, February 2011)
Halmos photographed Henry Helson again on January 17, 1974, at the Joint Mathematics Meetings in San Francisco, California.
Halmos photographed ring theorist Yitzchak (Israel) Herstein (1923-1988) in April of 1984 at the University of Notre Dame in South Bend, Indiana. Herstein earned his Ph.D. in 1948 from Indiana University with the dissertation “Divisor Algebras” written under Max Zorn. In 1951, he became a faculty member at the University of Chicago, where Halmos also was on the faculty. Herstein left Chicago in 1953 to teach at the University of Pennsylvania and Cornell, but returned to Chicago in 1962 and spent the rest of his career there. Halmos left Chicago for Michigan in 1961. (Sources, Mathematics Genealogy Project and MacTutor Archive)
Numerical analyst Magnus Hestenes (1906-1991) was photographed by Halmos on March 30, 1966, in Irvine, California. Hestenes earned his Ph.D. in 1932 from the University of Chicago under advisor Gilbert Ames Bliss. After serving as a faculty member at Chicago for several years, he joined the faculty at the University of California, Los Angeles, in 1947 and spent the rest of his career there. Best known for developing the conjugate-gradient method for solving linear systems, he advised 35 Ph.D. students at Chicago and UCLA. (Sources: Mathematics Genealogy Project and “Magnus Hestenes,” by Tony Chan, Numerical Analysis Digest 91:24, Sat., June 15, 1991. See also “Conjugacy and Gradients, by Magnus R. Hestenes,” in The History of Numerical Analysis and Scientific Computing, SIAM, and “Requiem for the Skillful,” by Saunders Mac Lane, AMS Notices 44:2, February 1997.)
Halmos photographed Edwin Hewitt (1920-1999) in November of 1968 in Tucson, Arizona. Hewitt earned his Ph.D. in 1942 from Harvard under advisor Marshall Stone. He became a faculty member at the University of Washington in Seattle in 1948 and spent the rest of his career there. At Washington, he advised 37 Ph.D. students, including former MAA president Ken Ross, with whom he wrote several papers and a book on harmonic analysis. (Sources: Mathematics Genealogy Project; MathSciNet; “Edwin Hewitt,” in Mathographies, Bellevue Community College, Washington; and MAA Presidents)
Group theorist Graham Higman (1917-2008) was photographed by Halmos on June 20, 1968, in London, England. Higman earned his Ph.D. in 1941 from Oxford with the dissertation “The Units of Group-Rings,” written under Henry Whitehead. In 1946, after doing non-mathematical war work from 1940 to 1946, he joined the mathematics faculty at the University of Manchester, where he worked in group theory with Max Newman, Bernhard Neumann, and Hannah Neumann. He moved to Oxford University in 1955 and remained there until he retired in 1984. His 50 Ph.D. students included the group theorist Peter Neumann, son of Bernhard and Hannah Neumann. (Mathematics Genealogy Project and MacTutor Archive)
Regarding sources for this page: Information for which a source is not given either appeared on the reverse side of the photograph or was obtained from various sources during 2011-12 by archivist Carol Mead of the Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas, Austin.
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Beery, Janet and Carol Mead, "Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection," Loci (January 2012), DOI: 10.4169/loci003801
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