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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 and early 2013.

Halmos photographed Harold Widom in 1985. At the time, Widom was a professor at the University of California, Santa Cruz, where he is now emeritus. In 1985, Halmos moved from Indiana University to the University of Santa Clara, California. Another photograph of Widom appears on page 55 of this collection, where you can read more about him.

Raymond L. Wilder (1896-1982) was photographed by Halmos in 1958. Wilder was on the faculty of the University of Michigan in Ann Arbor from 1926 to 1967, when he became Professor Emeritus. Another photograph of Wilder appears on page 43 of this collection, where you can read more about him.

Halmos photographed Raymond L. Wilder again on August 1, 1960, in Lansing, Michigan. As noted above, Wilder was a professor at the University of Michigan in Ann Arbor at this time. Halmos would leave the University of Chicago to join the faculty at the University of Michigan one year later, in 1961.

Jacob Wolfowitz (1910-1981), left, and Joseph Doob (1910-2004) were photographed by Halmos in 1959. Joseph Doob was Paul Halmos’ Ph.D. advisor at the University of Illinois. Two photos of him appear on page 12 of this collection, where you can read more about him; additional photos of Doob can be found on page 1, page 2, and page 14.

Jacob Wolfowitz was born in Warsaw in what was then the Russian Empire and emigrated to the U.S. in 1920 when he was 10 years old. He earned his Ph.D. from New York University in 1942 with the dissertation, “Additive Partition Functions and a Class of Statistical Hypotheses.” That year he joined the Statistical Research Group at Columbia University in New York City, where he collaborated with geometer, statistician, and inventor of sequential analysis Abraham Wald (1902-1950) to develop a theory of sequential analysis, among other topics. Wolfowitz remained at Columbia until 1951, the year after Wald, who had been at Columbia since 1938, died in a plane crash. Wolfowitz was on the faculty at Cornell University in Ithaca, New York, from 1951 to 1970, at the University of Illinois at Urbana-Champaign from 1970 to 1978, and at the University of South Florida in Tampa from 1978 onward. (Sources: MacTutor Archive, Mathematics Genealogy Project)

Halmos photographed Laurence C. Young (1905-2000) on August 31, 1967, at the Joint Mathematics Meetings in Toronto, Ontario, Canada. Laurence Chisholm Young was born in Göttingen, Germany, to British mathematicians Grace Chisholm Young and William Henry Young. He published his first book, *The theory of integration* (Cambridge University Press), in 1927. Four years later, in 1931, he earned a masters degree from Cambridge University under advisors J. E. Littlewood (see page 31 of this collection for a photograph of Littlewood) and Ralph H. Fowler and, according to the Mathematics Genealogy Project, also earned a doctoral degree in 1939 under these two advisors. From 1938 to 1948, he was Professor and founding Chair of Mathematics at the University of Cape Town, South Africa. From 1948 or 1949 onward, he was Professor of Mathematics at the University of Wisconsin, Madison, becoming emeritus in 1975. His 1969 book, *Lectures on the calculus of variations and optimal control theory,* summarized his major research results; his 1981 book, *History of mathematics and mathematics of history,* may be of greater interest to mathematical historians. (Sources: MacTutor Archive, Mathematics Genealogy Project)

Halmos photographed J.W.T. Youngs (1910-1970) in February of 1962 in Bloomington, Indiana, where Youngs was a faculty member at Indiana University. John William Theodore “Ted” Youngs was born in Bilaspur, India, and earned his Ph.D. in 1934 from Ohio State University in Columbus, probably under advisor Tibor Radó (1895-1965). (Youngs is not listed as a Ph.D. student of Radó, who was at Ohio State University from the founding of its graduate program in 1930 to the end of his life, in Radó’s Ohio State University obituary or in his Mathematics Genealogy Project entry; however, the memorial cited below notes Youngs “working alongside the famous Hungarian, Tibor Rado.”) After teaching at Ohio State and Purdue universities, Youngs was a mathematics professor at Indiana University for 18 years, from 1946 to 1964. In 1964, he became the founding chair of the mathematics department at the brand-new University of California at Santa Cruz, where he remained for the rest of his career and life. A topologist, Youngs is best known for his and Gerhard Ringel’s work on the (Percy) Heawood Conjecture on colorings of maps on surfaces of higher genus (specifically, the chromatic number of these surfaces). This work was done during the last decade of Youngs’ life, much of which was spent at UC Santa Cruz. At Santa Cruz, Youngs also developed an early “math for liberal arts” course titled “The Nature of Mathematics.” (Sources: WorldCat, University of California CaliSphere memorial, Ohio State University obituary: Radó, J.W.T. Youngs Fellows)

For an introduction to this article and to the Paul R. Halmos Photograph Collection, please see page 1. Watch for a new page featuring six new photographs each week during 2012 and early 2013.

**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.

Janet Beery (University of Redlands) and Carol Mead (Archives of American Mathematics, University of Texas, Austin), "Who's That Mathematician? Paul R. Halmos Collection - Page 56," *Loci* (June 2013), DOI:10.4169/loci003801