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In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader, Sheridan House, 1987.
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.
Abram Besicovitch (1891-1970) is pictured in his office at Trinity College, Cambridge, England (or possibilty his home in Cambridge) on June 8, 1968. A student of A. A. Markov at the University of St. Petersburg, where he earned his degree in 1912, Besicovitch taught in Russia during the revolutionary years. He finally escaped to Copenhagen in 1924, and eventually settled in England, where he was a functional analyst at Cambridge from 1927 onward. Besicovitch was a member of the Institute for Advanced Study in Princeton in 1954-55 and also visited various U.S. universities from 1958 to 1966. It is possible that his visits included the University of Chicago or the University of Michigan, where Paul Halmos taught during this period (he moved from Chicago to Michigan in 1961), and that the two became acquainted then. They certainly would have been interested in one another's mathematical work.
Halmos photographed R. H. Bing (1914-1986) in Miami, Florida on April 3, 1966. Bing was a Texas high school teacher turned R. L. Moore-trained topologist. He spent most of his career at the universities of Wisconsin and Texas. He and Halmos may have met at the Institute for Advanced Study in Princeton, where both were members during 1957-58. Bing served as president of the MAA in 1963-64 and as president of the AMS in 1977-78.
In 1965-66 Halmos took a year's leave from the University of Michigan to teach at the University of Miami in Coral Gables, Florida. Two years later, the sun-seeking Halmos accepted a position at the University of Hawaii in Honolulu. In 1966, Bing was a professor at the University of Wisconsin; in 1973, he returned to the University of Texas, Austin, where he had earned his Ph.D. in 1945.
This photograph shows R. H. Bing (left) with Burton W. Jones (1902-1983) in 1981. Jones earned his Ph.D. from the University of Chicago in 1928, working under Leonard Eugene Dickson. From 1930 to 1948, he was a professor at Cornell University, where his second, third, and fourth Ph.D. students were representation theorist Irving Reiner (1947), MAA book series eponym Mary Dolciani (1947), and number theorist William LeVeque (1948). His very first Ph.D. student was Irma Moses Reiner (1946), who describes Jones as a "good, approachable, and available" Ph.D. advisor, who "provided an excellent problem and was helpful in conferences while I was working on it." In 1948, Jones moved to the University of Colorado, Boulder, where he spent the rest of his career, chairing the mathematics department from 1949 to 1963 and retiring in 1971. He published number theory and abstract algebra textbooks and a popular book on mathematics, Elementary Concepts of Mathematics. Both UC Boulder and the MAA Rocky Mountain Section have mathematics teaching awards named in Jones' honor.
Halmos photographed the American algebraist Garrett Birkhoff (1911-1996), far left, and the Iranian mathematical physicist Abolghassem Ghaffari, far right, at the Third Iranian Mathematical Conference in Tehran, Iran, in 1972. He identified the two women in the photo only as "Mrs. Ghaffari" and "R. Birkhoff." Abolghassem Ghaffari studied and worked in Iran, France, England, and the U.S., before moving to the U.S. permanently in 1956. During the 1950s, he worked with Einstein and Oppenheimer in Princeton and, during the 1960s, he worked for NASA on the Apollo 11 mission. On June 15, 2011, Ghaffari celebrated his 104th birthday. The Ghaffari family is collecting photographs of A. Ghaffari and is particularly interested in photographs of him with Einstein and/or Oppenheimer. Please contact us if you can help.
Group and lattice theorist Garrett Birkhoff advised over 50 Ph.D. students during a long career at Harvard, but he may be best remembered for his abstract algebra text, A Survey of Modern Algebra, written with Saunders Mac Lane and more commonly known by its authors' surnames, "Birkhoff and Mac Lane." Halmos and Birkhoff probably would have first met when both were at the Institute for Advanced Study in Princeton in 1939-40.
Halmos photographed Errett Bishop (1928-1983) at Bishop's home in La Jolla, California, in February 1983. A Ph.D. student of Halmos at the University of Chicago (1955), Bishop spent his career at the University of California, Berkeley, and the University of California, San Diego (in La Jolla). He made important contributions to a number of areas of analysis, including its foundations.
Mathematical philosopher Max Black (1909-1988) at the AMS-MAA Joint Summer Meeting in Ithaca, New York, on Aug. 31, 1965. Black was at that time a philosophy professor at Cornell University in Ithaca, where he spent most of his career. Did he attend the mathematics meeting because it was in a convenient location for him, or did he regularly attend mathematics meetings?
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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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