## Section 5.5 Profile: John Corning Oxtoby (1910-1991)

John C. Oxtoby was born on September 14, 1910, in Saginaw, Michigan, the son of William Henry and Ida Jane (Corning) Oxtoby. He received two degrees in mathematics from the University of California at Berkeley, an A.B. in 1933 and an M.A. the following year. He was the president of the Pi Mu Epsilon fraternity at Berkeley for two years, 1932-1934. During this time he delivered one talk each year to the honorary organization, the first titled “Number ratios” and the second “Dimensional analysis”. For the next two years Oxtoby enrolled in the graduate program at Harvard University, where he served as the secretary- treasurer of the Harvard Mathematical Club for 1935-1936.

Following graduation Oxtoby remained at Harvard for three years as a Junior Fellow in the Society of Fellows. He was in good company. Between 1933 and 1944, the ranks of junior fellows included the famed economist Paul Samuelson, the noted psychologist B. F. Skinner, and the mathematical logician W. V. Quine, as well as the mathematicians Garrett Birkhoff, Creighton Buck, Lynn Loomis, and Stanislaw Ulam. During this time Oxtoby and Ulam proved that almost every measure-preserving homeomorphism of any “regularly connected” polyhedron of dimension \(\ge 2\) is metrically transitive. As the authors noted in their joint paper in the July 1939 issue of the Annals, “the effect of the ergodic theorem was to replace the ergodic hypothesis (of Ehrenfest) by the hypothesis of metric transitivity (of G. D. Birkhoff)”. In reviewing this paper Garrett Birkhoff wrote, “This constituted a notable modern extension of the tradition of Lagrange, Laplace, Poincaré, and G. D. Birkhoff”.

Clearly Oxtoby was a brilliant research mathematician. He had published several papers by the time he left Harvard in 1939. Since holding a Junior Fellowship carried more prestige than writing a doctoral dissertation, Oxtoby, like the others mentioned above, never felt the need to obtain a doctorate. He accepted an assistant professorship at Bryn Mawr College in the fall of 1939, and remained there until he retired as professor emeritus 40 years later, in 1979, at age 68. Oxtoby served as the head of the department from 1948 until 1976. Imagine – 28 years! He was appointed to the College’s prestigious Class of 1897 Professorship for the last four years of his active career.

Known as an especially effective teacher, Oxtoby received a Lindback Award for Distinguished Teaching in 1978. Two years later, and only one year after retiring, he was awarded an honorary doctorate by Widener University. What is the connection between Widener and Bryn Mawr, except that both schools are located in the same general area of suburban Philadelphia? One of Oxtoby’s three Ph.D. students, Francisco Navarro-Bermudez, was chairman of the mathematics department at Widener at the time.

John Oxtoby served as chairman of the Philadelphia Section in 1955-1956. He had been even more active in sectional activities during the 1940s, being an invited speaker at the annual meetings three times (1940, 1943, and 1949) and serving on the Program Committee twice (1944 and 1947), chairing it in 1944. In addition he was the MAA’s Hedrick Lecturer in 1956. He is perhaps best known today for his small but influential book Measure and Category: A Survey of the Analogies between Topological and Measure Space.

Oxtoby married Jean Ann Shaffer in 1945. The couple had three children, one of whom, David William Oxtoby, is an author of the 1994 textbook Chemistry: Science of Change. John Oxtoby died on January 2, 1991. His widow still resides in Haverford, where the couple lived for most of their married life.