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”.